LIBRARY  OF  THF   L.MVERSITV   OF  CALIFORNIA. 


PHYSICS  DEPARTMENT. 


Miss  ROSE  WHFUVi. 


T{ecetieJ  September.  1896. 
No.   6  3  &  JO  •         C/JSN  M> 


'v~^ 


ww* 


Vvw**v 


- 


•-: 


• 


©W  P1L 


x  Contents. 

BOOK  V. 
ACOUSTICS. 

CHAPTER 

I.  PRODUCTION,  PROPAGATION,  AND  REFLECTION  OF  SOUND 

II.  MEASUREMENT  OF  THE  NUMBER  OF  VIBRATIONS  . 

III.  THE  PHYSICAL  THEORY  OF  Music 

IV.  VIBRATIONS  OF  STRETCHED  STRINGS,  AND  OF  COLUMNS  OF  AIR 
V.  VIBRATIONS  OF  RODS,  PLATES,  AND  MEMBRANES 

VI.     GRAPHICAL  METHOD  OF  STUDYING  VIBRATORY  MOTIONS 

BOOK  VI. 
ON      HEAT. 

I.  PRELIMINARY  IDEAS.     THERMOMETERS  .  .  . 

II.  EXPANSION  OF  SOLIDS         .  .  .  .  .  . 

III.  EXPANSION  OF  LIQUIDS        .  .  .  ,   . 

IV.  EXPANSION  AND  DENSITY  OF  GASES  .... 
V.  CHANGES  OF  CONDITION.    VAPOURS  .... 

VI.  HYGROMETRY  ....... 

VII.  CONDUCTIVITY  OF  SOLIDS,  LIQUIDS,  AND  GASES  . 

VIII.  RADIATION  OF  HEAT  ...... 

IX.  CALORIMETRY  ....... 

X.  STEAM  ENGINE         ....... 

XL  SOURCES  OF  HEAT  AND  COLD         ..... 

XII.  MECHANICAL  EQUIVALENT  OF  HEAT          .... 

BOOK  VII. 
ON     LIGHT. 

I.  TRANSMISSION,  VELOCITY,  AND  INTENSITY  OF  LIGHT 

II.  REFLECTION  OF  LIGHT.     MIRRORS  . 

III.  SINGLE  REFRACTION.     LENSES        .  .  .  .  . 

IV.  DISPERSION  AND  ACHROMATISM       .  . 

V.  OPTICAL  INSTRUMENTS         ...... 

VI.  THE  EYE  CONSIDERED  AS  AN  OPTICAL  INSTRUMENT 

VII.  SOURCES  OF  LIGHT.     PHOSPHORESCENCE    . 

VIII.  DOUBLE  REFRACTION.    INTERFERENCE.    POLARISATION  . 


Contents.  xi 

BOOK  VIII. 

ON   MAGNETISM. 

CHAPTER  PAGE 

I.  PROPERTIES  OF  MAGNETS     ......      592 

II.  TERRESTRIAL  MAGNETISM.     COMPASSES      ....      598 

III.  LAWS  OF  MAGNETIC  ATTRACTIONS  AND  REPULSIONS       .  .611 

IV.  PROCESSES  OF  MAGNETISATION        .  .  .  .  .618 

BOOK   IX. 
FRICTIONAL  ELECTRICITY. 

I.     FUNDAMENTAL  PRINCIPLES  .  .  .628 

II.     QUANTITATIVE  LAWS  OF  ELECTRICAL  ACTION      .  .      635 

III.  ACTION  OF  ELECTRIFIED  BODIES  ON  BODIES  IN  THE  NATURAL 

STATE.    INDUCED  ELECTRICITY.     ELECTRICAL  MACHINES    .      647 

IV.  CONDENSATION  OF  ELECTRICITY     .  .  .  .671 

BOOK   X. 
DYNAMICAL  ELECTRICITY. 

I.  VOLTAIC  PILE.     ITS  MODIFICATIONS  ....  701 

II.  DETECTION  AND  MEASUREMENT  OF  VOLTAIC  CURRENTS  .  .  720 

III.  EFFECTS  OF  THE  CURRENT  .  .  .  .  .  732 

IV.  ELECTRODYNAMICS.     ATTRACTION  AND  REPULSION  OF  CURRENTS 

BY  CURRENTS     .......  763 

V.  MAGNETISATION  BY  CURRENTS.  ELECTROMAGNETS.  ELECTRIC 

TELEGRAPHS       .  .  .  .  .  .  .781 

VOLTAIC  INDUCTION             ......  804 

OPTICAL  EFFECTS  OF  POWERFUL  MAGNETS.     DIAMAGNETISM      .  852 

THERMO-ELECTRIC  CURRENT           .....  859 

DETERMINATION  OF  ELECTRICAL  CONSTANTS  .  .  .  870 

ANIMAL  ELECTRICITY  ......  883 

ELEMENTARY  OUTLINES  OF  METEOROLOGY  AND  CLIMATOLOGY  .  .  888 
PROBLEMS  AND  EXAMPLES  IN  PHYSICS  .....  929 
INDEX 953 


ADVERTISEMENT 

TO 

THE      TENTH      EDITION, 


IN  THE  PRESENT  EDITION  the  fresh  matter  has  increased  by  about 
twenty-five  pages  the  size  of  the  book  as  it  stood  in  the  last  Edition, 
The  new  matter  includes  twenty-four  additional  illustrations. 

The  continued  and  even  increasing  favour  with  which  the  work  has 
been  received,  both  as  a  Text  Book  for  Colleges  and  Schools,  and  also 
as  a  work  of  reference  for  the  general  reader,  renders  any  apology  for 
omissions  perhaps  unnecessary  ;  it  may,  however,  be  as  well  once  more  to 
point  out  that  the  book  is  intended  to  be  a  general  Elementary  Treatise 
on  Physics ;  and  that,  while  it  accordingly  aims  at  giving  an  account  of 
the  most  important  facts  and  general  laws  of  all  branches  of  Physics, 
an  attempt  to  treat  completely  and  exhaustively  of  any  one  branch,  would 
both  be  inconsistent  with  the  general  plan  of  the  book,  and  impossible 
within  the  available  space. 

E.  A. 

STAFF  COLLEGE  :  April  1881. 


EXTRACT  FROM  ADVERTISEMENT  TO    THE 
SEVENTH  EDITION. 

I  HAVE  ADDED  an  Appendix  containing  a  series  of  numerical  problems 
and  examples  in  Physics.  This  Appendix  is  based  upon  a  similar 
one  contained  in  the  French  edition  of  the  work.  But  I  have  been 
able  to  use  only  a  small  proportion  of  the  problems  contained  in 
that  Appendix,  as  the  interest  of  the  solution  was  in  most  cases  geome- 
trical or  algebraical.  Hence  I  have  substituted  or  added  others,  which 
have  been  so  selected  as  to  involve  in  the  solution  a  knowledge  of  some 
definite  physical  principle. 

Such  an  Appendix  has  from  time  to  time  been  urged  upon  me  by 
teachers  and  others  who  use  the  work.  It  will,  I  conceive,  be  most 
useful  to  those  students  who  have  not  the  advantage  of  regular  instruc- 
tion ;  affording  to  them  a  means  of  personally  testing  their  knowledge. 
Such  a  student  should  not  aim  solely  at  getting  a  result  which  numeri- 
cally agrees  with  the  answer.  He  should  habituate  himself  to  write  out 
at  length  the  several  steps  by  which  the  result  is  obtained,  so  that  he 
may  bring  clearly  before  himself  the  physical  principles  involved  in  each 
stage.  Some  of  the  solutions  of  the  problems  are  therefore  worked  out 
at  length. 

E.  A. 


TRANSLATOR'S  PREFACE  to  FIRST  EDITION. 

THE  Elements  de  Physique  of  Professor  GANOT,  of  which  the  present 
work  is  a  translation,  has  acquired  a  high  reputation  as  an  Introduction 
to  Physical  Science.  In  France  it  has  passed  through  Nine  large 
editions  in  little  more  than  as  many  years,  and  it  has  been  translated 
into  German  and  Spanish. 

This  reputation  it  doubtless  owes  to  the  clearness  and  conciseness 
with  which  the  principal  physical  laws  and  phenomena  are  explained, 
to  its  methodical  arrangement,  and  to  the  excellence  of  its  illustrations. 
In  undertaking  a  translation,  I  was  influenced  by  the  favourable  opinion 
which  a  previous  use  of  it  in  teaching  had  enabled  me  to  form. 

I  found  that  its  principal  defect  consisted  in  its  too  close  adaptation 
to  the  French  systems  of  instruction ;  and  accordingly,  my  chief  labour, 
beyond  that  of  mere  translation,  has  been  expended  in  making  such 
alterations  and  additions  as  might  render  it  more  useful  to  the  English 
student. 

I  have  retained  throughout  the  use  of  the  Centigrade  thermometer, 
and  in  some  cases  have  expressed  the  smaller  linear  measures  on  the 
metrical  system.  These  systems  are  now  everywhere  gaining  ground, 
and  an  apology  is  scarcely  needed  for  an  innovation  which  may  help  to 
familiarise  the  English  student  with  their  use  in  the  perusal  of  the  larger 
and  more  complete  works  on  Physical  Science  to  which  this  work  may 
serve  as  an  introduction. 


E.   ATKINSON. 


ROYAL  MILITARY  COLLEGE,  SANDHURST, 
1863. 


LIST  OF  TABLES. 


PAGE 

ABSORBING  powers       .        .  .     359 

Absorption  of  gases       .          .  117,  149 

-heat  by  gases  .  -375 

liquids  .      369 

vapours  371,375 

• various  bodies  369 

Atmosphere,  composition  of .  .     122 

BAROMETRIC  variations         .  133 

Boiling  points  .  .  .  302,  304 
Breaking  weight  of  substances  .  77 

CAPILLARITY  in  barometers  .         .  131 

Combustion,  heat  of  .  .  423 
Conducting  powers  of  solids  for 

heat 342 

liquids  for  heat  346 

Conductors  of  electricity        .          .  630 

DENSITIES  of  gases      .        .        .     283 

vapours  .         .          .     330 

Density  of  water  ....  274 
Diamagnetism  ....  858 
Diathennanous  power  .  .  368,  369 
Diffusion  of  solutions  .  .  .112 
Dulong  and  Petit's  law  .  .  394 

ELASTICITY 73 

Electrical  conductivity  .         .         .     879 
Electricity,  positive  and  negative  .     633 
Electromotive    force    of    different 
elements  . 


-series 


.  717 
.  706,  707 
Enclosmotic  equivalents  .  .  112 
Expansion,  coefficients  of  solids,  264,  265 

—  liquids  .     272 

gases      .     279 

Eye,  dimensions  of        .          .         '538 
refractive  indices  of  media  of .     538 

FREEZING  mixtures 
Eusing  points  of  bodies 

GLAISHER'S  factors 

Gravity,  force  of,  at  various  places 


PAGE 

HARDNESS,  scale  of     .        .  .78 

LATENT  heat,  of  evaporation  .     309 
fusion          .  .     399 

MAGNETIC  declination .         .  .     600 

inclination .         .  .     606 

intensity     .         .  .     609 


RADIATING  powers  .  .  359,  367 
Radiation  of  powders  .  .  .  380 
Refraction,  angle  of  double  .  .561 
Refractive  indices  .  .  .  475 

of  media  of  eye    .     538 

Reflecting  powers          .         .         .     358 


SOUND,  transmission  of,  in  tubes 
Specific  gravity  of  solids 

liquids     . 

heat  of  solids  and  liquids 

gases 


inductive  capacities   . 

TANGENT  galvanometer  and  volta- 
meter, comparison  between 
Temperatures,  various  remarkable  . 

at  different  latitudes  . 

thermal  springs 

measurement  of 

Tension  of  aqueous  vapour    . 

vapours  of  liquids 

Thermo-electric  series  . 


UNDULATIONS,  length  of 


185 
101 

102 
392 

397 
653 


756 
260 
925 
926 
280 
299 
300 
860 


556 


VELOCITY  of  sound  in  rocks  . 

192 

.    290 

284 

189 

IQO 

Tviafole    onrl 

•     337 

woods       ..... 

191 

ces        65       Vibrations  of  musical  scale     . 

203 

LIST  OF  PLATES. 

TABLE  OF  SPECTRA Frontispiece 

COLOURED  RINGS  PRODUCED  BY  POLARISED  LIGHT  IN  DOUBLE  REFRACT- 
ING CRYSTALS To  face  p.     579 

ISOGONIC  LINES  FOR  THE  YEAR  1860 601 

ISOCLINIC  LINES  FOR  THE  YEAR  1860  6c6 


I     I      I      I      I      I      I      I  I   Inch  [2  13  4| 


i          |2          [3          [4          15  '6          |7          |8          19      10 

Millimetres  Centimetres 


The  area  of  the  figure  within  the  heavy  lines  is 
that  of  a  square  decimetre.  A  cube,  one  of  whose 
sides  is  this  area,  is  a  cubic  decimetre  or  litre.  A 
litre  of  water  at  the  temperature  of  4°  C.  weighs  a 
kilogramme.  A  litre  of  air  at  o°  C.  and  76omm 
pressure  weighs  1*293  gramme. 

A  litre  is  176  pint  *  a  pint  is  o-568  of  a  litre. 

The  smaller  figures  in  dotted  lines  represent  the 
areas  of  a  square  centimetre  and  of  a  square  inch. 

A  cubic  centimetre  of  water  at  4°  C.  weighs  a 
gramme. 


Square  Inch 


Square  • 
Centi-  : 
metre 


Metres  Feet 

Millimetre             .         .         .                   0*03937  0-003281 

Centimetre       ....                0-39371  0-032819 

Decimetre    ....                   3'937o8  0-328090 

Metre 39*37079  3-280899 

Kilometre    ....            39370 '70000  3280*899167 

A  Hectare  or  10,000  square  metres  is  equal  to  2*47114  acres,  each  of  which  is  43,560 
square  feet.  A  kilometre  is  0-6214  of  a  statute  mile.  A  statute  mile  is  1-609  kilometres. 
A  knot  (in  telegraphy)  is  2,029  yards  or  1-1528  statute  mile. 

Meastires  of  Capacity. 

Cubic  Feet 

Cubic  Inches  1,728  c.  in.  =  i  c.  ft. 

Cubic  centimetre  or  millimetre     .  0*06103  0*000035 

Litre  or  cubic  decimetre  .         .     .         61*02705  0-035317 

Kilolitre  or  cubic  metre         .        .61,027*05152  SS'S10^! 

Measures  of  Weight. 

Avoirdupois  pounds 
English  grains  of  7,000  grains 

Milligramme 0-01543  0-0000022 

Gramme        .  .         .         15-43235  0*0022046 

Kilogramme    .         ....  15,432*34880  2*2046213 

i  grain  =  0-064799  gramme  ;  i  pound  avoirdupois  is  0*453593  kilogramme. 


IJII7BRSITY 


ELEMENTARY      TREATISE 


ON 


PHYSICS. 

BOOK    I. 

ON    MATTER,   FORCE,   AND    MOTION. 


CHAPTER    I. 
GENERAL   PRINCIPLES. 

1.  Object  of  Pbysics.— The  object  of  Physics  is  the  study  of  the  phe- 
nomena presented  to  us  by  bodies.     It  should,  however,  be  added,  that 
changes  in  the  nature  of  the  body  itself,  such  as  the  decomposition  of  one 
body  into  others,  are  phenomena  whose  study  forms  the  more  immediate 
object  of  chemistry. 

2.  Matter. — That  which  possesses  the  properties  whose   existence   is 
revealed  to  us  by  our  senses,  we  call  matter  or  substance. 

All  substances  at  present  known  to  us  may  be  considered  as  chemical 
combinations  of  sixty-seven  elementary  or  simple  substances.  This  number, 
however,  may  hereafter  be  diminished  or  increased  by  the  discovery  of  some 
more  powerful  means  of  chemical  analysis  than  we  at  present  possess. 

3.  Atoms,  molecules. — From  various  properties  of  bodies,  we  conclude 
that  the  matter  of  which  they  are  formed  is  not  perfectly  continuous,  but 
consists  of  an  aggregate  of  an  immense  number  of  exceedingly  small  por- 
tions or  atoms  of  matter.     These  atoms  cannot  be  divided  physically  ;  they 
are  retained  side  by  side,  without  touching  each  other,  being  separated  by 
distances  which  are  great  in  comparison  with  their  supposed  dimensions. 

A  group  of  two  or  more  atoms  forms  a  molecule,  so  that  a  body  may  be 
considered  as  an  aggregate  of  very  small  molecules,  and  these  again  as 
aggregates  of  still  smaller  atoms.  The  smallest  masses  of  matter  we  ever 
obtain  artificially  are  particles,  and  not  molecules  or  atoms.  Molecules 
retain  their  position  in  virtue  of  the  action  of  certain  forces  called  molecular 
forces. 

From  considerations  based  upon  various  physical  phenomena  Sir  W. 
Thomson  has  calculated  that  in  ordinary  solids  and  liquids  the  average 

B 


2  On  Matter,  Force,  and  Motion.  [3- 

distance  between  contiguous  molecules  is  less  than  the  one  hundred-millionth 
but  greater  than  the  one  two  thousand-millionth  of  a  centimetre. 

To  form  an  idea  of  the  degree  of  the  size  of  the  molecules  Sir  W. 
Thomson  gives  this  illustration  : — '  Imagine  a  drop  of  rain,  or  a  glass  sphere 
the  size  of  a  pea,  magnified  to  the  size  of  the  earth,  the  molecules  in  it  being 
increased  in  the  same  proportion.  The  structure  of  the  mass  would  then  be 
coarser  than  that  of  a  heap  of  fine  shot,  but  probably  not  so  coarse  as  that 
of  a  heap  of  cricket-balls.' 

The  number  of  molecules  of  gas  in  a  cubic  centimetre  of  air  is  calculated 
at  twenty-one  trillions. 

By  dissolving  in  alcohol  a  known  weight  of  fuchsine,  and  diluting  the 
liquid,  it  was  observed  that  a  solution  containing  not  more  than  o-oococco2 
of  a  gramme  in  one  cubic  centimetre  had  still  a  distinct  colour  ;  that  is,  that 
a  weight  of  not  more  than  the  ^-millionth  of  a  gramme  can  be  perceived 
by  the  naked  eye.  As  the  molecular  weight  of  this  substance  is  337  times 
that  of  hydrogen  it  follows  that  the  weight  of  an  atom  of  hydrogen  cannot  be 
greater  than  the  one  2o,ooo-millionth  of  a  gramme. 

Loschmidt  gives  the  diameter  of  the  molecules  of  hydrogen  at  o'ooooooo4 
of  a  centimetre  ;  and  according  to  Mousson  and  Quincke  the  diameter  of 
the  sphere  within  which  one  molecule  can  act  upon  an  adjacent  one  is 
between  the  0*00006  and  0-00008  of  a  millimetre,  and  is  therefore  from  5 
to  16  times  less  than  the  wave  length  of  light. 

4.  Molecular  state  of  bodies. — With  respect  to  the  molecules  of  bodies 
three  different  stages  of  aggregation  present  themselves. 

First,  the  solid  state,  as  observed  in  wood,  stone,  metals,  &c.,  at  the 
ordinary  temperature.  The  distinctive  character  of  this  state  is,  that  the 
relative  positions  of  the  molecules  of  the  bodies  is  fixed  and  cannot  be 
changed  without  the  expenditure  of  more  or  less  force.  As  a  consequence, 
solid  bodies  tend  to  retain  whatever  form  may  have  been  given  to  them  by 
nature  or  by  art. 

Secondly,  the  liquid  state,  as  observed  in  water,  alcohol,  oil,  &c.  Here 
the  relative  position  of  the  molecules  is  no  longer  fixed,  the  molecules  glide 
past  each  other  with  the  greatest  ease,  and  the  body  assumes  with  readiness 
the  form  of  any  vessel  in  which  it  may  be  placed. 

Thirdly,  the  gaseotis  state,  as  in  air  and  in  hydrogen.  In  gases  the 
mobility  of  the  molecules  is  still  greater  than  in  liquids  ;  but  the  distinctive 
character  of  a  gas  is  its  incessant  struggle  to  occupy  a  greater  space,  in  con- 
sequence of  which  a  gas  has  neither  an  independent  form  nor  an  indepen- 
dent volume,  for  this  is  due  to  the  pressure  to  which  it  is  subject. 

The  general  term_/7//zW  is  applied  to  both  liquids  and  gases. 

Most  simple  bodies,  and  many  compound  ones,  may  be  made  to  pass 
successively  through  all  the  three  states.  Water  presents  the  most  familiar 
example  of  this.  Sulphur,  iodine,  mercury,  phosphorus,  and  zinc,  are  other 
instances. 

5.  Physical  phenomena,  laws,  and   theories. — Every  change  which 
can  happen  to  a  body,  mere  alteration  of  its  chemical  constitution  being  ex- 
cepted,  may  be  regarded  as  a  physical  phenomenon.     The  fall  of  a  stone,  the 
vibration  of  a  string,  and  the  sound  which  accompanies  it,  the  attraction 
of  light  particles  by  a  rod  of  sealing-wax  which  has  been  rubbed  by  flannel, 


-6]  Physical  Agents.  3 

the  rippling  of  the  surface  of  a  lake,  and  the  freezing  of  water,  are  examples 
of  such  phenomena. 

A  physical  law  is  the  constant  relation  which  exists  between  any  pheno- 
menon and  its  cause.  As  an  example,  we  have  the  phenomenon  of  the 
diminution  of  the  volume  of  a  gas  by  the  application  of  pressure ;  the  cor- 
responding law  has  been  discovered,  and  is  expressed  by  saying  that  the 
volume  of  a  gas  is  inversely  proportional  to  the  pressure. 

In  order  to  explain  the  cause  of  whole  classes  of  phenomena,  suppositions, 
or  hypotheses,  are  made  use  of.  The  utility  and  probability  of  a  hypothesis 
or  theory  are  the  greater  the  simpler  it  is,  and  the  more  varied  and  numerous 
are  the  phenomena  which  are  explained  by  it ;  that  is  to  say,  are  brought 
into  regular  causal  connection  among  themselves  and  with  other  natural 
phenomena.  Thus  the  adoption  of  the  undulatory  theory  of  light  is  justified 
by  the  simple  and  unconstrained  explanation  it  gives  of  all  luminous  pheno- 
mena, and  by  the  connection  it  reveals  with  the  phenomena  of  heat. 

6.  Physical  agrents. — In  our  attempts  to  ascend  from  a  phenomenon  to 
its  cause,  we  assume  the  existence  of  physical  agents,  or  natural  forces  acting 
upon  matter  ;  as  examples  of  such  we  have  gravitation,  heat,  light,  magnet- 
ism, and  electricity. 

Since  these  physical  agents  are  disclosed  to  us  only  by  their  effects,  their 
intimate  nature  is  completely  unknown.  In  the  present  state  of  science,  we 
cannot  say  whether  they  are  properties  inherent  in  matter,  or  whether  they 
result  from  movements  impressed  on  the  mass  of  subtile  and  imponderable 
forms  of  matter  diffused  through  the  universe.  The  latter  hypothesis  is,  how- 
ever, generally  admitted.  This  being  so,  it  may  be  further  asked,  are  there 
several  distinct  forms  of  imponderable  matter,  or  are  they  in  reality  but  one 
and  the  same  ?  As  the  physical  sciences  extend  their  limits,  the  opinion 
tends  to  prevail  that  there  is  a  subtile,  imponderable,  and  eminently  elastic 
fluid  called  the  ether  distributed  through  the  entire  universe  ;  it  pervades 
the  mass  of  all  bodies,  the  densest  and  most  opaque,  as  well  as  the  lightest 
or  the  most  transparent.  It  is  also  considered  that  the  ultimate  particles  of 
which  matter  is  made  up  are  capable  of  definite  motions  varying  in  character 
and  velocity,  and  which  can  be  communicated  to  the  ether.  A  motion  of  a 
particular  kind  communicated  to  the  ether  can  give  rise  to  the  phenomenon 
of  heat ;  a  motion  of  the  same  kind,  but  of  greater  velocity,  produces  light ; 
and  it  may  be  that  a  motion  different  in  form  or  in  character  is  the  cause  of 
electricity.  Not  merely  do  the  atoms  of  bodies  communicate  motion  to  the 
atoms  of  the  ether,  but  this  latter  can  impart  it  to  the  former.  Thus  the 
atoms  of  bodies  are  at  once  the  sources  and  the  recipients  of  the  motion. 
All  physical  phenomena,  referred  thus  to  a  single  cause,  are  but  transforma- 
tions of  motion. 


B  2 


On  Matter,  Force,  and  Motion.  [7- 


CHAPTER   II. 

GENERAL   PROPERTIES   OF   BODIES. 

7.  Different  kinds  of  properties.— By  the  term  properties,  as  applied 
to  bodies,  we  understand  the  different  ways  in  which  bodies  present  them- 
selves to  our  senses.     We  distinguish  general  from  specific  properties.     The 
former  are  shared  by  all  bodies,  and  amongst  them  the  most  important  are 
impenetrability,  extension,   divisibility,  porosity,   compressibility,    elasticity, 
mobility,  and  inertia. 

Specific  properties  are  such  as  are  observed  in  certain  bodies  only,  or  in 
certain  states  of  these  bodies  ;  such  are  solidity,  fluidity,  tenacity,  ductility, 
malleability,  hardness,  transparency,  colour,  &c. 

With  respect  to  the  above  general  properties,  impenetrability  and  exten- 
sion might,  perhaps,  be  more  aptly  termed  essential  attributes  of  matter, 
since  they  suffice  to  define  it ;  and  that  divisibility,  porosity,  compressibility, 
and  elasticity  do  not  apply  to  atoms,  but  only  to  bodies  or  aggregates  of 
atoms  (3). 

8.  Impenetrability. — Impenetrability  is  the  property  in  virtue  of  which 
two  portions  of  matter  cannot  at  the  same  time  occupy  the  same  portion  of 
space.     Thus  when  a  stone  is  placed  in  a  vessel  of  water  the  volume  of  the 
water  rises  by  an  amount  depending  on  the  volume  of  the  stone  ;  this  method, 
indeed,  is  used  to  determine  the  bulk  of  irregularly  shaped  bodies  by  means 
of  graduated  measures. 

Strictly  speaking,  this  property  applies  only  to  the  atoms  of  a  body.  In 
many  phenomena  bodies  appear  to  penetrate  each  other  ;  thus,  the  volume 
of  a  compound  body  is  always  less  than  the  sum  of  the  volumes  of  its  con- 
stituents ;  for  instance,  the  volume  of  a  mixture  of  water  and  sulphuric 
acid,  or  of  water  and  alcohol,  is  less  than  the  sum  of  the  volumes  before 
mixture.  In  all  these  cases,  however,  the  penetration  is  merely  apparent, 
and  arises  from  the  fact  that  in  every  body  there  are  interstices  or  spaces 
unoccupied  by  matter  (13). 

9.  Extension. — Extension  or  magnitude  is  the  property  in  virtue  of  which 
every  body  occupies  a  limited  portion  of  space. 

Many  instruments  have  been  invented  for  measuring  linear  extension  or 
lengths  with  great  precision.  Two  of  these,  the  vernier  and  micrometer 
screw,  on  account  of  their  great  utility,  deserve  to  be  here  mentioned. 

10.  Vernier. — The  vernier  forms  a  necessary  part  of  all  instruments 
where  lengths  or  angles  have  to  be  estimated  with  precision  ;  it  derives  its 
name  from  its  inventor,  a  French  mathematician,  who  died  in   1637,  and 
consists  essentially  of  a  short  graduated  scale,  ad,  which  is  made  to  slide 
along  a  fixed  scale,  AB,  so  that  the  graduations  of  both  may  be  compared 


-11]  Micrometer  Screw.  5 

with  each  other.  The  fixed  scale,  AB,  being  divided  into  equal  parts,  the 
whole  length  of  the  vernier,  a  b,  may  be  taken  equal  to  nine  of  those  parts, 
and  is  itself  divided  into  ten  equal  parts.  Each  of  the  parts  of  the  vernier, 
-/  b,  will  then  be  less  than  a  part  of  the  scale  by  one  tenth  of  the  latter. 

This  granted,  in  order  to  measure  the  length  of  any  object,  mn,  let  us 
suppose  that  the  latter,  when  placed  as  in  the  figure,  has  a  length  greater 
than  four  but  less  than  five  parts  of  the  fixed  scale.  In  order  to  determine 
by  what  fraction  of  a  part  mn  exceeds  four,  one  of  the  ends,  #,  of  the  vernier, 
ab,  is  placed  in  contact  with  one  extremity  of  the  object,  mn,  and  the 
division  on  the  vernier  is  sought  which  coincides  with  a  division  on  the 
scale,  AB.  In  the  figure  this  coincidence  occurs  at  the  eighth  division  of 
the  vernier,  counting  from  the  end,  n,  and  indicates  that  the  fraction  to  be 
measured  is  equal  to  /oths  of  a  part  of  the  scale,  AB.  In  fact,  each  of 
the  parts  of  the  vernier  being  less  than  a  part  of  the  scale  by  y^th  of  the 
latter,  it  is  clear  that  on  proceeding  towards  the  left  from  the  point  of  co- 
incidence, the  divisions  of  the  vernier  are  respectively  one,  two,  three,  etc. 


Fig.  i. 

tenths  behind  the  divisions  of  the  scale  ;  so  that  the  end,  n,  of  the  object 
(that  is  to  say,  the  eighth  division  of  the  vernier)]  is  j^ths  behind  the 
division  4  on  the  scale  ;  in  other  words,  the  length  of  mn  is  equal  to  ^ths 
of  the  parts  into  which  the  scale  AB  is  divided.  Consequently,  if  the  scale 
AB  were  divided  into  inches,  the  length  of  mn  would  be  4/0  =  4f  inches. 
The  divisions  on  the  scale  remaining  the  same,  it  would  be  necessary'  to  in- 
crease the  length  of  the  vernier  in  order  to  measure  the  length  mn  more 
accurately.  For  instance,  if  the  length  of  the  vernier  were  equal  to  nineteen 
of  the  parts  on  the  scale,  and  this  length  were  divided  into  twenty  equal  parts, 
the  length  mn  could  be  determined  to  the  twentieth  of  a  part  on  the  scale, 
and  so  on.  In  instruments  like  the  theodolite,  intended  for  measuring  angles, 
the  scale  and  vernier  have  a  circular  form,  and  the  latter  usually  carries  a 
magnifier  in  order  to  determine  with  greater  precision  the  coincident  divisions 
of  vernier  and  scale. 

1 1.  Micrometer  screw. — Another  useful  little  instrument  for  measuring 
small  lengths  with  precision  is  the  micrometer  screw.  It  is  used  under 
various  forms,  but  the  principle  is  the  same  in  all,  and  may  be  illustrated  by 
reference  to  the  sphcrometer.  This  consists  of  an  accurately  turned  screw 
with  a  blunt  point  which  works  in  a  companion  supported  on  three  steel 
points  (fig.  2).  To  one  of  these  is  fixed  a  vertical  graduated  scale,  each 
division  of  which  is  equal  to  the  distance  between  two  threads  of  the  screw. 


6  On  Matter,  Force,  and  Motion,  [11— 

This  distance  may  be  accurately  determined  by  measuring  a  given  length  of 
the  screw  by  compasses,  and  counting  the  number  of  the  threads  in  this 
length.  A  milled  head  attached  to  the  screw  is  graduated  at  the  periphery 

into  any  given  number  of  parts,  say  500. 
Suppose  now  the  distance  between  the 
threads  is  I  millimetre,  when  the  head  has 
made  a  complete  turn  it  will  have  risen  or 
sunk  through  one  millimetre,  and  so  on  in 
proportion  for  any  multiple  or  fraction  of  a 
turn. 

In  order  to  determine  the  thickness  of  a 
piece  of  glass  for  instance,  the  apparatus  is 
placed  on  a  perfectly  plane  polished  surface, 
and  the  point  of  the  screw  is  brought  in 
contact  with  the  glass.  The  division  on  the 
Flg-  2-  vertical  scale  immediately  above  the  limb, 

and  that  on  the  limb  are  read  off.  After  removing  the  glass  plate  the  point 
is  brought  in  contact  with  the  plane  surface,  and  corresponding  readings  are 
again  made,  from  which  the  thickness  can  be  at  once  deduced. 

The  same  process  is  obviously  applicable  to  determining  the  diameter  of 
a  wire. 

To  ascertain  whether  a  surface  is  spherical,  three  points  are  applied  to 
the  surface,  and  the  screw  is  also  made  to  touch  as  described  above.  It  is 
then  moved  along  the  surface,  and  if  all  four  points  are  everywhere  in  con- 
tact the  surface  is  truly  spherical.  This  application  is  of  great  value  in 
ascertaining  the  exact  curvature  of  lenses. 

The  diameter  of  a  sphere  may  also  be  measured  by  its  means  ;  for  it 
can  be  shown  by  a  simple  geometrical  construction  that  the  distance  of  the 
movable  point  from  the  plane  of  the  fixed  points,  multiplied  by  the  diameter 
of  the  sphere,  is  equal  to  the  square  of  the  distance  of  the  movable  point 
from  one  of  the  fixed  points. 

12.  Divisibility — is  the  property  in  virtue  of  which  a  body  may  be  sepa- 
rated into  distinct  parts. 

Numerous  examples  may  be  cited  of  the  extreme  divisibility  of  matter.  (3.) 
The  tenth  part  of  a  grain  of  musk  will  continue  for  years  to  fill  a  room  with 
its  odoriferous  particles,  and  at  the  end  of  that  time  will  scarcely  be  dimin- 
ished in  weight.  Blood  is  composed  of  red,  flattened  globules,  floating  in 
a  colourless  liquid  called  serum.  In  man  the  diameter  of  one  of  these 
globules  is  less  than  the  3,5ooth  part  of  an  inch,  and  the  drop  of  blood  which 
might  be  suspended  from  the  point  of  a  needle  would  contain  about  a  million 
of  globules. 

Again,  the  microscope  has  disclosed  to  us  the  existence  of  insects  smaller 
even  than  these  particles  of  blood  ;  the  struggle  for  existence  reaches  even 
to  these  little  creatures,  for  they  devour  still  smaller  ones.  If  blood  runs  in 
the  veins  of  these  devoured  ones,  how  infinitesimal  must  be  the  magnitude 
of  its  component  globules  ! 

Although  experiment  fails  to  determine  whether  there  be  a  limit  to  the 
divisibility  of  matter,  many  facts  in  chemistry,  such  as  the  invariability  in 
the  relative  weights  of  the  elements  which  combine  with  each  other,  would 


-13] 


Porosity. 


ot 
7BRS1TT) 


lead' us  to  believe  that  such  a  limit  does  exist.  It  is  on  this  account  that 
bodies  are  conceived  to  be  composed  of  extremely  minute  and  indivisible 
parts  called  atoms  (3). 

13.  Porosity. — Porosity  is  the  quality  in  virtue  of  which  interstices  or 
pores  exist  between  the  molecules  of  a  body. 

Two  kinds  of  pores  may  be  distinguished  :  physical  pores,  where  the 
interstices  are  so  small  that  the  surrounding  molecules  remain  within  the 
sphere  of  each  other's  attracting  or  repelling  forces  ;  and  sensible  pores,  or 
actual  cavities  across  which  these  molecular  forces  cannot  act.  The  con- 
tractions and  expansions  resulting  from  variations  of  temperature  are  due  to 
the  existence  of  physical  pores,  whilst  in  the  organic  world  the  sensible  pores 
are  the  seat  of  the  phenomena  of  exhalation  and  absorption. 

In  wood,  sponge,  and  a  great  number  of  stones — for  instance,  pumice 
stone — the  sensible  pores  are  apparent  ;  physical  pores  never  are.  Yet, 
since  the  volume  of  every  body  may  be  diminished,  we  conclude  that  all 
possess  physical  pores. 

The  existence  of  sensible  pores  may  be  shown  by  the  following  experi- 
ment : — A  long  glass  tube,  A  (fig.  3),  is  provided  with  a  brass  cup  at  the 
top,  and  a  brass  foot  made  to  screw  on  to  the  plate  of  an  air-pump.  The 
bottom  of  the  cup  consists  of  a  thick  piece  of 
leather.  After  pouring  mercury  into  the  cup 
so  as  entirely  to  cover  the  leather,  the  air- 
pump  is  put  in  action,  and  a  partial  vacuum 
produced  within  the  tube,  By  so  doing  a 
shower  of  mercury  is  at  once  produced 
within  the  tube,  for  the  atmospheric  pressure 
on  the  mercury  forces  that  liquid  through 
the  pores  of  the  leather.  In  the  same  man- 
ner water  or  mercury  may  be  forced  through 
the  pores  of  wood,  by  replacing  the  leather 
in  the  above  experiment  by  a  disc  of  wood 
cut  perpendicular  to  the  fibres. 

When  a  piece  of  chalk  is  thrown  into 
water,  air-bubbles  at  once  rise  to  the  surface, 
in  consequence  of  the  air  in  the  pores  of  the 
chalk  being  expelled  by  the  water.  The 
chalk  will  be  found  to  be  heavier  after  im- 
mersion than  it  was  before,  and  from  the 
increase  of  its  weight  the  volume  of  its  pores 
may  be  easily  determined. 

The  porosity  of  gold  was  demonstrated 
by  the  celebrated  Florentine  experiment  made 
in  1661.  Some  academicians  at  Florence, 
wishing  to  try  whether  water  was  compres- 
sible, filled  a  thin  globe  of  gold  with  that 
liquid,  and,  after  closing  the  orifice  hermeti- 
cally, they  exposed  the  globe  to  pressure 
with  a  view  of  altering  its  form,  knowing  that 
any  alteration  in  form  must  be  accompanied  by  a  diminution  in  volume. 


Fig.  3. 


8  On  Matter,  Force,  and  Motion.  [13- 

The  consequence  was,  that  the  water  forced  its  way  through  the  pores  of  the 
gold,  and  stood  on  the  outside  of  the  globe  like  dew.  More  than  twenty 
years  previously  the  same  fact  was  demonstrated  by  Francis  Bacon  by  means 
of  a  leaden  sphere  ;  the  experiment  has  since  been  repeated  with  globes  of 
other  metals,  and  similar  results  obtained. 

14.  Apparent  and  real  volumes. — In  consequence  of  the  porosity  of 
bodies,  it  becomes  necessary  to  distinguish  between  their  real  and  apparent 
volumes.  The  real  volume  of  a  body  is  the  portion  of  space  actually  occu- 
pied by  the  matter  of  which  the  body  is  composed  ;  its  apparent  volume  is 
the  sum  of  its  real  volume  and  the  total  volume  of  its  pores.  The  real 
volume  of  a  body  is  invariable,  but  its  apparent  volume  can  be  altered  in 
various  ways. 

1 5.  Applications, — The  property  of  porosity  is  utilised  in  filters  of  paper, 
felt,  stone,  charcoal,  £c.     The  pores  of  these  substances  are  sufficiently  large 
to  allow  liquids  to   pass,  but  small  enough  to  arrest  the  passage  of  any  sub- 
stances which  these  liquids  may  hold  in  suspension.     Again,  large  blocks  of 
stone  are  often  detached  in  quarries  by  introducing  wedges  of  dry  wood  into 
grooves  cut  in  the  rock.     These  wedges  being  moistened,  water  penetrates 
their  pores,  and  causes  them  to  swell  with   considerable  force.     L)ry  cords, 
when  moistened,  increase  in  diameter  and  diminish  in  length — a  property  of 
which  advantage  has  been  taken  in  order  to  raise  great  weights. 

1 6.  Compressibility. —  Compressibility  is  the  property  in  virtue  of  which 
the  volume  of  a  body  may  be  diminished  by  pressure.     This  property  is  at 
once  a  consequence  and  a  proof  of  porosity. 

Bodies  differ  greatly  with  respect  to  compressibility.  The  most  com- 
pressible bodies  are  gases  ;  by  sufficient  pressure  they  may  be  made  to 
occupy  ten,  twenty,  or  even  some  hundred  times  less  space  than  they  do  under 
ordinary  circumstances.  In  most  cases,  however,  there  is  a  limit  beyond 
which,  when  the  pressure  is  increased,  they  become  liquids. 

The  compressibility  of  solids  is  much  less  than  that  of  gases,  and  is  found 
in  all  degrees.  Cloths,  paper,  cork,  woods,  are  amongst  the  most  com- 
pressible. Metals  are  so  also  to  a  great  extent,  as  is  proved  by  the  process 
of  coining,  in  which  the  metal  receives  the  impression  from  the  die.  There 
is,  in  most  cases,  a  limit  beyond  which,  when  the  pressure  is  increased,  bodies 
are  fractured  or  reduced  to  powder. 

The  compressibility  of  liquids  is  so  small  as  to  have  remained  for  a  long 
time  undetected  :  it  may,  however,  be  proved  by  experiment,  as  will  be  seen 
in  the  chapter  on  Hydrostatics. 

17.  Elasticity. — Elasticity   is  the  property  in  virtue  of  which   bodies 
resume  their  original  form  or  volume,  when  the  force  which  altered  that  form 
or  volume  ceases  to  act.     Elasticity  may  be  developed  in  bodies  by  pressure, 
by  traction  or  pit  I  ling,  flexion  or  bending,  and  by  torsion  or  twisting.     In 
treating  of  the  general   properties  of  bodies,  the  elasticity  developed  by 
pressure  alone  requires  consideration  ;  the  other  kinds  of  elasticity,  being 
peculiar  to  solid  bodies,  will  be  considered  amongst  their  specific  properties 
<arts.  89,  90,  91). 

Gases  and  liquids  are  perfectly  elastic  ;  in  other  words,  after  undergoing 
.a  change  in  volume  they  regain  exactly  their  original  volume  when  the 
pressure  becomes  what  it  originally  was.  Solid  bodies  present  different  de- 


-19]  Applications.  g 

grees  of  elasticity,  though  none  present  the  property  in  the  same  perfec- 
tion as  liquids  and  gases,  and  in  all  it  varies  according  to  the  time  during 
which  the  body  has  been  exposed  to  pressure.  Caoutchouc,  ivory,  glass, 
and  marble  possess  considerable  elasticity  ;  lead,  clay,  and  fats,  scarcely 
any. 

There  is  a  limit  to  the  elasticity  of  solids,  beyond  which  they  either  break 
or  are  incapable  of  regaining  their  original  form  and  volume.  This  is  called 
the  limit  of  elasticity ;  within  this  limit  all  substances  are  perfectly  elastic. 
In  sprains,  for  instance,  the  elasticity  of  the  tendons  has  been  exceeded. 
In  gases  and  liquids,  on  the  contrary,  no  such  limit  can  be  reached  ;  they 
always  regain  their  original  volume  when  the  original  pressure  is  restored. 

If  a  ball  of  ivory,  glass,  or  marble  be  allowed  to  fall  upon  a  slab  of  polished 
marble,  which  has  been  previously  slightly  smeared  with  oil,  it  will  rebound 
and  rise  to  a  height  nearly  equal  to  that  from  which  it  fell.  On  afterwards 
examining  the  ball  a  circular  blot  of  oil  will  be  found  upon  it,  more  or  less 
extensive  according  to  the  height  of  the  fall.  From  this  we  conclude  that  at  the 
moment  of  the  shock  the  ball  was  flattened,  and  that  its  rebound  was  caused 
by  the  effort  to  regain  its  original  form. 

1 8.  Mobility,  motion,  rest, — Mobility  is  the  property  in  virtue  of  which 
the  position  of  a  body  in  space  may  be  changed. 

Motion  and  rest  may  be  either  relative  or  absolute.  By  the  relative 
motion  or  rest  of  a  body  we  mean  its  change  or  permanence  of  position  with 
respect  to  surrounding  bodies  ;  by  its  absolute  motion  or  rest  we  mean  the 
change  or  permanence  of  its  position  with  respect  to  ideal  fixed  points  in 
space. 

Thus  a  passenger  in  a  railway  carriage  may  be  in  a  state  of  relative  rest 
with  respect  to  the  train  in  which  he  travels,  but  he  is  in  a  state  of  relative 
motion  \vith  respect  to  the  objects,  such  as  trees,  houses,  &c.,  past  which  the 
train  rushes.  These  houses  again  enjoy  merely  a  state  of  relative  rest,  for 
the  earth  itself  which  bears  them  is  in  a  state  of  incessant  relative  motion 
with  respect  to  the  celestial  bodies  of  our  solar  system,  inasmuch  as  it  moves 
at  the  rate  of  more  than  eighteen  miles  in  a  second.  In  short,  absolute 
motion  and  rest  are  unknown  to  us  ;  in  nature,  relative  motion  and  rest  are 
alone  presented  to  our  observation. 

19.  Inertia. — Inertia  is  a  purely  negative  though  universal  property  of 
matter  (26)  ;  it  is  the  property  that  matter  cannot  of  itself  change  its  own 
state  of  motion  or  of  rest.     If  a  body  is  at  rest  it  remains  so  until  some 
force  acts  upon  it ;  if  it  is  in  motion  this  motion  can  only  be  changed  by  the 
application  of  some  force. 

This  property  of  inertia  is  what  is  expressed  by  Newton's  first  law  of 
motion. 

A  body,  when  unsupported  in  mid-air,  does  not  fall  to  the  earth  in  virtue 
of  any  inherent  property,  but  because  it  is  acted  upon  by  the  force  of  gravity. 
A  billiard  ball  gently  pushed  does  not  move  more  and  more  slowly,  and 
finally  stop,  because  it  has  any  preference  for  a  state  of  rest,  but  because  its 
motion  is  impeded  by  the  friction  on  the  cloth  on  which  it  rolls,  and  by  the 
resistance  of  the  air.  If  all  impeding  causes  were  withdrawn,  a  body  once 
in  motion  would  continue  to  move  for  ever  in  a  straight  line  with  unchanging 
velocity. 

B3 


10  On  Matter,  Force,  and  Motion.  [20- 

20.  Applications. — Numerous  phenomena  may  be  explained  by  the 
inertia  of  matter.  For  instance,  before  leaping  a  ditch  we  run  towards  it,  in 
order  that  the  motion  of  our  bodies  at  the  moment  of  leaping  may  add  itself 
to  the  muscular,  effort  then  made. 

On  descending  carelessly  from  a  carriage  in  motion,  the  upper  part  of  the 
body  retains  its  motion,  whilst  the  feet  are  prevented  from  doing  so  by  friction 
against  the  ground  ;  the  consequence  is  we  fall  towards  the  moving  carriage. 
A  rider  falls  over  the  head  of  a  horse  if  it  suddenly  stops.  In  striking  the 
handle  of  a  hammer  against  the  ground  the  handle  suddenly  stops,  but  the 
head,  striving  to  continue  its  motion,  fixes  itself  more  firmly  on  the  handle. 

By  the  property  of  inertia  may  also  be  explained  the  following  experiments  : 
— Let  a  card  be  placed  upon  a  tumbler,  and  a  shilling  on  the  card  ;  if  the  edge 
of  the  card  be  smartly  flicked  with  the  finger  the  card  is  driven  away  and  the 
coin  falls  into  the  tumbler.  A  gentle  push  with  the  finger  will  move  a  door 
on  its  hinges  ;  but  if  a  pistol  bullet  be  fired  against  the  door  it  perforates  the 
door  without  moving  it.  A  clay  tobacco  pipe,  which  is  suspended  by  two 
vertical  hairs,  may  be  cut  in  two  by  a  powerful  stroke  with  a  sharp  sword 
without  breaking  the  hairs. 

A  string  which  gently  applied  will  raise  a  weight,  snaps  at  once  when  a 
sudden  pull  is  exerted.  Substances  which  explode  with  great  rapidity,  such 
as  fulminating  mercury,  chloride  of  nitrogen,  cannot  be  used  with  fire-arms, 
because  there  is  not  sufficient  time  to  transfer  the  motion  to  the  projectiles, 
and  hence  the  weapons  are  burst. 

The  terrible  accidents  on  our  railways  are  chiefly  due  to  inertia.  When 
the  motion  of  the  engine  is  suddenly  arrested  the  carriages  strive  to  continue 
the  motion  they  had  acquired,  and  in  doing  so  are  shattered  against  each 
other.  Hammers,  pestles,  stampers  are  applications  of  inertia.  So  are  also 
the  enormous  iron  fly-wheels,  by  which  the  motion  of  steam-engines  is 
regulated. 


-22  J  Measure  of  Space.  1 1 


CHAPTER   III. 

ON    FORCE,    EQUILIBRIUM,    AND    MOTION. 

21.  Measure  of  time. — To  obtain  a  proper  measure  of  force  it  is  neces- 
sary, as  a  preliminary,  to  define  certain  conceptions  which  are  presupposed 
in  that  measure ;  and,  in  the  first  place,  it  is  necessary  to  define  the  unit  of 
time.     Whenev er  a  second  is  spoken  of  without  qualification  it  is  understood 
to  be  a  second  of  mean  solar  time.     The  exact  length  of  this  unit  is  fixed  by 
the  following  considerations.     The  instant  when  the  sun's  centre  is  on  ai\ 
observer's  meridian — in  other  words,  the  instant  of  the  transit  of  the  sun's, 
centre — can  be  determined  with  exactitude,  and  thus  the  interval  which 
elapses  between  two  successive  transits  also  admits  of  exact  determination, 
and  is  called  an  apparent  day.     The  length  of  this  interval  differs  slightly 
from  day  to  day,  and  therefore  does  not  serve  as  a  convenient  measure  o£ 
time.     Its  average  length  is  not  open  to  this  objection,  and  therefore  serves: 
as  the  required  measure,  and  is  called  a  mean  solar  day.     The  short  hand 
of  a  common  clock  would  go  exactly  twice  round  the  face  in  a  mean  solar 
day  if  it  went  perfectly.     The  mean  solar  day  consists  of  2.4  equal  parts 
called  hours,  these  of  60  equal  parts  called  minutes,  and  these  again  of  60 
equal  parts  called  seconds.     Consequently,  the  second  is  the  86,4ooth  part  of 
a  mean  solar  day,  and  is  the  generally  received  unit  of  time. 

22.  Measure  of  space. — Space  may  be  either  length  or  distance,  which 
is  space  of  one  dimension  ;  area,  which  is  space  of  two  dimensions  ;  or 
volume,  which  is  space  of  three  dimensions.     In  England  the  standard  of 
length  is  the  British  Imperial  Yard,  which  is  the  distance  between  two  fixed 
points  on  a  certain  metal  rod,  kept  in  the  Tower  of  London,  when  the  tempera- 
ture of  the  whole  rod  is  60°  F.  =  15°- 5  C.     It  is,  however,  usual  to  employ  as 
a  unit,  2ifoot,  which  is  the  third  part  of  a  yard.     In  France  the  standard  of 
length  is  the  metre  ;  this  is  approximately  equal  to  the  ten-millionth  part  of 
a  quadrant  of  the  earth's  meridian,  that  is  of  the  arc  from  the  Equator  to  the 
North  Pole  ;  it  is  practically  fixed  by  the  distance  between  two  marks  on  a 
certain  standard  rod.    The  relation  between  these  standards  is  as  follows  : — • 

i  yard'    =0*914383  metre. 

i  metre  =  1*093633  yard. 

The  unit  of  length  having  been  fixed,  the  units  of  area  and  volume  are 
connected  with  it  thus  :  the  unit  of  area  is  the  area  of  a  square,  one  side  of 
which  is  the  unit  of  length.  The  unit  of  volume  is  the  volume  of  a  cube,  one 
edge  of  which  is  the  unit  of  length.  These  units  in  the  case  of  English 
measures  are  the  square  yard  (or  foot)  and  the  cubic  yard  (or  foot)  respec- 
tively ;  in  the  case  of  French  measures,  the  square  metre  and  cubic  metre 
respectively.  The  length  of  the  seconds  pendulum,  in  lat.  45°,  which  is 
about  that  of  Milan,  is  0-993 5m.,  and  thus  only  differs  from  a  metre  by  6-5 
millimetres. 


c  2  On  Matter,  Force,  and  Motion.  [23- 

23.  Measure  of  mass.  —  Two  bodies  are  said  to  have  equal  masses  when, 
if  placed  in  a  perfect  balance  in  vacua,  they  counterpoise  each  other.     Suppose 
sve  take  lumps  of  any  substance,  lead,  butter,  wood,  stone,  &c.,  and  suppose 
that  any  one  of  them  when  placed  on  the  one  pan  of  a  balance  will  exactly 
counterpoise   any  other  of  them  when  placed  on  the  opposite   pan—  the 
balance  being  perfect  and  the  weighing  performed  in  vacua  ;  this  being  the 
case,  these  lumps  are  said  to  have  equal  masses. 

The  British  unit  of  mass  is  the  standard  pound  (avoirdupois),  which  is  a 
certain  piece  of  platinum  kept  in  the  Exchequer  Office  in  London.  This  unit 
having  been  fixed,  the  mass  of  a  given  substance  is  expressed  as  a  multiple 
or  submultiple  of  the  unit. 

It  need  scarcely  be  mentioned  that  many  distances  are  ascertained  and 
expressed  in  yards  which  it  would  be  physically  impossible  to  measure 
directly  by  a  yard  measure.  In  like  manner  the  masses  of  bodies  are  fre- 
quently ascertained  and  expressed  numerically  which  could  not  be  placed  in 
a  balance  and  subjected  to  direct  weighing. 

24.  Density  and  relative  density.  —  If  we  consider  any  body  or  portion 
of  matter,  and  if  we  conceive  it  to  be  divided  into  any  number  of  parts  having 
equal  volumes,  then,  if  the  masses  of  these  parts  are  equal,  in  whatever  way 
the   division  be  conceived  as  taking  place,  that  body  is   one   of  uniform 
density.     The  density  of  such  a  body  is  the  mass  of  the  unit  of  volume.     Con- 
sequently, if  M  denote  the  mass,  V  the  volume,  and  D  the  density  of  the 
body,  we  have 

M=VD. 

If  now  we  have  an  equal  volume  V  o.f  any  second  substance  whose  mass  is 
M'  and  density  D',  we  shall  have 

M'-VD'. 

Consequently,  D  :  D'::M  :  M'  ;  that  is,  the  densities  of  substances  are  in 
the  same  ratio  as  the  masses  of  equal  volumes  of  those  substances.  If  now 
we  take  the  density  of  distilled  water  at  4°  C.  to  be  unity,  the  relative  density 
of  any  other  substance  is  the  ratio  which  the  mass  of  any  given  volume  of 
that  substance  at  that  temperature  bears  to  the  mass  of  an  equal  volume  of 
water.  Thus  it  is  found  that  the  mass  of  any  volume  of  platinum  is  22-069 
times  that  of  an  equal  volume  of  water,  consequently  the  relative  density  of 
platinum  is  22-069. 

The  relative  density  of  a  substance  is  generally  called  its  specific  gravity. 
Methods  of  determining  it  are  given  in  Book  III. 

In  French  measures  the  cubic  decimetre  or  litre  of  distilled  water  at  4°  C. 
contains  the  unit  of  mass,  the  kilogramme  ;  and  therefore  the  mass  in  kilo- 
grammes of  V  cubic  decimetres  of  a  substance  whose  specific  gravity  is  D, 
will  be  given  by  the  equation 


The  same  equation  will  give  the  mass  in  grammes  of  the  body,  if  V  is  given 
in  cubic  centimetres. 

It  has  been  ascertained  that  27-7274  cubic  inches  of  distilled  water  at  the 
temperature  of  I5°'5  C.  or  60°  F.  contain  a  pound  of  matter.     Consequently, 


-26]  Force.  13 

if  V  is  the  volume  of  a  body  in  cubic  inches,  D  its  specific  gravity,  its  mass 
M  in  pounds  avoirdupois  will  be  given  by  the  equation 

M.  VD  . 

277274 

In  this  equation  D  is,  properly  speaking,  the  relative  density  of  the  substance 
at  15^-5  C.  when  the  density  of  water  at  I5°'5  C.  is  taken  as  the  unit. 

25.  Velocity  and  its  measure. — When   a  material  point  moves,  it  de- 
scribes a  continuous  line  which  may  be  either  straight  or  curved,  and  is 
called  its  path  and  sometimes  its  trajectory.     Motion  which  takes  place 
along  a  straight  line  is  called  rectilinear  motion  ;  that  which  takes  place 
along  a  curved  line  is  called  cut  vilinear  motion.     The  rate  of  the  motion  of 
a  point  is  called  its  velocity.     Velocity  may  be  either  uniform  or  variable  ;  it 
is  uniform  when  the  point  describes  equal  spaces  or  portions  of  its  path  in 
all  equal  times  ;  it  is  variable  when  the  point  describes  unequal  portions  of 
its  path  in  any  equal  times. 

Uniform  velocity  is  measured  by  the  number  of  units  of  space  described 
in  a  given  unit  of  time.  The  units  commonly  employed  in  this  country  are 
feet  and  seconds.  If,  for  example,  a  velocity  5  is  spoken  of  without  qualifi- 
cation, this  means  a  velocity  of  5  feet  per  second.  Consequently,  if  a  body 
moves  for  /  seconds  with  a  uniform  velocity  v,  it  will  describe  vt  feet. 

The  following  are  a  few  examples  of  different  degrees  of  velocity  expressed 
in  this  manner.  A  snail  0-005  feet  *n  a  second  ;  the  Rhine  between  Worms 
and  Mainz  3-3  ;  military  quick  step  4/6  ;  moderate  wind  10  ;  fast  sailing 
vessel  18-0;  Channel  steamer  22*0  ;  railway  train  36  to  75  feet  ;  racehorse 
and  storm  50  feet  ;  eagle  100  feet ;  carrier  pigeon  120  feet  ;  a  hurricane  160 
feet  ;  sound  at  o°  1,090;  a  shot  from  an  Armstrong  gun  1,180  ;  a  Martini- 
Henry  rifle  bullet  1,330  ;  a  point  on  the  Equator  in  its  rotation  about  the 
earth's  axis  1,520;  velocity  of  the  vibratory  motion  of  particles  of  air  1,590; 
the  centre  of  the  earth  101,000  feet  ;  light,  and  also  electricity  in  a  medium 
destitute  of  resistance  192,000  miles. 

Variable  velocity  is  measured  at  any  instant  by  the  number  of  units  of 
space  a  body  would  describe  if  it  continued  to  move  uniformly  from  that 
instant  for  a  unit  of  time.  Thus,  suppose  a  body  to  run  down  an  inclined 
plane,  it  is  a  matter  of  ordinary  observation  that  it  moves  more  and  more 
quickly  during  its  descent  ;  suppose  that  at  any  point  it  has  a  velocity  1 5, 
this  means  that  at  that  point  it  is  moving  at  the  rate  of  1 5  ft.  per  second,  or 
in  other  words,  if  from  that  point  all  increase  of  velocity  ceased,  it  would  de- 
scribe 1 5  ft.  in  the  next  second. 

26.  Force. — When  a  material  point  is  at  rest,  it  has  no  innate  power  of 
changing  its  state  of  rest  ;  when  it  is  in  motion  it  has  no  innate  power  of 
changing  its  state  of  uniform  motion  in  a  straight  line.     This  property  of 
matter  is  termed  its  inertia  (19).     Any  cause  which  sets  a  point  in  motion, 
or  which  changes  the  magnitude  or  direction  of  its  velocity  if  in  motion,  is  a 

force.  Gravity,  friction,  the  elasticity  of  springs  or  gases,  electrical  or  magnetic 
attraction  or  repulsion,  &c.,  are  forces.  All  changes  observed  in  the  motion 
of  bodies  can  be  referred  to  the  action  of  one  or  more  forces. 

According  to  the  length  of  time  during  which  it  acts,  a  force  may  be 
either  momentary — such  as  the  forces  called  into  play  in  an  explosion,  an 
impact,  or  the  discharge  of  an  electrical  spark — or  it  may  be  continuous  and 


14  On  Matter,  Force,  and  Motion.  [26- 

permanent,  like  the  attraction  of  a  magnet  or  of  gravitation,  or  the  forces 
called  into  play  by  an  electrical  current.  The  effect  of  a  force  of  the  former 
kind  (which  is  called  an  impulsive  force)  is,  as  far  as  our  observation  permits, 
an  instantaneous  change  in  the  momentum  (28)  of  the  body  on  which  it  acts, 
while  the  effects  of  forces  of  the  latter  kind  are  produced  gradually,  and  re- 
quire the  lapse  of  time  to  exhibit  themselves.  In  order  that  impulsive  forces 
may  produce  any  appreciable  effects,  their  intensity  during  the  moment  of 
their  action  must  be  indefinitely  greater  than  that  of  continuous  forces.  An 
impulsive  force  is  measured  by  the  instantaneous  change  in  the  momentum 
of  the  body  on  which  it  acts.  If  the  strength  of  a  continuous  force  does  not 
van-,  it  is  called  a  constant  force. 

27.  Accelerative  effect  of  force. — If  we  suppose  a  force  to  continue 
unchanged  in  magnitude,  and  to  act  along  the  line  of  motion  of  a  point,  it 
will  communicate  in  each  successive  second  a  constant  increase  of  velocity. 
This  constant  increase  is  the  accelerative  effect  of  the  force.     Thus,  if  at  any 
given  instant  the  body  has  a  velocity  10,  and  if  at  the  end  of  the  first,  second, 
third,  &c.,  second  from  that  instant  its  velocity  is   13,  1 6,  19,  &c.,  the  ac- 
celerative  effect  of  the  force  is  3  ;  a  fact  which  is  expressed  by  saying  that 
the  body  has  been  acted  on  by  an  accelerating  force  3. 

If  the  force  vary  from  instant  to  instant,  its  accelerative  effect  will  also 
vary ;  when  this  is  the  case  the  accelejative  effect  at  any  instant  is  measured 
by  the  velocity  it  would  communicate  in  a  second  if  the  force  continued 
constant  from  that  instant. 

By  means  of  an  experiment  to  be  described  below  (80)  it  can  be  shown 
that  at  any  given  place  the  accelerative  effect  of  gravity  g  is  constant :  but 
it  is  found  to  have  different  values  at  different  places  ;  adopting  the  units  of 
feet  and  seconds  it  is  found  that  with  sufficient  approximation 

g=f(l  —0-00256  COS  2<£) 

at  a  place  whose  latitude  is  <£,  where/ denotes  the  number  32*1724,  that  is 
the  effect  of  gravity  in  latitude  45°. 

If  we  adopt  the  units  of  metres  and  seconds,  then/=  9-8059. 

28.  Momentum  or  quantity  of  motion  is  a  magnitude  varying  as  the 
mass  of  a  body  and  its  velocity  jointly,  and  is  therefore  expressed  numerically 
by  the  product  of  the  number  of  units  of  mass  which  it  contains,  m,  and  the 
number  of  units  of  velocity,  V,  in  its  motion,  or  by  ///  v.     Thus  a  body  con- 
taining 5  Ibs.  of  matter,  and  moving  at  the  rate  of  12  ft.  per  second,  has  a 
momentum  of  60. 

29.  Measure  of  force. — Force,  when  constant,  is  measured  by  the  mo- 
mentum it  communicates  to  a  body  in  a  unit  of  time.     If  the  force  varies,  it 
is  then  measured  at  any  instant  by  the  momentum  it  would  communicate  if 
it  continued  constant  for  a  unit  of  time  from  the  instant  under  consideration. 
On  the  British  system  of  weights  and  measures  the  unit  offeree  is  that  force 
which  acting  on  a  pound  of  matter  would  produce  in  one  second  a  velocity 
of  one  foot  per  second.     To  this  unit  the  term  poundal  has  been  applied. 
Consequently,  if  a  body  contains  m  Ibs.  of  matter,  and  is  acted  on  by  a  force 
whose  accelerative  effect  is  /  that  force  contains  a  number  of  units  of  force 
(F),  given  by  the  equation 

.F  -  mf. 


-30]  Representation  of  Forces.  15 

The  weight  of  a  body,  when  that  term  denotes  a  force,  is  the  force  exerted 
on  it  by  gravity ;  consequently,  if  m  is  the  mass  of  the  body,  and  g  the 
accelerating  force  of  gravity,  the  number  of  units  of  force  W  exerted  on  it 
by  gravity  is  given  by  the  equation 

W  =  mg 
or  (27)  W  =  ;/{/"(!  -0-00256  cos  2<£). 

From  this  it  is  clear  that  the  weight  of  the  same  body  will  be  different  at 
different  parts  of  the  earth's  surface  ;  this  could  be  verified  by  attaching  a 
piece  of  platinum  (or  other  metal)  to  a  delicate  spring,  and  noting  the  varia- 
tions in  the  length  of  the  spring  during  a  voyage  from  a  station  in  the 
Northern  Hemisphere  to  another  in  the  Southern  Hemisphere — for  instance, 
from  London  to  the  Cape  of  Good  Hope. 

When,  therefore,  a  pound is  used  as  a  unit  offeree  it  must  be  understood 
to  mean  the  force  W  exerted  by  gravity  on  a  pound  of  matter  in  London. 
Now,  in  London,  the  latitude  of  which  is  51°  30',  the  numerical  value  of  g  is 
32-1912,  so  that 

W=  I  x  32-1912  ; 

in  other  words,  when  a  pound  is  taken  as  the  unit  offeree  it  contains  32-1912 
units  of  force  according  to  the  measure  given  above.  It  will  be  observed 
that  a  pound  of  matter  is  a  completely  determinate  quantity  of  matter  irre- 
spective of  locality,  but  gravity  exerts  on  a  pound  of  matter  a  pound  (or 
32-1912  units)  of  force  at  London  and  other  places  in  about  the  same  latitude 
as  London  only  ;  this  ambiguity  in  the  term  pound  should  be  carefully 
noticed  by  the  student ;  the  context  in  any  treatise  will  always  show  in  which 
sense  the  term  is  used.  The  absolute  unit  of  force  as  defined  above  is  con- 
stant ;  it  is  about  equal  to  a  weight  of  half  an  ounce  at  London. 

30.  Representation  of  forces. — Draw  any  straight  line  AB  (fig.  4),  and 
fix  on  any  point  O  in  it.  We  may  suppose  a  force  to  act  on  the  point  O, 
along  the  line  AB,  either  towards  A  or  B  :  then  O  is 

called  the  point  of  application  of  the  force,  AB  its  line  B  5i  o 5  A 
of  action  ;  if  it  acts  towards  A,  its  direction  is  OA,  if  Fig.  4 

toward  B,  its  direction  is  OB.     It  is  rarely  necessary 

to  make  the  distinction  between  the  line  of  action  and  direction  of  a  force  ; 
it  being  very  convenient  to  make  the  convention  that  the  statement — a  force 
acts  on  a  point  O  along  the  line  OA — means  that  it  acts  from  O  to  A.  Let 
us  suppose  the  force  which  acts  on  O  along  OA  to  contain  P  units  of  force  ; 
from  O  towards  A  measure  ON  containing  P  units  of  length,  the  line  ON  is 
said  to  represent  the  force.  The  analogy  between  the  line  and  the  force  is 
very  complete ;  the  line  ON  is  drawn  from  O  in  a  given  direction  OA,  and 
contains  a  given  number  of  units  P,  just  as  the  force  acts  on  O  in  the  direc- 
tion OA,  and  contains  a  given  number  of  units  P.  It  is  scarcely  necessary 
to  add,  that  if  an  equal  force  were  to  act  on  O  in  the  opposite  direction,  it 
would  be  said  to  act  in  the  direction  OB,  and  would  be  represented  by  OM, 
equal  in  magnitude  to  ON. 

When  we  are  considering  several  forces  acting  along  the  same  line  we 
may  indicate  their  directions  by  the  positive  and  negative  signs.  Thus  the 
forces  mentioned  above  would  be  denoted  by  the  symbols  +  P  and  —  P 
respectively. 


1 6         .  On  Matter,  Force,  and  Motion.  [31- 

31.  Forces  acting-  along-  the  same  line. — If  forces  act  on  the  point  O 
in  the  direction  OA  equal  to  P  and  O  units  respectively,  they  are  equivalent 
to  a  single  force  R  containing  as  many  units  as  P  and  O  together  ;  that  is, 

R  =  P  +  Q. 

If  the  sign  +  in  the  above  equation  denote  algebraical  addition,  the  equation 
will  continue  true  whether  one  or  both  the  forces  act  along  OA  or  OB.  It 
is  plain  that  the  same  rule  can  be  extended  to  any  number  of  forces,  and  if 
several  forces  have  the  same  line  of  action  they  are  equivalent  to  one  force 
containing  the  same  number  of  units  as  their  algebraical  sum.  Thus  if 
forces  of  3  and  4  units  act  on  O  in  the  direction  OA,  and  a  force  of  8  in  the 
direction  OB,  they  are  equivalent  to  a  single  force  containing  R  units  given 
by  the  equation 

R  =  3  +  4-8=-i; 

that  is,  R  is  a  force  containing  one  unit  acting  along  OB.  This  force  R  is 
called  their  resultant.  If  the  forces  are  in  equilibrium  R  is  equal  to  zero. 
In  this  case  the  forces  have  equal  tendencies  to  move  the  point  O  in  opposite 
directions. 

32.  Resultant  and  components. — In  the  last  article  we  saw  that  a  single 
force  R  could  be  found  equivalent  to  several  others  ;  this  is  by  no  means 
peculiar  to  the  case  in  which  all  the  forces  have  the  same  line  of  action  ;  in 

fact,  when  a  material  point,  A  (fig.  5),  remains  in  equili- 
brium under  the  action  of  several  forces,  S,  P,  Q,  it  does 
so  because  any  one  of  the  forces,  as  S,  is  capable  of 
neutralising  the  combined  effects  of  all  the  others.  If  the 
force  S,  therefore,  had  its  direction  reversed,  so  as  to  act 
along  AR,  the  prolongation  of  AS,  it  would  produce  the 
same  effect  as  the  system  of  forces  P,  Q. 

Now,  a  force  whose  effect  is  equivalent  to  the  com- 
bined effects  of  several  other  forces  is  called  their  result- 
ant, and,  with  respect  to  this  resultant,  the  other  forces 
are  termed  components. 

When  the  forces   P,  Q  act  on  a  point  they  can  only 
have  one  .resultant ;  but  any  single  force  can  be  resolved 
into  components  in  an  indefinite  number  of  ways. 

If  a  point  move  from  rest,  under  the  action  of  any  number  of  forces,  it 
will  begin  to  move  in  the  direction  of  their  resultant. 

33.  Parallelogram   of  forces, — When   two  forces   act  on  a  point  their 
resultant  is  found  by  the  following  theorem,  known  as  the  principle  of  the 
parallelogram  of  forces  : — If  two  forces  act  on  a  point,  and  if  lines  be  drawn 

from  that  point  represe?iting  the  forces  in  magnitude  and  direction,  and  on 
these  lines  as  sides  a  parallelogram  be  constructed,  their  resultant  will  be 
represented  in  magnitude  and  direction  by  that  diagonal  which  passes  through 
the  point.  Thus  let  P  and  Q  (fig.  6)  be  two  forces  acting  on  the  point  A 
along  AP  and  AQ  respectively,  and  let  AB  and  AC  be  taken  containing  the 
same  number  of  units  of  length  that  P  and  Q  contain  units  of  force  ;  let  the 
parallelogram  ABDC  be  completed,  and  the  diagonal  AD  drawn  ;  then  the 
theorem  states  that  the  resultant,  R,  of  P  and  Q  is  represented  by  AD  ;  that 
is  to  say,  P  and  Q  together  are  equal  to  a  single  force  R  acting  along  the 


Fig.  7- 


-33]  Parallelogram  of  Forces.  17 

line  AD,  and  containing  as  many  units  of  force  as  AD  contains  units  of 
length. 

Proofs  of  this  theorem  are  given  in  treatises  on  Mechanics  ;  we  will  here 
give  an  account  of  a  direct  experimental  verification  of  its  truth  ;  but  before 
doing  so  we  must  premise  an  account  of  a  very  simple  experiment. 

Let  A  (fig.  7)  be  a  small  pulley,  and  let  it  turn  on  a  smooth,  hard,  and 
thin  axle  with  little  or  no  friction  ;  let  W  be  a  weight  tied  to  the  end  of  a 
fine  thread  which  passes  over 
the  pulley  ;  let  a  spring  CD  be 
attached  by  one  end  to  the  end 
C  of  the  thread  and  by  the  end 

D  to  another  piece  of  thread,  A 

the  other  end  of  which  is  fastened 
to  a  fixed  point  B  ;  a  scale  CE 
can  be  fastened  by  one  end  to 
the  point  C  and  pass  inside  the 
spring  so  that  the  elongation  of 
the  spring  can  be  measured. 
Now  it  will  be  found  on  trial 
that  with  a  given  weight  W  the  elongation  of  the  spring  will  be  the  same 
whatever  the  angle  contained  between  the  parts  of  the  string  WA  and  BA. 
Also  it  would  be  found  that  if  the  whole  were  suspended  from  a  fixed  point, 
instead  of  passing  over  the  pulley,  the  weight  would  in  this  case  stretch  the 
spring  to  the  same  extent  as  before.  This  experiment  shows  that  when  care 
is  taken  to  diminish  to  the  utmost  the  friction  of  the  axle  of  the  pulley,  and 
the  imperfect  flexibility  of  the  thread,  the  weight  of  W  is  transmitted  without 
sensible  diminution  to  B,  and  exerts  on  that  point  a  pull  or  force  along  the 
line  BA  virtually  equal  to  W. 

This  being  premised,  an  experimental  proof,  or  illustration  of  the  parallel- 
ogram of  forces,  may  be  made  as  follows  : — 

Suppose  H  and  K  (fig.  8)  to  be  two  pulleys  with  axles  made  as  smooth 
and  fine  as  possible  ;  let  P  and  Q  be  two  weights  suspended  from  fine  and 
flexible  threads  which,  after  passing  over  H  and 
K,  are  fastened  at  A  to  a  third  thread  AL  from 
which  hangs  a  weight  R  ;  let  the  three  weights 
come  to  rest  in  the  positions  shown  in  the  figure. 
Now  the  point  A  is  acted  on  by  three  forces  in 
equilibrium,  viz.  P  from  A  to  H,  Q  from  A  to 
K,  and  R  from  A  to  L  ;  consequently,  any  one  of 
them  must  be  equal  and  opposite  to  the  re- 
sultant of  the  other  two.  Now  if  we  suppose 
the  apparatus  to  be  arranged  immediately  in 

front  of  a  large  slate,  we  can  draw  lines  upon  it  coinciding  with  AH,  AK,  and 
AL.  If  now  we  measure  off  along  AH  the  part  AB  containing  as  many 
inches  as  P  contains  pounds,  and  along  AK  the  part  AC  containing  as  many 
inches  as  Q  contains  pounds,  and  complete  the  parallelogram  ABCD,  it  will 
be  found  that  the  diagonal  AD  is  in  the  same  line  as  AL,  and  contains  as 
many  inches  as  R  weighs  pounds.  Consequently,  the  resultant  of  P  and  Q 
is  represented  by  AD.  Of  course,  any  other  units  of  length  and  force  might 


i8 


On  Matter ',  Force,  and  Motion. 


[33 


have  been  employed.  Now  it  will  be  found  that  when  P,  Q,  and  R  are 
changed  in  any  way  whatever,  consistent  with  equilibrium,  the  same  con- 
struction can  be  made, — the  point  A  will  have  different  positions  in  the 
different  cases  ;  but  when  equilibrium  is  established,  and  the  parallelogram 
ABCD  is  constructed,  it  will  be  found  that  AD  is  vertical,  and  contains  as 
many  units  of  length  as  R  contains  units  of  force,  and  consequently  it  repre- 
sents a  force  equal  and  opposite  to  R  ;  that  is,  it  represents  the  resultant  of  P 
and  Q. 

34.  Resultant  of  any  number  of  forces  acting-  in  one  plane  on  a 
point. — Let  the  forces  P,  Q,  R,  S  (fig.  9)  act  on  the  point  A,  and  let  them 
be  represented  by  the  lines,  AB,  AC,  AD,  AE,  as 
shown  in  the  figure.  First,  complete  the  parallelo- 
gram ABFC  and  join  AF  ;  this  line  represents  the 
resultant  of  P  and  Q.  Secondly,  complete  the 
parallelogram  AFGD  and  join  AG  ;  this  line  re- 
presents the  resultant  of  P,  O,  R.  Thirdly,  com- 
plete the  parallelogram  AGHE  and  join  AH  ;  this 
line  represents  the  resultant  of  P,  Q,  R,  S.  It  is 
manifest  that  the  construction  can  be  extended  to 
any  number  of  forces,.  A  little  consideration  will 
show  that  the  line  AH  might  be  determined  by  the 
following  construction  :— Through  B  draw  BF 
parallel  to,  equal  to,  and  towards  the  same  part  as  AC  ;  through  F  draw 
FG  parallel  to,  equal  to,  and  towards  the  same  part  as  AD  ;  through  G  draw 
GH  parallel  to,  equal  to,,  and  towards  the  same  part  as  AE  ;  join  AH,  then 
AH  represents  the  required  resultant. 

In  place  of  the  above  construction,  the  resultant  can  be  determined  by 
calculation  in  the  following  manner  :^— Through  A  draw  any  two  rectangular 
axes  AX  and  AY  (fig,  10),  and  let  a,  /3,  y  be  the  angles  made  with  the  axis 
AX  by  the  lines  representing  the  pressures,  then  P,  Q,  R  can  be  resolved 
I  Y  into  P  cos  a,  Q  cos  /3,  R  cos  y,  acting  along  AX,  and 

P  sin  a,  O  sin  #,  R  sin  y,  acting  along  AY.  Now  the 
former  set  of  forces  can  be  reduced  to  a  single  force 
X  by  addition,  attention  being  paid  to  the  sign  of  each 
component ;  and  in  like  manner  the  latter  forces  can 
be  reduced  to  a  single  force  Y,  that  is, 

X  =  P  cos  a  4-  Q  cos  /3  +  R  cos  y  +    .  .  . 
Y  =  P  sin  a  +  Q  sin  /3  +  R  sin  y  +   .  .  . 

Since  the  addition  denotes  the  algebraical  sum  of  the 
quantities  on  the  right-hand  side  of  the  equations,  both  sign  and  magnitude 
of  X  and  Y  are  known.  Suppose  U  to  denote  the  required  resultant,  and  <£ 
the  angle  made,  by  the  line  representing  it,  with  the  axis  AX  ; 

then  U  cos  </>  =  X,  and  U  sin  <jf>  =  Y. 

These  equations  give  U2  =  X'2  +  Y2,  which  determines  the  magnitude  of  the 
resultant,  and  then,  since  both  sin  $  and  cos  <£  are  known,  0  is  determined 
without  ambiguity. 

Thus  let  P,  Q,  and  R  be  forces  of  100,  150,  and  120  units,  respectively, 


Fig. 


-35]  Conditions  of  Equilibrium  of  Forces.  19 

and  suppose  XAP,  XAQ,  and  XAR  to  be  angles  of  45°,  120°,  and  210°  re- 
spectively. Then  their  components  along  Ax  are  70*7,  -  75,  — 103*9,  an<i 
their  components  along  AY  are  707,+  129-9,  — 60.  The  sums  of  these  two 
sets  being  respectively— 108-2  and  140-6,  we  have  U  cos  <£=  —  io8'2  and 
U  sin  0=  140-6; 
therefore  IP  -  (io8'2)2  +  (140-6)- 

or  U  =  177-4 

hence  177-4  cos  0  =  -  108*2,  and  177-4  sin  0-  104-6. 

If  we  made  use  of  the  former  of  these  equations  only,  we  should  obtain  <p 
equal  to  232°  25',  or  127°  35',  and  the  result  would  be  ambiguous  :  in  like 
manner,  if  we  determine  $  from  the  second  equation  only,  we  should  have 
<£  equal  to  52°  25',  or  127°  35';  but  as  we  have  both  equations,  we  know  that 
$  equals  127°  35',  and  consequently  the  force  U  i§  completely  determined  as 
indicated  by  the  dotted  line  AU. 

35.  Conditions  of  equilibrium  of  any  forces  acting-  in  one  plane 
on  a  point. — If  the  resultant  of  the  forces  is  zero,  they  have  no  joint 
tendency  to  move  the  point,  and  consequently  are  in  equilibrium.  This 
obvious  principle  enables  us  to  deduce  the  following  constructions  and 
equations,  which  serve  to  ascertain  whether  given  forces  will  keep  a  point  at 
rest. 

Suppose  that  in  the  case  represented  in.  fig.  9,  T  is  the  force  which  will 
balance  P,  Q,  R,  S,  It  is  clear  that  T,  mus,t  act  on  A  along  H  A  produced, 
and  in  magnitude  must  be  proportional  to  H  A  ;  for  then,  the  resultant  of 
the  five  forces  will  equal  zero,  sin.ce  the  broken,  line  ABFGHA  returns  to  the 
point  A.  This  construction  is  plainly  equivalent  to  the  following  :  Let  P,  Q, 
R  (fig.  u)  be  forces  acting  on  the  point  O,  as  indicated,  their  magnitudes 
and  directions  being  given.  It  is 
known  that  they  are  balanced  by  a 
fourth  force,  S,  and  it  is  requirepl  to 
determine  the  magnitude  and  di- 
rection of  S,  Take  any  point  D, 
and  draw  any  line  parallel  U>  and 
towards  the  same  part  as  O  P,  draw 
AB  parallel  to,  and  towards  the 
same  part  as  OQ,  and  take  AB 
such  that  P  :  Q  : :  D  A  :  A  B. 
Through  B  draw  B  C  parallel  to 
and  towards  the  %ame  part  as  O  R, 
taking  BC  such  tha.t  Q  :  R::AB  :  B  C  ;  join  C  D  ;  through  O  draw  O  S 
parallel  to  and  towards  the  same  part  as  C  D,  then  the  required  force  acts 
along  O  S,  and  is  in  magnitude  proportional  to  C  D. 

It  is  to  be  observed  that  this  construction  can  be  extended  to  any  number 
of  forces,  and  will  apply  to  the  case  in  which  these  directions  are  not  in 
one  plane,  only  in  this  case  the  broken  line  ABCD  would  not  lie  wholly  in 
one  plane.  The  above  construction  is  frequently  called  the  Polygon  of 
Forces. 

The  case  of  three  forces  acting  on  a  point  is,  of  course,  included  in  the 
above  ;  but  its  importance  is  such  that  we  may  give  a  separate  statement  of 


2o  On  Matter,  Force,  and  Motion.  [35- 

it.  Let  P,  Q,  R  (fig.  12)  be  three  forces  in  equilibrium  on  the  point  O.  From 
any  point  B  draw  B  C  parallel  to  and  towards  the  same  part  O  P,  from  C 
draw  C  A  parallel  to  and  towards  the  same  part  as  O  Q,  and  take  C  A  such 
that  P  :  Q : :  B  C  :  C  A ;  then,  on  joining  A  B,  the  third  force  R  must  act  along 
O  R  parallel  to  and  towards  the  same  part  as  A  B,  and  must  be  proportional 
in  magnitude  to  AB.  This  construction  is  frequently  called  the  Triangle  of 
Forces.  It  is  evident  that  while  the  sides  of  the  triangle  are  severally  pro- 
portional to  P,  Q,  R,  the  angles  A,  B,  C  are  supplementary  to  Q  O  R,  R  O  P, 
POO  respectively  ;  consequently,  every  trigonometrical  relation  existing 
between  the  sides  and  angles  of  A  B  C  will  equally  exist  between  the  forces 
P,  Q,  R,  and  the  supplements  of  the  angles  between  their  directions.  Thus 
in  the  triangle  A  B  C  it  is  known  that  the  sides  are  proportional  to  the  sines 
of  the  opposite  angles  ;  now,  since  the  sines  of  the  angles  are  equal  to  the 
sines  of  their  supplements,  we  at  once  conclude  that  when  three  forces  are  in 
equilibrium,  each  is  proportional  to  the  sine  of  the  angle  between  the  directions 
of  the  other  two. 

We  can  easily  obtain  from  the  equations  which  determine  the  resultant 
of  any  number  offerees  (34)  equations  which  express  the  conditions  of  equi- 
librium of  any  number  offerees  acting  in  one  plane  on  a  point ;  in  fact,  if  U 
=  o  we  must  have  X  =  o  and  Y  =  o  ;  that  is  to  say,  the  required  conditions  of 
equilibrium  are  these  : — 

o  =  P  cos  a  +  Q  cos  /3  +  R  cos  y  -f .  .  . 
and  o  =  P  sin  a  +  O  sin  /3  +  R  sin  y  +  .  .  . 

The  first  of  these  equations  shows  that  no  part  of  the  motion  of  the  point  can 
take  place  along  Ax,  the  second  that  no  part  can  take  place  along  Ay.  In 
other  words,  the  point  cannot  move  at  all. 

36.  Composition  and  resolution  of  parallel  forces. — The  case  of  the 
equilibrium  of  three  parallel  forces  is  merely  a  particular  case  of  the  equili- 
brium of  three  forces  acting  on  a  point.  In  fact,  let  P 
and  Q  be  two  forces  whose  directions  pass  through  the 
points  A  and  B,  and  intersect  in  O  ;  let  them  be  balanced 
by  a  third  force  R  whose  direction  produced  intersects 
the  line  AB  in  C.  Now  suppose  the  point  O  to  move 
along  A  O,  gradually  receding  from  A,  the  magnitude  and 
direction  of  R  will  continually  change,  and  also  the  point 
C  will  continually  change  its  position,  but  will  always  lie 
between  A  and  B.  In  the  limit  P  and  Q  become  parallel 
forces,  acting  towards  the  same  part  balanced  by  a  parallel 
force  R  acting  towards  the  contrary  part  through  a  point 
.  X  between  A  and  B.  The  question  is  : — First,  on  this 

limiting  case  what  is  the  value  of  R  ;  secondly,  what  is  the 
position  of  X  ?     Now  with  regard  to  the  first  point  it  is  plain  that  if  a  tri- 
angle abc  were  drawn  as  in  art.  35,  the  angles  a  and  b  in  the  limit  will  vanish, 
and  c  will  become  180°,  consequently  ab  ultimately  equals  ac  +  cb  ; 
or  R  =  p  +  Q. 

With  regard  to  the  second  point  it  is  plain  that 

OC  sin  POR  =  OC  sin  AOC  =  AC  sin  CAO 
and  OC  sin  ROQ  =  OC  sin  BOC  =  CB 


-37]  Centre  of  Parallel  Forces.  2 1 

therefore         AC  sin  CAO  :  CB  sin  CBO::sin  FOR  :  sin  ROQ 

::Q:P(3S)- 

Now  in  the  limit,  when  OA  and  OB  become  parallel,  OAB  and  OB  A 
become  supplementary  ;  that  is,  their  sines  become  equal ;  also  AC  and  C  B 
become  respectively  AX  and  XB  ;  consequently 

AX  :  XB::Q:  P, 

a  proportion  which  determines  the  position  of  X.     This  theorem  at  once 
leads  to  the  rules  for  the  composition  of  any  two  parallel  forces,  viz. — 

I.  When  two  parallel  forces  P  and  Q  act  towards  the  same  part,  at  rigidly 
connected  points  A  and  B,  their  resultant  is  a  parallel  force  acting  towards 
the  same  part,  equal  to  their  sum,  and  its  direction  divides  the  line  A  B  into 
two  parts  A  C  and  C  B  inversely  proportional  to  the  forces  P  and  Q. 

II.  When  two   parallel  forces   P  and  O  act  towards  contrary  parts  at 
rigidly  connected  points  A  and  B,  of  which  P  is  the  greater,  their  resultant 
is  a  parallel  force  acting  towards  the  same  part  as  P,  equal  to  the  excess  of 
P  over  Q,  and  its  direction  divides  B  A  produced  in  a  point  C  such  that  C  A 
and  C  B  are  inversely  proportional  to  P  and  O. 

In  each  of  the  above  cases  if  we  were  to  apply  R  at  the  point  C,  in  opposite 
directions  to  those  shown  in  the  figure,  it  would  plainly  (by  the  above  theorem) 


FiS-  J4-  Fig.  15. 

balance  P  and  Q,  and  therefore  when  it  acts  as  shown  in  figs.  14  and  15  it  is 
the  resultant  of  P  and  Q  in  those  cases  respectively.  It  will,  of  course,  follow 
that  the  force  R  acting  at  C  can  be  resolved  into  P  and  O  acting  at  A  and  B 
respectively. 

If  the  second  of  the  above  theorems  be  examined,  it  will  be  found  that  no 
force  R  exists  equivalent  to  P  and  Q  when  these  forces  are  equal.  Two 
such  forces  constitute  a  couple,  which  may  be  defined  to  be  two  equal 
parallel  forces  acting  towards  contrary  parts  ;  they  possess  the  remarkable 
property  that  they  are  incapable  of  being  balanced  by  any  single  force  what- 
soever. . 

In  the  case  of  more  than  two  parallel  forces  the  resultant  of  any  two  can 
e  found,  then  of  that  and  a  third,  and  so  on  to  any  number  ;  it  can  be  shown 
t  however  great  the  number  of  forces  they  will  either  be  in  equilibrium  or 
will  reduce  to  a  single  resultant  or  to  a  couple. 

7.  Centre  of  parallel  forces.— On  referring  to  figs.  14  and  15,  it  will  be 
remarked  that  if  we  conceive  the  points  A  and  B  to  be  fixed  in  the  directions 


22  On  Matter,  Force,  and  Motion.  [37- 

AP  and  BQ  of  the  forces  P  and  O,  and  if  we  suppose  those  directions  to  be 
turned  round  A  and  B,  so  as  to  continue  parallel  and  to  make  any  given 
angles  with  their  original  directions,  then  the  direction  of  their  resultant  will 
continue  to  pass  through  C  ;  that  point  is  therefore  called  the  centre  of  the 
parallel  forces  P  and  Q. 

It  appears  from  investigation,  that  whenever  a  system  of  parallel  forces 
reduces  to  a  single  resultant,  those  forces  will  have  a  centre  ;  that  is  to  say, 
if  we  conceive  each  of  the  forces  to  act  at  a  fixed  point,  there  will  be  a  point 
through  which  the  direction  of  their  resultant  will  pass  when  the  directions 
of  the  forces  are  turned  through  any  equal  angles  round  their  points  of 
application  in  such  a  manner  as  to  retain  the  parallelism  of  their  directions. 

The  most  familiar  example  of  a  centre  of  parallel  forces  is  the  case  in 
which  the  forces  are  the  weights  of  the  parts  of  a  body  ;  in  this  case  the 
forces  all  acting  towards  the  same  part  will  have  a  resultant,  viz.  their  sum  ; 
and  their  centre  is  called  the  centre  of  gravity  of  the  body. 

38.  Moments  of  forces.-— Let  P  (fig.  16)  denote  any  force  acting  from  B 
to  P,  take  A  any  point,  let  fall  AN  a  perpendicular  from  A  on  BP.     The 
product  of  the  number  of  Units  of  force  in   P,  and  the  number  of  units  of 
length  in  AN,  is  called  the  moment  of  P  with  respect  to  A.     Since  the  force 
P  can  be  represented  by  a  straight  line,  the  moment  of  P  can  be  represented 
by  an  area.     In  fact,  if  BC  is  the  line  representing  P,  the  moment  is  properly 
represented  by  twice  the  'area  of  the  triangle  ABC.     The  perpendicular  AN 
is  sometimes  called  the  arm  of  the  pressure.     Now  if  a  watch  were  placed 
with  its  face  upwards  on  the  paper,  the  force  P  would  cause  the  arm  AN  to 

turn  found  A  in  the  contrary  direction  to  the  hands  of  the 
Watch.  Under  these  circumstances,  it  is  usual  to  con- 
sider the  moment  of  P  with  respect  to  the  point  A  to  be 
positive.  If  P  acted  from  C  to  B,  it  would  turn  NA  in 
the  same  direction  as  the  hands  of  the  watch,  and  now  its 
moment  is  reckoned  negative. 

The  following  remarkable  relation  exists  between  any 
forces  acting  in  one  plane  on  a  body  and  their  resultant. 

Take  the  moments  of  the  forces  and  of  their  resultant  with  respect  to  any 

one  point  in  the  plane.     Then  the  moment  of  the  resultant  equals  the  sum 

of  the  moments  of  the  several  forces,  regard  being  had  to  the  signs  of  the 

moments. 

If  the  point  about  which  the  moments  are  measured  be  taken  in  the 

direction  of  the  resultant,  its  moment  With  respect  to  that  point  will  be  zero  ; 

and  consequently  the  sum  of  the  moments  with  respect  to  such  point  will  be 

zero. 

39.  Equality  of  action  and  reaction.- — We  will  proceed  to  exemplify 
some  of  the  principles  ho\v  laid  doWn  by  investigating  the   conditions  of 
equilibrium  of  bodies  in  a  few  simple  cases  ;  but  before  doing  so  we  must ' 
notice  a  law  which  holds  good  whenever  a  mutual  action  is  called  into  play 
between  two  bodies.     Reaction  is  always  equal  and  contrary  to  actio?i;  that 
is  to  say,  the  mutual  actions  of  two  bodies  on  each  other  are  always  forces 
equal  in  amount  and  opposite  in  direction.     This  law  is  perfectly  general, 
and  is  equally  true  when  the  bodies  are  in  motion  as  well  as  when  they  are 
at  rest.     A  very  instructive  example  of  this  law  has  already  been  given  (33), 


-41] 


Pulleys. 


in  which  the  action  on  the  spring  CD  (fig.  7)  is  the  weight  W  transmitted 
by  the  spring  to  C,  and  balanced  by  the  reaction  of  the  ground  transmitted 
from  B  to  D.  Under  these  circumstances  the  spring  is  said  to  be  stretched 
by  a  force  \V.  If  the  spring  were  removed,  and  the  thread  were  continuous 
from  A  to  B,  it  is  clear  that  any  part  of  it  is  stretched  by  two  equal  forces, 
viz.  an  action  and  reaction,  each  equal  to  W,  and  the  thread  is  said  to  sustain 
a  tension  W.  When  a-  body  is  urged  along  a  smooth  surface,  the  mutual 
action  can  only  take  place  along  the  common  perpendicular  at  the  point  of 
contact.  If,  however,  the  bodies  are  rough,  this  restriction  is  partially  re- 
moved, and  now  the  mutual  action  can  take  place  in  any  direction  not 
making  an  angle  greater  than  some  determinate  angle  with  the  common  per- 
pendicular. This  determinate  angle  has  different  values  for  different  sub- 
stances, and  is  sometimes  called  the  limiting  angle  of  resistance,  sometimes 
the  angle  of  repose. 

40.  Tfce  lever  is  a  name  given  to  any  bar  straight  of  curved,  AB  (fig.  17) 
resting  on  a  fixed  point  of  edge  c  called  the  fulcrum.     The  forces  acting  on 
the  lever  are  the  weight  or  fesistance  Q,  the 

power  P,  and  the  feaction  of  the  fulcrum. 
Since  these  are  in  equilibrium,  the  fesultant 
of  P  and  Q  must  act  through  c,  fof  othef- 
wise  they  could  not  be  balanced  by  the  fe- 
action. Draw  cb  at  fight  angles  to  QB  and 
ca  to  PA  produced  ;  then  obsefving  that 
P  x  ca,  and  Q  *  cb  are  the  moments  of  P  and 
Q  with  respect  to  <:,  and  that  they  have  con- 
trary signs,  we  have  by  (38), 

P  x  ca  =  Q  x  cb  ; 

an   equation    commonly  expressed   by  the 

rule,  that  in  the  lever  the  power  is  to  the  Fig.  17. 

weight  in  the  inverse  ratio  of  their  arms. 

Levers  are  divided  into  three  kinds,  according  to  the  position  of  the 
fulcrum  with  respect  to  the  points  of  application  of  the  power  and  the  weight. 
In  a  letter  of  the  first  kind  \hz  fulcrum  is  between  the  power  and  resistance, 
as  in  fig.  17,  and  as  in  a  pokef  and  in  the  common  steelyard  ;  a  pair  of 
scissors  and  a  carpenter's  pincers  are  double  levers  of  this  kind.  In  a  lever 
of  the  second  kind the  resistance  is  between  the  power  and  the  fulcrum,  as  in 
a  wheelbarrow,  or  a  pair  of  nutcrackers,  or  a  door  ;  in  a  lever  of  the  third 
kind  the  power  is  between  the  fulcrum  and  the  resistance,  as  in  a  pair  of 
tongs  or  the  treadle  of  a  lathe. 

41.  Pulleys. — The  pulley  is  a  hard  circular  disc  of  wood  or  of  metal,  in 
the  edge  of  which  is  a  groove,  and  which  can  turn  freely  on  an  axis  in  the 
centre.     Pulleys  are  either  fixed,  as  in  fig.  18,  where  the  stirrup  or  fork  is 
rigidly  connected  with  some  immovable  body,  and  where  the  axis  rotates  in 
the  stirrup  ;  or  it  may  be  movable,  as  in  fig.  19,  where  the  axis  is  fixed  to 
the  fork,  and  it  passes  through  a  hole  in  the  centre  of  the  disc.     The  rope 
which  passes  round  the  pulley  in  fig.  18,  supports  a  weight  at  one  end  ;  while 
at  the  other  a  pull  is  applied  to  hold  this  weight  in  equilibrium. 


On  Matter,  Force,  and  Motion. 


[41- 


We  may  look  upon  the  power  and  the  resistance  as  acting  at  the  circum- 
ference of  the  circle  ;  hence  as  the  radii  are  equal,  if  we  consider  the  pulley 

as  a  lever,  the  two  arms  are 
equal,  and  equilibrium  will 
prevail  when  the  power  and 
the  resistance  are  equal. 
The  fixed  pulley  affords  thus 
no  mechanical  advantage, 
but  is  simply  convenient  in 
changing  the  direction  of  the 
application  of  a  force. 

In  the  case  of  the  mov- 
able pulley  the  one  end  of 
the  rope  is  suspended  to  a 
fixed  point  in  a  beam,  and 
the  weight  is  attached  to  the 
hook  on  which  the  pulley 
acts.  The  tension  of  the 
rope  is  everywhere  the  same  ; 
one  portion  of  the  weight  is 


Fig.  18. 


Fig.  19. 


supported  by  the  fixed  part 
and  the  other  by  the  power,  and  these  are  equal  to  each  other,  and  are 
together  equal  to  the  weight,  including  the  pulley  itself;  hence  in  this  case 

P  =  *Q- 

If  several  pulleys  are  joined  together  on  a  common  axis  in  a  special 
sheath,  which  is  fixed,  and  a  rope  passes  round  all  those  and  also  round  a 
similar  but  movable  combination  of  pulleys,  such  an  arrangement,  which  is 
represented  in  fig.  20,  is  called  a  block  and  tackle. 

If  we  consider  the  condition  of  the  rope  it  will  be  found  to  have  every- 
where the  same  tension  ;  the  weight  Q  which  is  attached  to  the  hook 
common  to  the  whole  system  is  supported  by  the  six  portions  of  the  rope  ; 
hence  each  of  these  portions  will  sustain  one  sixth  of  the  weight  ;  the  force 
which  is  applied  at  the  free  end  of  the  rope  which  passes  over  the  upper 
pulley,  and  which  determines  the  tension,  will  have  the  same  value  ;  that  is 
to  say,  it  will  support  one  sixth  of  the  weight. 

The  relation  between  power  and   resistance  in  a  block  and  tackle   is 

expressed  by  the  equation  P  =  -*     in  which   P  is  the  power,  Q  the  weight, 

n 

and  n  the  number  of  cords  by  which  the  weight  is  supported. 

42.  The  wheel  and  axle. — The  older  form  of  this  machine,  fig.  21,  is 
that  of  an  axle,  to  which  is  rigidly  fixed,  concentric  with  it,  a  wheel  of  larger 
diameter.  The  power  is  applied  tangentially  on  the  wheel,  and  the  resistance 
tangentially  to  the  axle,  as  for  instance  in  the  treadmill  and  water-wheel. 
Sometimes,  as  in  the  case  of  the  capstan,  the  power  is  applied  to  spokes 
fixed  in  the  axle,  which  represent  semi-diameters  of  the  wheel ;  in  other 
cases,  as  in  the  windlass,  the  handle  is  rigidly  fixed  to  the  axis. 

In  all  its  modifications  we  may  regard  the  wheel  and  axle  as  an  applica- 
tion of  the  lever,  the  arms  of  which  are  the  radii  of  the  wheel  and  axle 
respectively,  and  in  all  cases  equilibrium  exists  where  the  power  is  to  the 


-42] 


Wheel  and  Axle. 


25 

Thus  in 


resistance  as  the  radius  of  the  axle  is  to  the  radius  of  the  wheel, 
fig.  21,  P  :  Q  =  ab  :  ac,  or  P  x  ac  =  Q  x  ab. 

Frequent  applications  of  wheels  of  different  diameters  are  met  with  in 
which  the  motion  of  one 
wheel  is  transmitted  to  an- 
other, either  by  means  of 
teeth  fitting  in  each  other  on 
the  circumference  of  the 
wheels,  as  in  fig.  22,  or  by 
means  of  bands  passing  over 
the  two  wheels,  as  in  the 
illustration  of  Ladd's  Mag- 
neto-Electrical Machine  (see 
Book  viii.). 

In  fig.  22,  which  repre- 
sents the  essential  parts  of  a 
crab  winch,  in  order  to  raise 

the  weight  O  a  power/  must  ^    jg  4  Fig  2I 

be  applied  at  the   circumfe- 
rence of  the  wheel  such  that 


Q  ^p  in  which 
R 


r  and  R 


are  the  radii  of  the  axle  b 
and  of  the  toothed  wheel  a 
respectively. 

The  rotation  of  the  wheel 
a  is  effected  by  means  of  the 
smaller  wheel  c  or  crab,  the 
teeth  of  which  fit  in  those  of 
a.  But  if  this  wheel  c  is  to 
exert  at  its  circumference  a 
power/,  the  power  P  which 
is  applied  at  the  end  of 

the  handle  must  be  P  =   —/,  in  which  r'  is  the  radius  of  c,  R'the  length  of 
R 

a  lever  at  the  end  of  which  P  acts,  and  consequently 


Fig.  22. 


— Q.' 

'~ 


The  radius  of  the  wheel  c  is  to  that  of  the  wheel  a  as  their  respective  cir- 
cumferences ;  and,  as  the  teeth  of  each  are  of  the  same  size,  the  circum- 
ferences will  be  as  the  number  of  teeth. 

Trains  of  wheelwork  are  used,  not  only  in  raising  great  weights  by  the 
exertion  of  a  small  power  ;  as  in  screw  jacks,  cranes,  crab  winches,  &c.,  but 
also  in  clock  and  watch  works,  and  in  cases  in  which  changes  in  velocity  or 
in  power  or  even  in  direction  are  required.  Numerous  examples  will  be  met 
with  in  the  various  apparatus  described  in  this  work. 

C 


26 


On  Matter,  Force,  and  Motion. 


[43- 


43.  Inclined  Plane. — The  properties  and  laws  of  the  inclined  plane  may 
be  conveniently  demonstrated  by  means  of  the  apparatus  represented  in 
fig.  23.  RS  represents  the  section  of  a  smooth  piece  of  hard  wood  hinged  at 
R  ;  by  means  of  a  screw  it  can  be  clamped  at  any  angle  x  against  the  arc- 
shaped  support,  by  which  at  the 
same  time  the  angle  can  be  mea- 
sured ;  a  is  a  cylindrical  roller,  to 
the  axis  of  which  is  attached  a 
string  passing  over  a  pulley  to  a 
scale-pan  P. 

It  is  thus  easy  to  ascertain  by 
direct  experiments  what  weights 
R  must  be  placed  in  the  pan  P  in 
order  to  balance  a  roller  of  any 
given  weight,  Or  to  cause  it  to 
move  with  a  given  angle  of  incli- 
nation. 
The  line  RS  represents  the 


Fig.  23. 


lengfh,  ST  the  height,  and  RT  the  base  01  inclined  plane. 

In  ascertaining  the  theoretical  conditions  of  equilibrium  we  have  a  useful 
application  of  the  parallelogram  ot  forces.  Let  the  line  ab,  fig.  23,  represent 
the  force  which  the  weight  W  of  the  cylinder  exerts  acting  vertically  down- 
wards ;  this  may  be  decomposed  into  two  others  ;  one,  ad,  acting  at  right 
angles  against  the  plane,  and  representing  the  pressure  which  the  weight 
exerts  against  the  plane  ;  and  which  is  counterbalanced  by  the  reaction  or 
the  plane  ;  the  other,  ac,  represents  the  component  which  tends  to  move  the 
weight 'down  "the  plane,  and  this  component  has  to  be  held  in  equilibrium  by 
the  weight,  P,  equal  to  it  and  acting  in  opposite  directions. 

It  can  be  readily  shown  that  the  triangle  abc  is  similar  to  the  triangle 
SRT,  and  that. the  sides  ac  and  ab  are  in  the  same  proportion  as  the  sides 
ST  and  SR.  But  the  line  ac  represents  the  power,  and  the  line  ab  the 
weight ;  hence 

ST  :  SR  =  P  :  W; 

that  is,  on  an  inclined  plane,  equilibrium  obtains  when  the  power  is  to  the 
weight  as  the  height  of  the  inclined  plane  to  its  length. 

S  T 

Since  the  ratio  -_    is  the  sine  of  the  angle  x,  we  may  also  state  the 
S  R 

principle  thus  : 

P=Wsinx 

The  component  da  or  be,  which  represents  the  actual  pressure  against  the 
plane,  is  equal  to  W  cos  x ;  that  is,  the  pressure  against  the  plane  is  to  the 
weight,  as  the  base  is  to  the  length  of  the  inclined  plane. 

In  the  above  case  it  has  been  considered  that  the  power  acts  parallel  to 
the  inclined  plane.  It  maybe  applied  so  as  to  act  horizontally.  It  will  then 
be  seen  from  fig.  24  that  the  weight  W  may  be  decomposed  into  two  forces, 
one  of  which,  ab,  acts  at  right  angles  to  the  plane,  and  the  other,  ac,  parallel  to 
the  base.  It  is  this  latter  which  is  to  be  kept  in  equilibrium  by  the  power. 
From  the  similarity  of  the  two  triangles  acb  and  STR,  ac  \bc=ST  \  TR 
=  h\b\  but  be  is  equal  to  W,  and  ac  is  equal  to  P,  hence  the  power  which 


_44J  The  Wedge.  27 

must  be  applied  at  b  to  hold  the  weight  W  in  equilibrium  is  as  the  height 
of  the  inclined  plane  is  to  the  base,  or  as  the  tangent  of  the  angle  of  inclina- 
tion x ;  that  is,  P  =  W  tan  x.  The  pressure  upon  the  plane  in  this  case  may 

be  easily  shown  to  be  ab  =  — — ,  that 
cos  x 

is  =  .     This  is  sometimes  called 

cos  x 

the  relative  weight  on  the  plane. 

If  the  force  P  which  is  to  counter- 
balance W  is  not  parallel  to  the  plane, 
but  forms  an  angle,  E,  with  it,  this 
force  can  be  decomposed  into  one 
which  is  parallel  to  it,  and  one  which 
is  at  right  angles.  Of  these  only  the  first  is  operative  and  is  equal  to  P  cos  E. 

In  most  cases  of  the  use  of  the  inclined  plane,  such  as  in  moving  carriages 
and  waggons  along  roads,  in  raising  casks  into  waggons  or  warehouses,  the 
power  is  applied  parallel  to  the  inclined  plane.  An  instance  of  a  case  in 
which  a  force  acts  parallel  to  the  base  is  met  with  in  the  screw. 

Owing  to  the  unevenness  of  the  surfaces  in  actual  use,  the  laws  of  equili- 
brium and  of  motion  on  an  inclined  plane  undergo  modification.  The/r/t-- 
tion,  for  instance,  which  comes  into  play  amounts  on  ordinary  roads  to  from 
^  to  i,  and  on  railways  to  from  ^  to  £0  of  the  relative  weight.  This  must 
be  looked  upon  as  a  hindrance  to  be  continually  overcome,  and  must  be 
deducted  from  the  force  required  to  keep  a  body  from  falling  down  an  in- 
clined plane,  or  must  be  added  to  it  in  the  case  in  which  a  body  is  to  be 
moved  up  tl\e  plane.  Hence  the  use  of  the  inclined  plane  in  unloading  heavy 
casks  into  cellars,  £c. 

A  body  on  an  inclined  plane  which  cannot  rotate  does  not  move  provided 
the  inclination  is  below  a  certain  amount  (39).  The  determination  of  this 
limiting  angle  of  resistance,  at  which  a  body  on  an  inclined  plane  just  begins 
to  move,  may  serve  as  a  rough  illustration  of  a  mode  of  ascertaining  the 
4  coefficient  of  friction.' 

For  in  the  case  in  which  the  power  is  applied  parallel  to  the  plane,  the 
component  of  the  weight  which  presses  against  the  plane  or  the  actual  load, 
L,  is  W  cos  x ;  and  the  component  which  tends  to  move  the  body  down  the 
plane  is  equal  to  W  sin  x.  If  the  friction,  R,  is  just  sufficient  to  hold  this  in 

equilibrium,  the  coefficient  of  friction  will  be  —  = —tan  x. 

L     W  cos  x 

Thus  if  we  place  on  the  plane  a  block  of  the  same  material,  by  gradually 
increasing  the  inclination  it  will  begin  to  move  at  a  certain  angle,  which  will 
depend  on  the  nature  of  the  material ;  this  angle  is  the  limiting  angle  of 
resistance,  and  its  tangent  is  the  coefficient  of  friction  for  that  material. 

44.  The  Wedge. — The  ordinary  form  of  the  wedge  is  that  of  a  three- 
sided  prism  of  iron  or  steel,  one  of  whose  angles  is  very  acute.  Its  most 
frequent  use  is  in  splitting  stone,  timber,  etc.  Fig.  25  represents  in  section 
the  application  of  the  wedge  to  this  purpose.  The  side  ad  is  the  back,  the 
vertex  of  the  angle  acb  which  the  two  faces  ac  and  be  make  with  each  other 
represents  the  edge,  and  the  faces  ac  and  be  the  sides  of  the  wedge.  The 
power  P  is  usually  applied  at  right  angles  to  the  back  ;  and  we  may  look 

c  2 


28 


On  Matter,  Force,  and  Motion. 


[44- 


upon  the  cohesion  between  the  fibres  of  the  wood  as  representing  the  resist- 
ance to  be  overcome  ;  as  corresponding  to  what  in  other  machines  is  the 
weight.  Suppose  this  to  act  at  right  angles  to  the  two 
faces  of  the  wedge,  and  to  be  represented  by  the  lines 
fe  and  ge  ;  complete  the  parallelogram  gef,  then  the 
diagonal  he  will  represent  the  resultant  of  the  reaction 
of  the  fibres  tending  to  force  the  wedge  out  ;  the  force 
which  must  be  applied  to  hold  this  wedge  in  equili- 
brium must  therefore  be  equal  to  eh.  Now  efh  is 
similar  to  the  triangle  acb,  therefore  ab  :  ac  =  eh  .  ef; 
but  these  lines  represent  the  pressure  applied  at  the 
back  of  the  wedge,  and  the  pressure  on  the  face  ac, 
hence  if  P  represent  the  former  and  O  the  latter, 
there  is  equilibrium  when  P  :  O  =  ab  :  be,  that  is, 
when  the  power  is  to  the  resistance  in  the  same  ratio 
as  the  back  of  the  wedge  bears  to  one  of  the  sides. 
The  relation  between  power  and  resistance  is  more 
favourable,  the  sharper  the  edge,  that  is,  the  smaller 
the  angle  which  the  sides  make  with  each  other. 

The  action  of  all  sharp  cutting  instruments,  such 
as  chisels,  knives,  scissors,  &c.,  depends  on  the  principle  of  the  wedge.  It 
is  also  applied  when  very  heavy  weights  are  to  be  raised  through  a  short 
distance,  as  in  launching  ships,  and  in  bracing  columns  and  walls  to  the 
perpendicular. 

45.  The  Screw. — Let  us  suppose  a  piece  of  paper  in  the  shape  of  a 
right-angled  triangle  aee'  be  applied  with  its  vertical  side  ac'e'  against  a 
cylinder,  and  parallel  to  the  axis,  and  be  wrapped  round  the  cylinder  ;  the 
hypotenuse  will  describe  on  the  surface  of  the  cylinder  a  screw  line  or 
helix  (fig.  26)  ;  the  points  abode  will  occupy  the  positions  respectively  a  b' 
c  d'  e' .  If  the  dimensions  be  so  chosen  that  the  base  of  the  triangle  cc  is 
equal  to  the  circumference  of  the  cylinder,  then  the  hypotenuse  abc  be- 
comes an  inclined  plane  traced  on  the  surface  of  the  cylinder  ;  the  distance 
ac'  being  the  height  of  the  plane. 


Fig.  25. 


Fig.  28. 


Fig  26. 

An  ordinary  screw  consists  of  an  elevation  on 
a  solid  cylinder  ;  this  elevation  may  be  either 
square,  as  in  fig.  27,  or  acute,  and  such  screws 
are  called  square  or  sharp  screws  accordingly. 

When  a  corresponding  groove  is  cut  in  the 
hollow  cylinder  or  nut  of  the  same  diameter  as 


the  bolt,  this  gives  rise  to  an  internal  or  companion  screw  or  nut,  fig.  28. 


-46]  Virtual  Velocity.  29 

The  vertical  distance  between  any  two  threads  of  a  screw  measured 
parallel  to  the  axis  is  called  the  pitch,  and  the  angle  ace  or  aee'  is  called  the 
inclination  of  the  screw. 

In  practice,  a  raised  screw  is  used  with  its  companion  in  such  a  manner 
that  the  elevations  of  the  one  fitjinto,  and  coincide  with,  the  depressions  01 
the  other.  The  screw  is  a  modification  of  the  inclined  plane,  and  the  condi- 
tions of  equilibrium  are  those  which  obtain  in  the  case  of  the  plane.  The 
resistance,  which  is  either  a  weight  to  be  raised  or  a  pressure  to  be  exerted, 
acts  in  the  direction  of  the  vertical,  and  the  power  acts  parallel  to  the  base  ; 
hence  we  have  P  :  R  =  h  :  b,  and  the  length  of  the  base  is  the  circumference 
of  the  cylinder  ;  whence  P  :  R  =  /i  :  2nr ;  r  being  the  radius  of  the  cylinder, 
and  //  the  pitch  of  the  screw. 

The  power  is  usually  applied  to  the  screw  by  means  of  a  lever,  as  in  the 
bookbinders'  press,  &c.,  and  the  principle  of  the  screw  may  be  stated  to  be 
generally  that  the  power  of  the  screw  is  to  the  resistance  in  the  same  ratio 
as  that  of  the  pitch  of  the  screw  to  the  circumference  of  the  circle  through 
which  the  power  acts. 

46.  Virtual  Velocity. — If  the  point  of  application  of  a  force  be  slightlyk 
•  displaced,  the  resolved  part  of  the  displacement  in  the  direction  of  the  force 
is  termed  the  virtual  velocity  of  the  force,  and  is  considered  as  positive  or 
negative,  according  as  it  is  in  the  same  direction  as  the  force,  or  in  the 
opposite   direction.     Thus,  in  fig.  29  let  the  point  of 
application  A  of  the  force  P  be  displaced  to  A',  and 
draw  A'a  perpendicular  to  AP.     Then  Aa  is  the  virtual 
velocity  of  the  force  P,  and  being,  in  this  case,  in  the 
direction  of  P,  is  to  be  considered  positive. 

The  principle  of  virtual  velocities  asserts  that  if  any 
machine   or   system   be "  kept    in  equilibrium  by  any  Fig-  29. 

number  of  forces,  and  the  machine  or  system  then  re- 
ceive any  very  small  displacement,  the  algebraic  sum  of  the  products  formed 
by  multiplying  each  force  by  its  virtual  velocity  will  be  zero.  Of  course,  the 
displacement  of  the  machine  is  supposed  to  be  such  as  not  to  break  the 
connection  of  its  parts  ;  thus  in  the  wheel  and  axle  the  only  possible  dis- 
placement is  to  turn  it  round  the  fixed  axle  ;  in  the  inclined  plane  the  weight 
must  still  continue  to  rest  on  the  plane  ;  in  the  various  systems  of  pulleys 
the  strings  must  still  continue  stretched,  and  must  not  alter  in  length,  &c. 

The  complete  proof  of  this  principle  is  beyond  the  scope  of  the  present 
work,  but  we  may  easily  establish  its  truth  in  any  of  the  machines  we  have 
already  considered.  It  will  be  found  in  every  case  that,  if  the  machine 
receive  a  small  displacement,  the  virtual  velocities  of  P  and  W  will  be  of 
opposite  signs,  and  that,  neglecting  the  signs,  P  x  P's  virtual  velocity  =  W  x  W's 
virtual  velocity.  Thus,  to  take  the  case  of  a  bent  lever,  let  P  and  Q  be  the 
forces  acting  at  the  extremities  of  the  arms  of  the  bent  lever  AFB  (fig.  30), 
and  let  the  lever  be  turned  slightly  round  its  fulcrum  F,  bringing  A  to  A',  and 
B  to  B'.  Draw  A'a  and  B'£  perpendicular  to  P  and  Q  respectively  ;  then  Aa 
is  the  virtual  velocity  of  P,  and  B^  that  of  Q,  the  former  being  positive  and 
the  latter  negative.  Let  Yp,  Yq  be  the  perpendiculars  from  the  fulcrum 
upon  P  and  Q,  or  what  we  have  called  (art.  40)  the  arms  of  P  and  Q.  Now, 
as  the  displacement  is  very  small,  the  angles  FAA',  FBB' will  be  very  nearly 


3O  On  Matter,  Force,  and  Motion.  [46- 

right   angles;   and,    therefore,    the  right-angled  triangles  AaA',   B^B'   will 
ultimately    be    similar    to    the   triangles    YpA,    F^B   respectively,    whence 

BB'='FB'  " 

BB' 

FA'  *UU  F^  =  FB- 
triangles  FAA',  FBB'  are  similar, 
as  they  are  both  isosceles,  and 
their  vertical  angles  are  equal,  so 


and 


Yp 
But     the 


that 


AA' 
FA 


BB' 
FB 


whence 


P' 


P  x 


Yq 


1 


]L—  -s-.    Now  the  denominators  of 

Fig.  30. 

these  two  equal  fractions  are  equal, 
if  the  lever  be  in  equilibrium  (art.  40).     Hence  the  numerators  are  equal,  or 

P  x  P's  virtual  velocity  =  O  x  Q's  virtual  velocity. 

As  a  further  and  simpler  example,  take  the  case  of  the  block  and  tackle 
described  in  article  41.  Suppose  the  weight  to  be  raised  through  a  space  h  ; 
then  the  virtual  velocity  of  the  weight  is  h,  and  is  negative.  Now  as  the 
distance  between  the  block  and  tackle  is  less  than  before  by  the  space  h,  and 
as  the  rope  passes  over  this  space  n  times,  in  order  to  keep  the  rope  still 
tight  the  power  will  have  to  move  through  a  space  equal  to  nh.  This  is  the 
virtual  velocity  of  P,  and  is  positive,  and  as  W  =  ;zP,  we  see  that 

W  x  W's  virtual  velocity  =  P  x  P's  virtual  velocity. 

47.  Friction. — In  the  cases  of  the  actions  of  machines  which  have  been 
described,  the  resistances  which  are  offered  to  motion  have  not  been  at  all 
considered.  The  surfaces  of  bodies  in  contact  are  never,  perfectly  smooth  ; 
even  the  smoothest  present  inequalities  which  can  neither  be  detected  by  the 
touch  nor  by  ordinary  sight  ;  hence  when  one  body  moves  over  the  surface 
of  another  the  elevations  of  one  sink  into  the  depressions  of  the  other,  like 
the  teeth  of  wheels,  and  thus  offer  a  certain  resistance  to  motion  ;  this  is 
what  is  called  friction.  It  must  be  regarded  as  a  force  which  continually 
acts  in  opposition  to  actual  or  possible  motion. 

Friction  is  of  two  kinds  :  sliding,  as  when  one  body  glides  over  another  ; 
this  is  least  when  the  two  surfaces  in  contact  remain  the  same,  as  in  the 
motion  of  an  axle  in  its  bearing  ;  and  rolling  iriction,  which  occurs  when  one 
body  rolls  over  another,  as  in  the  case  of  an  ordinary  wheel.  The  latter  is 
less  than  the  former,  for  by  the  rolling  the  inequalities  of  one  body  are  raised 
over  those  of  the  other. 

Friction  is  directly  proportional  to  the  pressure'  of  the  two  surfaces 
against  each  other.  That  portion  of  the  pressure  which  is  required  to  over- 
come friction  is  called  the  coefficient  of  friction. 

Friction  is  independent  of  the  extent  of  the  surfaces  in  contact  if  the  pres- 
sure is  the  same.  Thus,  suppose  a  board  with  a  surface  of  a  square  deci- 
metre resting  on  another  board  to  be  loaded  with  a  weight  of  a  kilogramme. 


-48] 


Resistance  to  Motion  in  a  Fluid  Medium. 


If  this  load  be  distributed  over  a  similar  board  of  two  square  decimetres 
surface,  the  total  friction  will  be  the  same,  while  the  friction  per  square 
centimetre  is  one  half,  for  the  pressure  on  each  square  centimetre  is  one  half 
of  what  it  was  before.  Friction  is  diminished  by  polishing  and  by  smearing, 
but  is  increased  by  heat.  It  is  greater  as  a  body  passes  from  the  state  of 
rest  to  that  of  motion  than  during  motion,  but  seems  independent  of  the 
velocity.  The  coefficient  of  friction  depends  on  the  nature  of  the  substances 
in  contact ;  thus  for  oak  upon  oak  it  is  0*418  when  the  fibres  are  parallel, 
and  0^293  when  they  cross  ;  for  beech  upon  beech  it  is  0*36.  Greasy  sub- 
stances which  are  not  absorbed  by  the  body  diminish  friction  ;  but  increase 
it  if  they  are  absorbed.  Thus  moisture  and  oil  increase,  while  tallow,  soap, 
and  graphite  diminish,  the  friction  of  wooden  surfaces.  In  the  sliding  fric- 
tion of  cast  iron  upon  bronze  the  coefficient  was  found  to  be  0*25  without 
grease  ;  with  oil  it  was  0-17,  fat  OTI,  soap  0-03,  and  with  a  mixture  of  fat 
and  graphite  0*02.  The  coefficient  of  rolling  friction  for  cast-iron  wheels  on 
iron  rails  as  in  railways  is  about  0-004  '•>  for  ordinary  wheels  on  an  ordinary 
road  it  is  0*04,  hence  a  horse  can  draw  ten  times  as  great  a  load  on  rails  as 
on  an  ordinary  road. 

As  rolling  friction  is  considerably  less  than  sliding  friction,  it  is  a  great 
saving  of  power  to  convert  the  latter  into  the  former ;  as  is  done  in  the  case 
of  the  casters  of  chairs  and  other  furniture,  and  also  in  that  of  friction  wheels. 
On  the  other  hand,  it  is  sometimes  useful  to  change  rolling  into  sliding  fric- 
tion, as  when  drags  are  placed  on  carriage  wheels. 

Without  friction  on  the  ground,  neither  men  nor  animals,  neither  ordinary 
carriages  nor  railway  carriages,  could  move.     Friction  is  necessary  for  the 
transmission  of  power  from  one  wheel  to  another  by 
means  of  bands  or  ropes  ;    and  without   friction   we 
could  hold  nothing  in  the  hands. 

48.  Resistance  to  Motion  in  a  Fluid  Medium. — 
A  body  in  moving  through  any  medium  such  as  air  or 
water  experiences  a  certain  resistance  :  for  the  moving 
body  sets  in  motion  those  parts  of  the  medium  with 
which  it  is  in  contact,  whereby  it  loses  an  equivalent 
amount  of  its  own  motion. 

This  resistance  increases  with  the  surface  ot  the 
moving  body  ;  thus  a  soap  bubble  or  a  snow  flake  falls 
more  slowly  than  does  a  drop  of  water  of  the  same 
weight.  It  also  increases  with  the  density  of  the 
medium  ;  thus  in  rarefied  air  it  is  less  than  in  air  under 
the  ordinary  pressure  ;  and  in  this  again  it  is  less  than 
in  water. 

The  influence  of  this  resistance  may  be  illustrated 
by  means  of  the  apparatus  represented  in  fig.  31, 
which  consists  of  two  vanes,  w  iu,  fixed  to  a  horizontal 
axis,  x x;  to  which  also  is  attached  a  bobbin  s.  The  rotation  of  the  vanes  is 
effected  by  means  of  the  falling  of  a  weight  attached  to  the  string  coiled 
round  the  bobbin.  The  vanes  can  be  adjusted  either  at  right  angles  or 
parallel  to  the  axis.  In  the  former  position  the  vanes  rotate  rapidly  when 
the  weight  is  allowed  to  act ;  in  the  latter,  however,  where  they  press  with 


Fig.  31. 


32  On  Matter ;  Force,  and- Motion.  [48- 

their  entire  surface  against  the  air,  the  resistance  greatly  lessens  the  rapidity 
of  rotation. 

The  resistance  increases  with  the  velocity  of  the  moving  body,  and  for 
moderate  velocities  is  proportional  to  the  square  ;  for,  supposing  the  veloci- 
ties of  a  body  made  twice  as  great,  it  must  displace  twice  as  much  matter, 
and  must  also  impart  to  the  displaced  particles  twice  the  velocity.  For  high 
velocities  the  resistance  in  a  medium  increases  in  a  more  rapid  ratio  than 
that  of  the  square,  for  some  of  the  medium  is  carried  along  with  the  moving 
body,  and  this,  by  its  friction  against  the  other  portions  of  the  medium, 
causes  a  loss  of  velocity. 

It  is  this  resistance  which  so  greatly  increases  the  difficulty  and  cost  of 
attaining  very  high  speeds  in  steam-vessels.  Use  is  made,  on  the  other  hand, 
of  this  resistance  in  parachutes  (fig.  151)  and  in  the  wind-vanes  for  diminish- 
ing the  velocity  of  falling  bodies  (fig.  55),  the  principle  of  which  is  illustrated 
by  the  apparatus,  fig.  31.  Light  bodies  fall  more  slowly  in  air  than  heavy 
ones  of  the  same  surface,  for  the  moving  force  is  smaller  compared  with  the 
resistance.  The  resistance  to  a  falling  body  may  ultimately  equal  its  weight  ; 
it-  then  moves  uniformly  forward  with  the  velocity  which  it  has  acquired. 
Thus,  a  rain-drop  falling  from  a  height  of  3,000  feet  would,  when  near  the 
ground,  have  a  velocity  of  nearly  440  feet,  or  that  of  a  musket-shot  ;  owing, 
however,  to  the  resistance  of  the  air,  its  actual  velocity  is  probably  not  more 
than  30  feet  in  a  second.  On  railways  the  resistance  of  the  air  is  appre- 
ciable ;  with  a  carriage  exposing  a  surface  of  22  square  feet,  it  amounts  to 
1 6  or  17  pounds  when  the  speed  of  the  train  is  16  feet  a  second  or  u  miles 
an  hour. 

By  observing  the  rate  of  diminution  in  the  number  of  oscillations  of  a 
horizontal  disc  suspended  by  a  thread,  when  immersed  in  water,  Meyer  de- 
termined the  coefficient  of  the  resistance  of  water,  and  found  that  at  10°  it 
was  equal  to  o-oi567  gramme  on  a  square  centimetre;  and  for  air  it  was 
about  ~  as  much. 

49.  Uniformly  Accelerated  Rectilinear  Motion. — Let  us  suppose  a 
body  containing  m  units  of  mass  to  move  from  rest  under  the  action  of  a 
force  of  F  units,  the  body  will  move  in  the  line  of  action  of  the  force,  and 
will  acquire  in  each  second  an  additional  velocity /given  by  the  equation 

F  =  ;«/; 
consequently,  if  v  is  its  velocity  at  the  end  of  /  seconds,  we  have 

v=ft.  (i) 

To  determine  the  space  it  will  describe  in  /  seconds,  we  may  reason  as 
follows  : — The  velocity  at  the  time  /  being  ft,  that  at  a  time  t  +  r  will  be  / 
(/  +  r).  If  the  body  moved  uniformly  during  the  time  r  with  the  former 
velocity  it  would  describe  a  space  s  equal  to  fit ;  if  with  the  latter  velocity,  a 
space  Sj_  equal  to/(/  +  r)r.  Consequently, 

sl  :  s  :\  t  +  T  :  t\ 

therefore,  when  r  is  indefinitely  small,  the  limiting  values  of  s  and  sl  are 
equal.  Now  since  the  body's  velocity  is  continually  increasing  during  the 
time  T,  the  space  actually  described  is  greater  than  s,  and  less  than  sr  But 


-49]  Uniformly  Accelerated  Rectilinear  Motion.  33 

since  the  limiting  values  of  s  and  s^  are  equal,  the  limiting  value  of  the  space 

described  is  the  same  as  that  of  s  or  sv     In  other  words,  if  we  suppose  the 

whole  time  of  the  body's  motion  to  be  divided 

into  any  number  of  equal  parts,  if  we  determine 

the  velocity  of  the  body  at  the  beginning  of  each  ^ 

of  these  parts,  and  if  we  ascertain  the  spaces  xf~~^ 

described   on   the  supposition   that    the    body 


^ 


moves  uniformly  during  each  portion  of  time, 
the  limiting  value  of  the  sum  of  these  spaces 
will  be  the  space  actually  described  by  the  body. 
Draw  a  line  AC  (fig.  32)  and  at  A  construct  an  p-lg  32- 

angle  CAB,  whose   tangent   equals  /;    divide 

AC  into  any  number  of  equal  parts  in  D,  E,  F,...and  draw  PD,  QE,  RF,... 
BC  at  right  angles  to  AC,  then  since  PD  =  AD  xf,  QE  =  AE  xf,  RF  =  AF  xf, 
BC  =  AC  xf,  &c.,  PD  will  represent  the  velocity  of  the  body  at  the  end  of 
the  time  represented  by  AD,  and  similarly  QE,  RF,...BC,  will  represent  the 
velocity  at  the  end  of  the  times  AE,  AF,...AC.  Complete  the  rectangles  De, 
E/j  Yg...  These  rectangles  represent  the  space  described  by  the  body  on 
the  above  supposition  during  the  second,  third,  fourth,... portions  of  the  time. 
Consequently,  the  space  actually  described  during  the  time  AC  is  the  limit 
of  the  sum  of  the  rectangles  ;  the  limit  being  continually  approached  as  the 
number  of  parts  into  which  AC  is  divided  is  continually  increased.  But  this 
limit  is  the  area  of  the  triangle  ABC  :  that  is  £AC  x  CE  or  £AC  x  AC  xf. 
Therefore,  if  AC  represents  the  time  /  during  which  the  body  describes  a 
space  s,  we  have 

Since  this  equation  can  be  written 

we  find,  on  comparison  with  equation  (i),  that 

7/2  =  2/r.  (3) 

To  illustrate  these  equations,  let  us  suppose  the  accelerative  effect  of  the 
force  to  be  6  ;  that  is  to  say,  that,  in  virtue  of  the  action  of  the  force,  the  body 
acquires  in  each  successive  second  an  additional  velocity  of  6  ft.  per  second, 
and  let  it  be  asked  what,  on  the  supposition  of  the  body  moving  from  rest, 
will  be  the  velocity  acquired  and  the  space  described  at  the  end  of  12 
seconds  ;  equations  I  and  2  enable  us  to  answer  that  at  that  instant  it  will 
be  moving  at  the  rate  of  72  ft.  per  second  and  will  have  described  432  ft. 

The  following  important  result  follows  from  equation  2.  At  the  end  of 
the  first,  second,  third,  fourth,  &c.,  second  of  the  motion  the  body  will  have 
described  \f,  \fx  4,  ±fx  9,  $fx  16,  &c.,  ft.,  and  consequently  during  the 
first,  second,  third,  fourth,  &c.,  second  of  the  motion  will  have  described  £/j 
i/"*  3>  $f*  5>  $f*  7,  &c-j  ft-?  namely,  spaces  in  arithmetical  progression. 

The  results  of  the  above'  article  can  be  stated  in  the  form  of  laws  which 
apply  to  the  state  of  a  body  moving  from  a  state  of  rest  under  the  action  of 
a  constant  force  : — 


34  On  Matter,  Force,  and  Motion.  [49- 

I.  The  velocities  are  proportional  to  the  times  during  which  the  motion 
has  lasted. 

II.  The  spaces  described  are  proportional  to  the  squares  of  the  times  em- 
ployed in  their  description. 

III.  The  spaces  described  are  proportional  to  the  squares  of  the  velocities 
acquired  during  their  description. 

I  V.  The  spaces  described  in  equal  successive  periods  of  time  increase  by  a 
constant  quantity. 

Instead  of  supposing  the  body  to  begin  to  move  from  a  state  of  rest,  we 
may  suppose  it  to  have  an  initial  velocity  V,  in  the  direction  of  the  force.  In 
this  case  equations  i,  2,  and  3  can  be  easily  shown  to  take  the  following 
forms,  respectively  :  — 


If  the  body  move  in  a  direction  opposite  to  that  of  the  force,  f  must  be 
reckoned  negative. 

The  most  important  exemplification  of  the  laws  stated  in  the  present 
article  is  in  the  case  of  a  body  falling  freely  in  vacua.  Here  the  force  causing 
the  acceleration  is  that  of  gravity,  and  the  acceleration  produced  is  denoted 
by  the  letter  g  ;  it  has  already  been  stated  (27  and  29)  that  the  numerical 
value  of  g  is  32*1912  at  London,  when  the  unit  of  time  is  a  second  and  the 
unit  of  distance  a  foot.  Adopting  the  metre  as  unit  of  distance  the  value  of 
g  at  London  is  9-8117. 

50.  Motion  on  an  Inclined  Plane.  —  Referring  to  (43),  suppose  the  force 
P  not  to  act  ;  then  the  mass  M  is  acted  on  by  an  unbalanced  force  M^  sin  x, 
in  the  direction  SR,  consequently  the  accelerating  force  down  the  plane  is 
g  sin  x,  and  the  motion  becomes  a  particular  case  of  that  discussed  in  the 
last  article.  If  it  begins  to  move  from  rest,  it  will  at  the  end  of  /  seconds 
acquire  a  velocity  v  given  by  the  equation 

v  =gt  sin  x, 
and  will  describe  a  length  s  of  the  plane  given  by  the  equation 


Also,  if  v  is  the  velocity  acquired  while  describing  s  feet  of  the  plane, 

v~  —  2gs  sin  x. 

Hence  (fig.  23)  if  a  body  slides  down  the  plane  from  S  to  R  the  velocity  which 
it  acquires  at  R  is  equal  to  \/2g  .  RS  sin  R  or  ^/2g  .  ST  ;  that  is  to  say,  the 
velocity  which  the  body  has  at  R  does  not  depend  on  the  angle  x,  but  only 
on  the  perpendicular  height  ST.  The  same  would  be  true  if  for  RS  we  sub- 
stituted any  smooth  curve,  and  hence  we  may  state  generally,  that  when  a 
body  moves  along  any  smooth  line  under  the  action  of  gravity,  the  change 
of  velocity  it  experiences  in  moving  from  one  point  to  another  is  that  due  to 
the  vertical  height  of  the  former  point  above  the  latter. 

51.  Motion  of  Projectiles.  —  The  equations  given  in  the  above  article 
apply  to  the  case  of  a  body  thrown  vertically  upwards  or  downwards  with  a 
certain  initial  velocity.  We  will  now  consider  the  case  of  a  heavy  body 


-51]  Motion  of  Projectiles.  35 

thrown  in  a  horizontal  direction.  Let  a,  fig.  33,  be  such  a  body  thrown  with 
an  initial  velocity  of  v  feet  in  a  second,  and  let  the  line  ab  represent  the  space 
described  in  any  interval ;  then,  at  the  end  of  «  & 
the  2,  3,  4.. .equal  interval,  the  body,  in  virtue  * 
of  its  inertia,  will  have  reached  the  points  c  d  e, 
&c.  But,  during  all  this  time  the  body  is  under  * 
the  influence  of  gravity,  which  if  it  alone  acted, 
would  cause  the  body  to  fall  through  the  dis- 
tances represented  on  the  vertical  line  ;  these  are 
determined  by  the  successive  values  of  %gt-, 
which  is  the  formula  for  the  space  described  by 
a  freely  falling  body  (49).  The  effect  of  the 
combined  action  of  the  two  forces  is  that  at  the 
end  of  the  first  interval,  &c.,  the  body  will  be 
at  b',  at  the  end  of  the  second  interval  at  cf,  of 
the  third  at  d',  &c.,  the  spaces  bb',  cc',  dd'... 
being  proportional  to  the  squares  of  ab,  ac,  ad, 
respectively,  and  the  line  joining  these  points 
represents  the  path  of  the  body.  By  taking  the 
intervals  of  time  sufficiently  small  we  get  a  regu- 
larly curved  line  of  the  form  known  as  the  parabola. 

If  the  direction  in  which  the  body  is  thrown  makes  an  angle  of  a  with 
the  horizon  (fig.  34),  then  after  /  seconds  it  would  have  travelled  a  distance 


.  33- 


Fig-  34- 

ab  =  vt,  where  v  is  the  original  velocity  ;  during  this  time,  however,  it  will  have 
fallen  through  a  distance  bc  =  %gP\  the  height  which  it  will  have  actually 
reached  is  =bd—bc  =  vt  sin  a  —  ^gt*  \  and  the  horizontal  distance  will  be 
ad=ab  cos  a  =  i>t  cos  a.  The  range  of  the  body,  or  the  greatest  distance 
through  which  it  is  thrown,  will  be  reached  when  the  height  is  again  =  0  ;  that 

is,  when  vt  sin  a  —  $gt*  ^0,  from  which  /--—         a.     Introducing  this  value 

of/  into  the  equation  for  the  distance  d.  we  have  d=2v  — ,  which 

g 

by  a  trigonometrical   transformation  = c>  sm  2a.     The    greatest    height    is 

g 

attained  in  half  the  time  of  flight,  or  when  t  =  v  sin  a,  from   which   we  get 


h  = 


?/-  sin-  a 


g 


It  follows  from  the  formula  that  the   height  is  greatest  when   sin  a  is 


36  On  Matter,  Force,  and  Motion.  [51- 

greatest,  which  is  the  case  when  it  =  90°,  or  when  the  body  is  thrown  vertically 
upwards  ;  the  range  is  greatest  where  sin  ia  is  a  maximum,  that  is,  when 
20  =  90°  or  «  =45°. 

In  these  formulas  it  has  been  assumed  that  the  air  offers  no  resistance. 
This  is,  however,  far  from  the  case,  and  in  practice,  particularly  if  the  velo- 
city of  projection  is  very  great,  the  path  differs  from  that  of  a  parabola.  Fig. 
34  approximately  represents  the  path,  allowing  for  the  resistance  of  the  air. 
The  divergence  from  the  true  theoretical  path  is  the  greater  from  the  fact 
that  in  the  modern  rifled  arms  the  projectiles  are  not  spherical  in  shape, 
and  also  because,  along  with  their  motion  of  translation,  they  have,  in  con- 
sequence of  the  rifling,  a  rotatory  motion  about  their  axis. 

52.  Composition  of  Velocities. — The  principle  for  the  composition  of 
velocities  is  the  same  as  that  for  the  composition  of  forces  :  this  follows  evi- 
dently from  the  fact  that  forces  are  measured  by  the  momentum  they  com- 
municate, and  are  therefore  to  one  another  in  the  same  ratio  as  the  velocities 
they  communicate  to  the  same  body.     Thus  (fig.  6,  art.  33)  if  the  point  has 
at  any  instant  a  velocity  AB  in  the  direction  AP,  and  there  is  communicated 
to  it  a  velocity  AC  in  the  direction  AO,  it  will  move  in  the  direction  AR  with 
a  velocity  represented  by  AD.     And  conversely,  the  velocity  of  a  body  re- 
presented by  AD  can  be  resolved  into  two  component  velocities  AB  and  AC. 
This  suggests  the  method  of  determining  the  motion  of  a  body  when  acted 
on  by  a  force  in  a  direction  transverse  to  the  direction  of  its  velocity ;  namely, 
suppose  the  time  to  be  divided  into  a  great  number  of  intervals,  and  suppose 
the  velocity  actually  communicated  by  the  force  to  be  communicated  at  once, 
then  by  the  composition  of  velocities  we  can  determine  the  motion  during 
each  interval,  and  therefore  during  the  whole  time  ;  the  actual  motion  is  the 
limit  to  which  the  motion,  thus  determined,  approaches  when  the  number  of 
intervals  is  increased. 

53.  Motion  in  a  Circle. — Centrifugal  Force. — When  a  body  is  once  in 
motion,  unless  it  be    acted   upon  by  some  force,  it   will   move  uniformly 
forward  in  a  straight  line  with  unchanged  velocity  (26).    If,  therefore,  a  body 
moves  uniformly  in  any  other  path  than  a  straight   line — in  a  circle,  for 
instance — this  must   be  because   some   force  is  constantly  at  work  which 
continuously  deviates  it  from  this  straight  line. 

We  have  already  seen  an  example  of  this  in  the  case  of  the  motion  of 
projectiles  (51),  and  will  now  consider  it  in  the  case  of  central  motion,  or 
motion  in  a  circle,  of  which  we  have  an  example  in  the  motion  of  the  celestial 
bodies  or  in  the  motion  of  a  sling. 

In  the  latter  case,  if  the  string  is  cut,  the  stone,  ceasing  to  be  acted  upon 
by  the  tension  of  the  string,  will  move  in  a  straight  line  with  the  velocity 
which  it  already  possesses  ;  that  is,  in  the  direction  of  the  tangent  to  the  curve 
at  the  point  where  the  stone  was  when  the  string  was  cut.  The  tension  of 
the  string,  the  effect  of  which  is  to  pull  the  stone  towards  the  centre  of  the 
circle,  and  to  cause  the  stone  to  move  in  its  circular  path,  is  called  the  centri- 
petal or  central  force  ;  the  reaction  of  the  stone  upon  the  string,  which  is 
equal  and  opposite  to  this  force,  is  called  its  centrifugal  force.  The  amount 
of  these  forces  may  be  arrived  at  as  follows  : — 

Let  us  suppose  a  body  moving  in  a  circle  with  given  uniform  velocity  to 
be  at  the  point  a  (fig.  35)  ;  then,  had  it  not  been  acted  on  by  a  force  in  the 


-54] 


Motion  in  cr  Vertical  Circle. 


37 


direction  ac,  it  would,  in  a  small  succeeding  interval  of  time  /,  have  continued 
to  move  in  the  direction  of  the  tangent  at  #,  and  have  passed  through  a 
distance  which  we  will  represent  by  ab.  In  conse- 
quence, however,  of  this  force  it  has  not  followed  this 
direction,  but  has  arrived  at  the  point  d  on  the  curve  ; 
hence  the  force  has  made  it  traverse  the  distance  bd=ae 
in  this  interval.  If  f  be  the  accelerating  force  which 
draws  the  body  towards  the  centre,  ae=  \ft~,  and  if 
ad  be  very  small,  it  may  be  taken  as  equal  to  ab  or  z//, 
where  it  is  the  velocity  of  the  moving  body.  Now  if 
an  is  the  diameter  of  the  circle,  the  triangle  adn  is 
inscribed  in  a  semicircle  and  is  right-angled,  whence 
ad1  =  ae  x  an  =  ae  x  2r.  Substituting  their  values  for 
ad  and  ae  in  this  equation,  we  find  that  v^-f-  =  \ft-  x  2r, 

from  which  /=  — ;  that  is,  in  order  that  a  body,  with  a 

certain  velocity,  may  move  in  a  circle,  it  must  be  drawn 
to  the  centre  by  a  force  which  is  directly  as  the  square 
of  the  velocity  with  which  the  body  moves,  and  which  is 
inversely  as  the  radius  of  the  circle.  In  order  to  express 
this  in  the  ordinary  units  of  weight,  we  must  multiply  the 


above  expression  by  the  mass,  which  gives  F  =  — 

—.  To  keep  the  body  in   a  circle  an  attraction   to- 

Sr 

wards  the  centre  is  needed,  which  is  constantly  equal  to 


and  this  attraction  is  constantly  neutralised  by  the  - 


Fig-  35- 


centrifugal  force. 

The  above  expression  may  be  put  in  a  form  which  is  sometimes  more  con- 
venient.    If  T  be  the  time  in  seconds  required  to  traverse  the  circumference 


with   the  velocity  v,  then   v> 


from  which  F  =  4*"ir*r 


If  a  rigid  body  rotates  about  a  fixed  axis,  all  parts  of  the  body  describe 
circumferences  of  various  diameters,  but  all  in  the  same  time.  The  velocity 
of  the  motion  of  individual  particles  increases  with  the  distance  from  the  axis 
of  rotation.  By  angular  velocity  is  understood  the  velocity  of  a  point  at  unit 
distance  from  the  axis  of  rotation.  If  this  is  denoted  by  o>,  the  velocity  v  of  a 


point  at  a  distance  from  the  axis  is  o>r,  from  which  to  =  - 


27T 


and  f 


r       T 

The  existence  of  centrifugal  force  may  be  demonstrated  by  means  of 
numerous  experiments,  such  as  the  centrifugal  railway.  If  a  small  can  of 
water  hung  by  the  handle  to  a  string  be  rapidly  rotated  in  a  vertical  circle, 
no  water  will  fall  out,  for,  at  a  suitable  velocity,  the  liquid  will  press  against 
the  bottom  of  the  vessel  with  a  force  at  right  angles  to  the  circle,  and  greater 
than  its  own  weight. 

54.  Motion  in  a  Vertical  Circle.— Let  ACBD  be  a  circle  whose  plane 
is  vertical  and  radius  denoted  by  r.  Suppose  a  point  placed  at  A,  and 
allowed  to  slide  down  the  curve,  what  velocity  will  it  have  acquired  on 


On  Matter,  Force,  and  Motion. 


[54- 


reaching  any  given  point  P  ?  Draw  the  vertical  diameter  CD,  join  CA,  CP, 
and  draw  the  horizontal  lines  AMB  and  PNP'.  Now,  assuming  the  curve 
to  be  smooth,  the  velocity  acquired  in  falling  from 
A  to  P  is  that  due  to  MN,  the  vertical  height  of  A 
above  P  (50)  ;  if,  therefore,  v  denote  the  velocity  of 
the  point  at  P,  we  shall  have 


Fig.  36- 


Now  by  similar  triangles  DCP,  PCN  we  have 

DC  :  CP::CP  :  CN  ; 
consequently,  if  we  denote  by  s  the  chord  CP, 

2rNC  =s~ ; 

in  like  manner  if  a  denote  the  chord  CA, 
=    - 


2rMN=^-j2, 


therefore 


and 


Now  v  will  have  equal  values  when  ^  has  the  same  value,  whether  positive 
or  negative,  and  for  any  one  value  of  s  there  are  two  equal  values  of  v,  one 
positive  and  one  negative.  That  is  to  say,  since  CP'  is  equal  to  CP,  the 
body  will  have  the  same  velocity  at  P'  that  it  has  at  P,  and  at  any  point  the 
body  will  have  the  same  velocity  whether  it  is  going  up  the  curve  or  down 
the  curve.  Of  course  it  is  included  in  this  statement  that  if  the  body  begins 
to  move  from  A  it  will  just  ascend  to  a  point  B  on  the  other  side  of  C,  such 
that  A  and  B  are  in  the  same  horizontal  line.  It  will  also  be  seen  that  at  C 
the  value  of  s  is  -zero ;  consequently,  if  V  is  the  velocity  acquired  by  the 
body  in  falling  from  A  to  C,  we  have 

V  = 

and,  on  the  other  hand,  if  the  body  begins  to  move  from  C  with  a  velocity  V 
it  will  reach  a  point  A  such  that  the  chord  AC  or  a  is  given  by  the  same 
equation.       In    other   words,    the   velocity   at    the 
lowest  point  is  proportional  to  the  chord  of  the  arc 
described. 

55.  Motion  of  a  Simple  Pendulum. — By  a 
simple  pendulum  is  meant  a  heavy  particle  sus- 
pended by  a  fine  thread  from  a  fixed  point,  about 
which  it  oscillates  without  friction.  So  far  as  its 
changes  of  velocity  are  concerned  they  will  be  the 
same  as  those  of  the  point  in  the  previous  article ; 
for  the  tension  of  the  thread,  acting  at  each  position 
in  a  direction  at  right  angles  to  that  of  the  motion 
of  the  point,  will  no  more  affect  its  motion  than 
the  reaction  of  the  smooth  curve  affects  that  of  the  point  in  the  last  article. 
The  time  of  an  oscillation — that  is,  the  time  in  which  the  poirf  moves  from  A 
to  B — can  be  easily  ascertained  when  the  arc  of  vibration  i*>  ^nall ;  that  is, 
when  the  chord  and  the  arc  do  not  sensibly  differ. 


Q 


Fig-  37- 


-56]  Motion  of  a  Simple  Pendulum.  39 

Thus,  let  AB  (fig.  37)  equal  the  arc  or  chord  ACB  (fig.  36)  ;  with  centre 
C  and  radius  AC  or  a  describe  a  circle,  and  suppose  a  point  to  describe  the 

circumference  of  that  circle  with  a  uniform  velocity  V  or  a  *  /  -.    At  any  in- 

stant let  the  point  be  at  Q,  join  CQ,  draw  the  tangent  QT,  also  draw  QP  at 
right  angles  and  QN  parallel  to  AB,  then  the  angles  NQT  and  CQP  are 
equal.  Now  the  velocity  of  O  resolved  parallel  to  AB  is  V  cos  TQN  or 

,i    .  [&  cos  CQP  ;  that  is,  if  CP  equals  s,  the  velocity  of  O  parallel  to  AB  is 


But  it  we  suppose  a  point  to  move  along  AB  in  such  a  manner  that  its 
velocity  in  each  position  is  the  same  as  that  of  the   oscillating  body,  its 

velocity  at  P  would  also  equal  *  /  £  (a1  —  s-}  •    and,   therefore,   this    point 

would  describe  AB  in  the  same  time  that  Q  describes  the  semicircumference 
AQB.     If  then     be  the  required  time  of  an  oscillation,  we  have 


This  result  is  independent  of  the  length  of  the  arc  of  vibration,  provided  its 
amplitude,  that  is  AB,  be  small  —  not  exceeding  4  or  5  degrees,  for  instance. 
It  is  evident  from  the  formula  that  the  time  of  a  vibration  is  directly  pro- 
portional to  the  square  root  of  the  length  of  the  pendulum,  and  inversely 
proportional  to  the  square  root  of  the  accelerating  force  of  gravity. 

As  an  example  of  the  use  of  the  formula  we  may  take  the  following  :  —  It 
has  been  found  that  39*13983  inches  is  the  length  of  a  simple  pendulum, 
whose  time  of  oscillation  at  Greenwich  is  one  second  ;  the  formula  at  once 
leads  to  an  accurate  detennination  of  the  accelerating  force  of  gravity  g  ;  for 
using  feet  and  seconds  as  our  units  we  have  /=  i,  r=  3-26165,  and  TT  stands 
for  the  known  number  3*14159,  therefore  the  formula  gives  us 

g=  (3-MI59)2  *  3-26165  =  32-1912. 
This  is  the  value  employed  in  (29). 

Other  examples  will  be  met  with  in  the  Appendix; 

56.  Graphic  Representation  of  the  Changes  of  Velocity  of  an  Oscil- 
lating: Body.  —  The  changes  which  the  velocity  of  a  vibrating  body  undergoes 
may  be  graphically  represented  as  follows  :  —  Draw  a  line  of  indefinite  length 
and  mark  off  AH  (fig.  38)  to  represent  the  time  of  one  vibration,  HH'  to  re- 


present the  time  of  the  second  vibration,  and  so  on.  During  the  first  vibra- 
tion the  velocity  increases  from  zero  to  a  maximum  at  the  half-vibration,  and 
then  decreases  during  the  second  half-vibration  from  the  maximum  to  zero. 
Consequently,  a  curved  line  or  arc  AQH  may  be  drawn,  whose  ordinate  QM 
at  any  point  Q  will  represent  the  velocity  of  the  body  at  the  time  represented 


4O  On  Matter,  Force,  and  Motion.  [56- 

by  AM.  If  a  similar  curved  line  or  arc  HPH'  be  drawn,  the  ordinate  PN 
of  any  point  P  will  represent  the  velocity  at  a  time  denoted  by  AN.  But 
since  the  direction  of  the  velocity  in  the  second  oscillation  is  contrary  to  that 
of  the  velocity  in  the  first  oscillation,  the  ordinate  NP  must  be  drawn  in  the 
contrary  direction  to  that  of  MO.  If,  then,  the  curve  be  continued  by  a  suc- 
cession of  equal  arcs  alternately  on  opposite  sides  of  AD,  the  variations  of 
the  velocity  of  the  vibrating  body  will  be  completely  represented  by  the 
varying  magnitudes  of  the  ordinates  of  successive  points  of  the  curve.  The 
last  article  shows  this  to  be  the  curve  of  sines  for  a  pendulum. 

57.  Conical  Pendulum.  —  When  a  point  P  (fig.  39)  is  suspended  from  a 
point  A  as  a  simple  pendulum,  it  can  be  caused  to  describe  a  horizontal  circle 
with  a  uniform  velocity  V.  A  point  moving  in  such  a  manner  constitutes 
what  is  called  a  co?iical  pendulum,  and  admits  of  many 
useful  and  interesting  applications.  We  will,  in  this 
place,  ascertain  the  relation  which  exists  between  the 
length  r  of  the  thread  AP,  the  angle  of  the  cone  PAN 
or  6,  and  the  velocity  V.  Since  the  point  P  moves  in  a 
circle  whose  radius  is  PN,  with  a  velocity  V,  a  force  R 
v  must  act  on  it  in  the  direction  PN  given  by  the  equa- 
tion (53) 


Now  the  only  forces  acting  are  the  tension  of  the  thread  T  along  PA, 
and  the  weight  of  the  body  M^*  vertically  ;  consequently,  their  resultant  must 
be  a  force  R  acting  along  PN.  And  therefore  these  forces  will  be  parallel 
to  the  sides  of  the  triangle  ANP,  so  that  (35) 


therefore 


or 


Now  PN  =  r  sin  6  and  PN  =  tan  6, 

AN 
therefore 

V2  =gr  sin  0  tan  6. 

One  conclusion  from  this  may  be  noticed.  With  centre  A  and  radius 
AP,  describe  the  arc  PC.  Now  when  the  angle  PAC  is  small,  the  sine,  PN, 
does  not  sensibly  differ  from  the  chord,  nor  the  cosine,  AN,  from  the  radius, 
therefore  in  this  case  we  have 


(chdPC)*orV  =  ch  /^ 

radius  V   r 


On  comparing  this  result  with  (54)  we  see  that  when  the  angle  PAN  is 
small,  the  velocity  of  P  moving  in  a  conical  pendulum  is  the  same  as  P 


-58]  Impulsive  Forces.  41 

would  have  at  the  lowest  point  C  if  it  oscillated  as  a  simple  pendulum  ;  con- 
sequently, if  we  conceive  the  point  P  to  be  making  small  oscillations  about 
the  point  A,  and  denote  the  velocity  at  the  lowest  point  by  V,  and  if,  when 
at  the  extreme  point  of  the  arc  of  vibration,  there  is  communicated  to  it  a 
velocity  V  in  a  direction  at  right  angles  to  the  plane  of  vibration,  its  motion 
will  be  changed  into  that  of  a  conical  pendulum. 

58.  Impulsive  Forces.  —  When  a  force  acts  on  a  body  for  an  inappreci- 
ably short  time,  and  yet  sensibly  changes  its  velocity,  it  is  termed  an  instan- 
taneous or  impulsive  force.  Such  a  force  is  called  into  play  when  one  body 
strikes  against  another.  A  force  of  this  character  is  nothing  but  a  finite 
though  very  large  force,  acting  for  a  time  so  short  that  its  duration  is  nearly, 
or  quite,  insensible.  In  fact,  if  M  is  the  mass  of  the  body,  and  the  force 
contains  M/  units,  it  will,  in  a  time  /,  communicate  a  velocity//  ;  now,  how- 
ever small  /  may  be,  M/and  therefore  f  may  be  so  large  that  ft  may  be  of 
sensible  or  even  considerable  magnitude.  Thus  if  M  contain  a  pound  of 
matter,  and  if  the  force  contain  ten  thousand  units,  though  /  were  so  short 
as  to  be  only  the  j^oth  °f  a  second,  the  velocity  communicated  by  the  force 
would  be  one  of  10  ft.  per  second.  It  is  also  to  be  remarked  that  the  body 
will  not  sensibly  move  while  this  velocity  is  being  communicated  ;  thus,  in 
the  case  supposed,  the  body  would  only  move  through  \ft~  or  the  ^^  °^  a 
foot  while  the  force  acts  upon  it. 

When  one  body  impinges  on  another  it  follows  from  the  law  of  the 
equality  of  action  and  reaction  (39)  that  whatever  force  the  first  body  exerts 
upon  the  second,  the  second  will  exert  an  equal  force  upon  the  first  in  the 
opposite  direction  ;  now  forces  are  proportional  to  the  momenta  generated 
in  the  same  time  ;  consequently,  these  forces  generate,  during  the  whole  or 
any  part  of  the  time  of  impact,  in  the  bodies  respectively,  equal  momenta 
with  contrary  signs  ;  and  therefore  the  sum  of  the  momenta  of  the  two  bodies 
will  remain  constant  during  and  at  the  end  of  the  impact.  It  is  of  course 
understood  that  if  the  two  bodies  move  in  contrary  directions  their  momenta 
have  opposite  signs  and  the  sum  is  an  algebraical  sum.  In  order  to  test  the 
physical  validity  of  this  conclusion,  Newton  made  a  series  of  experiments, 
which  may  be  briefly  described  thus  :  —  Two  balls  A  and  B  are  hung  from 
points  C,  D  in  the  same  horizontal  line  by  threads  in  such  a  manner  that 
their  centres  A  and  B  are  in  the  same  horizontal  line.  With  centre  C  and 
radius  CA  describe  a  semicircle  EAF,  and  with  centre  D  and  radius  DB 
describe  a  semicircle  GBH  on  the  wall  in  front  of  which  the  balls  hang. 
Let  A  be  moved  back  to  R,  and  be  allowed 

to  descend  to  A  ;  it  there  impinges  on  B  ;  *«        u          V        D          *       H 
both  A  and  B  will  now  move,  along  the  arch    \         \ 
AF  and  BH  respectively  ;  let  A  and  B  come 
to  their  highest  points  at  r  and  k  respectively. 
Now  if  V  denote  the  velocity  with  which  A 
reaches  the  lowest  point,  v  and  u  the  ve- 
locities with  which  A  and  B  leave  the  lowest 
points  after  impact,  and  r  the  radius  AC,  it  Fig.  40. 

follows  from  (54)  that 


V  =  chd  Ar  A*  v  =  chd  Ar  *        ,  and  u  =  chd 


A  fs  ; 


42  On  Matter,  Force^  and  Motion.  [58- 

therefore  if  A  and  B  are  the  masses  of  the  two  balls,  the  momentum  at  the 
instant  before  impact  was  A  x  chd  AR,  and  the  momentum  after  impact  was 
A  x  chd  Ar+  B  x  chd  B/£.  Now  when  the  positions  of  the  points  R,  r,  and 
k  had  been  properly  corrected  for  the  resistance  of  the  air,  it  was  found  that 
these  two  expressions  were  equal  to  within  quantities  so  small  that  they 
could  be  properly  referred  to  errors  of  observation.  The  experiment  suc- 
ceeded equally  under  every  modification,  whether  A  impinged  on  B  at  rest 
or  in  motion,  and  whatever  the  materials  of  A  and  B  might  be. 

59.  Direct  Collision  of  Two  Bodies.  —  Let  A  and  B  be  two  bodies  mov- 
ing with  velocities  V  and  U  respectively,  along  the  same  line,  and  let  their 
mutual  action  take  place  in  that  line  ;  if  the  one  overtake  the  other,  what 
will  be  their  respective  velocities  at  the  instant  after  impact?  We  will 
answer  this  question  in  two  extreme  cases. 

i.  Let  us  suppose  the  bodies  to  be  quite  inelastic.  In  this  case,  when  A 
touches  B,  it  will  continue  to  press  against  B  until  their  velocities  are  equal- 
ised, when  the  mutual  action  ceases.  For  whatever  deformation  the  bodies 
may  have  undergone,  they  have  no  tendency  to  recover  their  shapes.  If, 
therefore,  x  is  their  common  velocity  after  impact,  we  shall  have  AJT  +  B.r 
their  joint  momentum  at  the  end  of  impact,  but  their  momentum  before  im- 
pact was  AV  +  BU.  Whence 


an  equation  which  determines  x.. 

ii.  Let  us  suppose  the  bodies  perfectly  elastic.  In  this  case  they  recover 
their  shapes,  with  a  force  exactly  equal  to  that  with  which  they  were  com- 
pressed. Consequently,  the  whole  momentum  lost  by  the  one,  and  gained  by 
the  other,  must  be  exactly  double  of  that  lost  while  compression  took  place  ; 
that  is,  up  to  the  instant  at  which  their  velocities  were  equalised.  But  these 
are  respectively  AV  —  A_r  and  B.r—  BU  ;  therefore,  if  v  and  u  are  the  required 
final  velocities, 

A?/  =  AV-2(AV-A.r)  or  v=  -V  +  2.r 

Bar  =  BU  +  2(B:r-  BU)  or  u  =  2x-  U, 
hence 

(A  +  B)  v  =  2BU  +  (A  -  B)V 
and 

(A  +  B)  «  =  2AV  -  (A  -  B)U. 

The  following  conclusion  from  these  equations  may  be  noticed  :  suppose  a 
ball  A,  moving  with  a  velocity  V,  to  strike  directly  an  equal  ball  B  at  rest. 
In  this  case  A  =  B,  and  U  =  o,  consequently  v  —  o  and  u  =  V  ;  that  is,  the 
former  ball  A  is  brought  to  rest,  and  the  latter  B  moves  on  with  a  velocity  V. 
If  now  B  strike  on  a  third  equal  ball  C  at  rest,  B  will  in  turn  be  brought  to 
rest,  and  C  will  acquire  the  velocity  V.  And  the  same  is  true  if  there  is  a 
fourth,  or  fifth,  or  indeed  any  number  of  balls.  This  result  may  be  shown 
with  ivory  balls,  and  if  carefully  performed  is  a  very  remarkable  experi- 
ment. 

60.  Work:  Meaning-  of  the  Term.  —  It  has  been  pointed  out  (19,  26) 
that  a  moving  body  has  no  power  of  itself  to  change  either  the  direction  or 
the  speed  of  its  motion,  and  that,  if  any  such  change  takes  place,  it  is  a  proof 
that  the  body  is  acted  upon  by  some  external  force.  But  although  change  of 


-61]  Measure  of  Work.  43 

motion  thus  always  implies  the  action  of  force,  forces  are  often  exerted  with- 
out causing  any  change  in  the  motion  of  the  bodies  on  which  they  act.  For 
instance,  when  a  ship  is  sailing  at  a  uniform  speed  the  force  exerted  on  it  by 
the  wind  causes  no  change  in  its  motion,  but  simply  prevents  such  a  change 
being  produced  by  the  resistance  of  the  water  ;  or,  when  a  railway-train  is 
running  with  uniform  velocity,  the  force  of  the  engine  does  not  change,  but 
only  maintains  its  motion  in  opposition  to  the  forces,  such  as  friction  and  the 
resistance  of  the  air,  which  tend  to  destroy  it. 

These  two  classes  of  cases — namely,  first,  those  in  which  forces  cause  a 
change  of  motion  ;  and  secondly,  those  in  which  they  prevent,  wholly  or  in 
part,  such  a  change  being  produced  by  other  forces — include  all  the  effects 
to  which  the  action  of  forces  can  give  rise.  When  acting  in  either  of  these 
ways,  a  force  is  said  to  do  'work  :  an  expression  which  is  used  scientifically 
in  a  sense  somewhat  more  precise,  but  closely  accordant  with  that  in  which 
it  is  used  in  common  language.  A  little  reflection  will  make  it  evident  that, 
in  all  cases  in  which  we  are  accustomed  to  speak  of  work  being  done — 
whether  by  men,  horse-power,  or  steam-power,  and  however  various  the  pro- 
ducts may  be  in  different  cases — the  physical  part  of  the  process  consists  solely 
in  producing  or  changing  motion,  or  in  keeping  up  motion  in  opposition  to 
resistance,  or  in  a  combination  of  these  actions.  The  reader  will  easily 
convince  himself  of  this  by  calling  to  mind  what  the  definite  actions  are  which 
constitute  the  work  done  by  (say)  a  navvy,  a  joiner,  a  mechanic,  a  weaver ;  that 
done  by  a  horse,  whether  employed  in  drawing  a  vehicle,  or  in  turning  a  gin  ; 
or  that  of  a  steam-engine,  whether  it  be  used  to  drag  a  railway-train  or  to 
drive  machinery.  In  all  cases  the  work  done  is  reducible,  from  a  mechanical 
point  of  view,  to  the  elements  that  have  been  mentioned,  although  it  maybe 
performed  on  different  materials,  with  different  tools,  and  with  different 
degrees  of  skill. 

It  is,  moreover,  easy  to  see  (comp.  52)  that  any  possible  change  01 
motion  may  be  represented  as  a  gain  by  the  moving  body  of  an  additional 
(positive  or  negative)  velocity  either  in  the  direction  of  its  previous  motion, 
or  at  right  angles  to  it ;  but  a  body  which  gains  velocity  is  (27)  said  to  be 
accelerated.  Hence,  what  has  been  said  above  may  be  summed  up  as 
follows  : — When  a  force  produces  acceleration,  or  when  it  maintains  motion 
unchanged  in  opposition  to  resistance,  it  is  said  to  do  WORK. 

61.  Measure  of  Work. — In  considering  how  work  is  to  be  measured, 
or  how  the  relation  between  different  quantities  of  work  is  to  be  expressed 
numerically,  we  have,  in  accordance  with  the  above,  to  consider  first,  work 
of  acceleration  ;  and  secondly,  work  against  resistance.  But  in  order  to  make 
the  evaluation  of  the  two  kinds  of  work  consistent,  we  must  bear  in  mind 
that  one  and  the  same  exertion  of  force  will  result  in  work  of  either  kind 
according  to  the  conditions  under  which  it  takes  place  :  thus,  the  force  of 
gravity  acting  on  a  weight  let  fall  from  the  hand  causes  it  to  move  with  a 
continually  accelerated  velocity  until  it  strikes  the  ground  ;  but  if  the  same 
weight,  instead  of  being  allowed  to  fall  freely  through  the  air,  be  hung  to  a 
cord  passing  round  a  cylinder  by  means  of  which  various  degrees  of  friction 
can  be  applied  to  hinder  its  descent,  it  can  be  made  to  fall  with  a  very  small 
and  practically  uniform  velocity.  Hence,  speaking  broadly,  it  may  be  said 
that,  in  the  former  case,  the  work  done  by  gravity  upon  the  weight  is  work  of 


44  On  Matter,  Force,  and  Motion.  [61  - 

acceleration  only,  while  in  the  latter  case  it  is  work  against  resistance  (friction) 
only.  But  it  is  very  important  to  note  that  an  essential  condition,  without 
which  a  force,  however  great,  cannot  do  work  either  of  one  kind  or  the  other, 
is  that  the  thing  acted  on  by  it  shall  move  while  the  force  continues  to  act. 
This  is  obvious,  for  if  no  motion  takes  place  it  clearly  cannot  be  either 
accelerated  or  maintained  against  resistance.  The  motion  of  the  body  on 
which  a  force  acts  being  thus  necessarily  involved  in  our  notion  of  work 
being  done  by  the  force,  it  naturally  follows  that,  in  estimating  how  much 
work  is  done,  we  should  consider  how  much — that  is  to  say,  how  far — the 
body  moves  while  the  force  acts  upon  it.  This  agrees  with  the  mode  of 
estimating  quantities  of  work  in  common  life,  as  will  be  evident  if  we  consider 
a  very  simple  case — for  instance,  that  of  a  labourer  employed  to  carry  bricks 
up  to  a  scaffold  :  in  such  a  case  a  double  number  of  bricks  carried  would 
represent  a  double  quantity  of  work  done,  but  so  also  would  a  double  height 
of  the  scaffold,  for  whatever  amount  of  work  is  done  in  raising  a  certain 
number  to  a  height  of  twenty  feet,  the  same  amount  must  be  done  again  to 
raise  them  another  twenty  feet,  or  the  amount  of  work  done  in  raising  the , 
bricks  forty  feet  is  twice  as  great  as  that  done  when  they  are  raised  only 
twenty  feet.  It  is  also  to  be  noted  that  no  direct  reference  to  time  enters 
into  the  conception  of  a  quantity  of  work  :  if  we  want  to  know  how  much 
work  a  labourer  has  done,  we  do  not  ask  how  long  he  has  been  at  work,  but 
what  he  has  done — for  instance,  how  many  bricks  he  has  carried,  and  to  what 
height ; — and  our  estimate  of  the  total  amount  of  work  is  the  same  whether 
the  man  has  spent  hours  or  days  in  doing  it. 

The  foregoing  relations  between  force  and  work  may  be  put  into  definite 
mathematical  language  as  follows  : — If  the  point  of  application  of  a  force: 
moves  in  a  straight  line,  and  if  the  part  of  the  force  resolved  along  this  line ; 
acts  in  the  direction  of  the  motion,  the  product  of  that  component  and  the  \ 
length  of  the  line  is  the  work  done  by  the  force.  If  the  component  acts  in  J 
the  opposite  direction  to  the  motion,  the  component  may  be  considered  as  a  •' 
resistance  and  the  product  is  work  done  against  the  resistance.  Thus,  inl 
(43),  if  we  suppose  a  to  move  up  the  plane  from  R  to  S,  the  work  done  by  P 
is  P  x  RS  ;  the  work  done  against  the  resistance  W  is  W  sin  .r  x  RS.  It  willl 
be  observed  that  if  the  forces  are  in  equilibrium  during  the  motion,  so  that] 
the  velocity  of  a  is  uniform,  P  equals  W  sin  x,  and  consequently  the  work  < 
done  by  the  power  equals  that  done  against  the  resistance.  Also  since  RSI 
sin  x  equals  ST,  the  work  done  against  the  resistance  equals  W  x  ST.  In; 
other  words,  to  raise  W  from  R  to  S  requires  the  same  amount  of  work  as  to] 
raise  it  from  T  to  S. 

If,  however,  the  forces  are  not  in  equilibrium,  the  motion  of  a  will  not  bel 
uniform,  but  accelerated  ;  the  work  done  upon  it  will  nevertheless  still  bej 
represented  by  the  product  of  the  force  into  the  distance  through  which  itl 
acts.  In  order  to  ascertain  the  relation  between  the  amount  of  work  donel 
and  the  change  produced  by  it  in  the  velocity  of  the  moving  mass,  we  must! 
recall  one  or  two  elementary  mechanical  principles.  Let  F  be  the  resultant^ 
force  resolved  along  the  direction  of  motion,  and  S  the  distance  throughj 
which  its  point  of  application  moves  :  then,  according  to  what  has  been  said,! 
the  work  done  by  the  force  =  FS.  Further,  it  has  been  pointed  out  (29)  thatl 
a  constant  force  is  measured  by  the  momentum  produced  by  it  in  a  unit  ofl 


-61]  Measure  of  Work.  45 

time  :  hence,  if  T  be  the  time  during  which  the  force  acts,  V  the  velocity  of 
the  mass  M  at  the  beginning  of  this  period,  and  Vl  the  velocity  at  the  end, 
the  momentum  produced  during  the  time  T  is  MVX  —  MV,  and  conse- 
quently the  momentum  produced  in  a  unit  of  time,  or,  in  other  words,  the 
measure  of  the  force,  is 


_ 

The  distance  S  through  which  the  mass  M  moves  while  its  velocity 
changes  from  the  value  V  to  the  value  Vl  is  the  same  as  if  it  had  moved 
during  the  whole  period  T  with  a  velocity  equal  to  the  average  value  of  the 
varying  velocity  which  it  actually  possesses.  But  a  constant  force  acting 
upon  a  constant  mass  causes  its  velocity  to  change  at  a  uniform  rate  ;  hence, 
in  the  present  case,  the  average  velocity  is  simply  the  arithmetical  mean  of 
the  initial  and  final  velocities,  or 


Combining  this  with  the  last  equation,  we  get  as  the  expression  for  the 
work  done  by  the  force  F  : 


or,  in  words,  when  a  cojistant  force  acts  on  a  mass  so  as  to  change  its  velocity, 
the  work  done  by  the  force  is  equal  to  half  the  product  of  the  mass  into  the 
change  of  the  square  of  the  velocity. 

The  foregoing  conclusion  has  been  arrived  at  by  supposing  the  force  F 
to  be  constant,  but  it  is  easy  to  show  that  it  holds  good  equally  if  F  is  the 
average  magnitude  of  a  force  which  varies  from  one  part  to  another  of  the 
total  distance  through  which  it  acts.  To  prove  this,  let  the  distance  S  be 
subdivided  into  a  very  great  number  n  of  very  small  parts  each  equal  to  s, 
so  that  ns  =  S.  Then  by  supposing  s  to  be  sufficiently  small,  we  may  with- 
out any  appreciable  error  consider  the  force  as  constant  within  each  of  these 
intervals  and  as  changing  suddenly  as  .its  point  of  application  passes  from 
one  interval  to  the  next.  Let  F15  F2,  F3  .  .  .  .  F«,  be  the  forces  acting 
throughout  the  ist,  2nd,  3rd  .  .  .  «th  interval  respectively,  and  let  the 
velocity  at  the  end  of  the  same  intervals  be  vlt  -z'2,  vs,  .  .  .  .  vn  (  =  Vj), 
respectively  ;  then,  for  the  work  done  in  the  successive  intervals,  we 
have  — 


or,  for  the  total  work, 


46  On  Matter,  Force,  and  Motion.  [61- 

where  the  quantity  of  the  left-hand  side  of  the  equation  may  also  be  written 

i        0+    •    •    ~*~    nns  =  YS,  if  we  put  F  to  stand  for  the  average  (or  arith- 

n 
metical  mean)  of  the  forces  F1}  F2,  &c. 

An  important  special  case  of  the  application  of  the  above  formula  arises 
when  either  the  initial  or  the  final  velocity  of  the  mass  M  is  nothing  ;  that  is 
to  say,  when  the  effect  of  the  force  is  to  make  a  body  pass  from  a  state  of 
rest  into  one  of  motion,  or  from  a  state  of  motion  into  one  of  rest.  The 
general  expression  then  assumes  one  of  the  following  forms,  namely  :  — 

FS=|MV12  or, 


the  first  of  which  denotes  the  quantity  of  work  which  must  be  done  on  a  body 
of  mass  M  in  order  to  give  to  it  the  velocity  V15  while  the  second  expresses 
the  work  that  must  be  done  in  order  to  bring  the  same  mass  to  rest  when  it 
is  moving  with  the  velocity  V0,  the  negative  sign  in  the  latter  case  showing 
that  the  force  here  acts  in  opposition  to  the  actual  motion,  and  is  therefore 
to  be  regarded  as  a  resistance. 

In  practice,  the  case  which  most  frequently  occurs  is  where  work  of  ac- 
celeration and  work  against  resistance  are  performed  simultaneously.  Thus, 
recurring  to  the  inclined  plane  already  referred  to  in  art.  43  ;  if  the  force  P 
(where  P  is  the  constant  force  with  which  the  string  pulls  W  up  the  plane) 
be  greater  than  W  sin  x,  the  body  W  will  move  up  the  incline  with  a  con- 
tinually increasing  velocity,  and  if  the  point  of  application  of  P  be  displaced 
from  R  to  S,  the  total  amount  of  work  done,  namely,  P  x  RS,  consists  of  a 
portion  =  W  sin  x  RS,  done  against  the  resistance  of  the  weight  W,  and  of  a 
portion  =  (P  —  W  sin  x]  RS  expended  in  accelerating  the  weight.  Hence,  to 
determine  the  velocity  v  with  which  W  arrives  at  the  top  of  the  incline  we 
have  the  equation 

(P~-Wsin;r)  RS  =  £\W; 

for  the  portion  of  P  which  is  in  excess  of  what  is  required  to  produce  equili- 
brium with  the  weight  W,  namely,  P—  W  sin  .r,  corresponds  to  the  resultant 
force  F  supposed  in  the  foregoing  discussion,  and  RS  to  the  distance  through 
which  this  resultant  force  acts. 

62.  Unit  of  Work,  —  For  strictly  scientific  purposes  a  unit  of  work  is 
taken  to  be  the  work  done  by  a  unit  of  force  when  its  point  of  application 
moves  through  one  foot  in  the  direction  of  its  action  ;  but,  as  a  convenient 
and  sufficiently  accurate  standard  for  practical  purposes,  the  quantity  of  work 
which  is  done  in  lifting  I  pound  through  the  height  of  I  foot  is  commonly 
adopted  as  the  unit,  and  this  quantity  of  work  is  spoken  of  as  one  '  foot- 
pound.' It  is,  however,  important  to  observe  that  the  foot-pound  is  not  per- 
fectly invariable,  since  the  weight  of  a  pound,  and  therefore  the  work  done 
in  lifting  it  through  a  given  height,  differs  at  different  places  ;  being  a  little 
greater  near  the  Poles  than  near  the  Equator. 

On  the  metrical  system  the  kilogrammetre  is  the  unit  ;  it  is  the  weight  of 
a  kilogramme  raised  through  a  height  of  a  metre.  This  is  equal  to  7-24 
foot-pounds,  and  one  foot-pound  =  -1381  of  a  kilogrammetre. 


_64]  Varieties  of  Energy.  47 

63.  Energy. — The  fact  that  any  agent  is  capable  of  doing  work  is  usually 
expressed  by  saying  that  it  possesses  Energy,  and  the  quantity  of  energy  it 
possesses  is  measured  by  the  amount  of  work  it  can  do.  For  example,  in 
the  case  of  the  inclined  plane  above  referred  to,  the  working  power  or  energy 
of  the  force  P  is  P  x  RS  ;  and  if  this  force  acts  under  the  conditions  last 
supposed,  by  the  time  its  own  energy  is  exhausted  (in  consequence  of  its 
point  of  application  having  arrived  at  S,  the  limit  of  the  range  through  which 
it  is  supposed  able  to  act),  it  has  conferred  upon  the  weight  W  a  quantity  of 
energy  equal  to  that  which  has  been  expended  ;  for,  in  the  first  place,  W 
has  been  raised  through  a  vertical  height  equal  to  ST,  and  could  by  falling 
again  through  the  same  height  do  an  amount  of  work  represented  by  W  x  ST  ; 
and  in  the  second  place  W  can  do  work  by  virtue  of  the  velocity  that  has 
been  imparted  to  it,  and  can  continue  moving  in  opposition  to  any  given 
resistance  R  through  a  distance  s,  such  that 


The  energy  possessed  by  the  mass  M  in  consequence  of  having  been  raised 
from  the  ground  is  commonly  distinguished  as  energy  of  position  vr  potential 

energy,  and  is  measured  by  the  product  of  the  force  tending  to  cause  motion 
into  the  distance  through  which  the  point  of  application  of  the  force  is 
capable  of  being  displaced  in  the  direction  in  which  the  force  acts.  The 
energy  possessed  by  a  body  in  consequence  of  its  velocity,  is  commonly  dis- 
tinguished as  energy  of  motion  or  kinetic  energy  :  it  is  measured  by  half  the 
product  of  the  moving  mass  into  the  square  of  its  velocity. 

64.  Varieties  of  Energy. — It  will  be  seen,  on  considering  the  definition 
of  work  given  above,  that  a  force  is  said  to  do  work  when  it  produces  any 
change  in  the  condition  of  bodies  ;  for  the  only  changes  which,  according  to 
the  definition  of  force  given  previously  (26),  a  force  is  capable  of  producing, 
are  changes  in  the  state  of  rest  or  motion  of  bodies  and  changes  of  their 
place  in  opposition  to  resistances  tending  to  prevent  motion  or  to  produce 
motion  in  an  opposite  direction.  There  are,  however,  many  other  kinds  of 
physical  changes  which  can  be  produced  under  appropriate  conditions,  and 
the  recent  progress  of  investigation  has  shown  that  the  conditions  under 
which  changes  of  all  kinds  occur  are  so  far  analogous  to  those  required  for 
the  production  of  work  by  mechanical  forces  that  the  term  work  has  come 
to  be  used  in  a  more  extended  sense  than  formerly,  and  is  now  often  used  to 
signify  the  production  of  any  sort  of  physical  change. 

Thus  work  is  said  to  be  done  when  a  body  at  a  low  temperature  is  raised 
to  a  higher  temperature,  just  as  much  as  when  a  weight  is  raised  from  a 
lower  to  a  higher  level ;  or  again,  work  is  done  when  any  electrical,  magnetic, 
or  chemical  change  is  produced.  This  extension  of  the  meaning  of  the  term 
work  involves  a  similar  extension  of  the  meaning  of  energy,  which  in  this  wider 
sense  may  be  defined  as  the  capacity  for  producing  physical  change. 

As  examples  of  energy  in  this  more  general  sense  the  following  may  be 

•  mentioned  : — (a]  the  energy  possessed  by  gunpowder  in  virtue  of  the  mutual 
chemical  affinities  of  its  constituents,  whereby  it  is  capable  of  doing  work  by 
generating  heat  or  by  acting  on  a  cannon-ball  so  as  to  change  its  state  of 
rest  into  one  of  rapid  motion  ;  (b]  the  energy7  of  a  charged  Leyden  jar  which, 
according  to  the  way  in  which  the  jar  is  discharged,  can  give  rise  to  changes 


48  On  Matter,  Force,  and  Motion.  [64- 

of  temperature,  to  changes  of  chemical  composition,  to  mechanical  changes, 
or  to  changes  of  magnetic  or  electrical  condition  ;  (c}  the  energy  of  a  red-hot 
ball  which,  amongst  other  effects  it  is  capable  of  producing,  can  raise  the 
temperature  and  increase  the  volume  of  bodies  colder  than  itself,  or  can 
change  ice  into  water  or  water  into  steam ;  the  energy  of  the  stretched 
string  of  a  bow ;  here  work  has  been  consumed  in  stretching  the  string  ; 
when  it  is  released  the  work  reappears  in  the  velocity  imparted  to  the  arrow. 

65.  Transformation*  of  Energy. — It  has  been  found  by  experiment 
that  when  one  kind  of  energy  disappears  or  is  expended,  energy  of  some 
other  kind  is  produced,  and  that,  under  proper  conditions,  the  disappearance 
of  any  one  of  the  known  kinds  of  energy  can  be  made  to  give  rise  to  a  greater 
or  less  amount  of  any  other  kind.  One  of  the  simplest  illustrations  that  can 
be  given  of  this  transformation  of  energy  is  afforded  by  the  oscillations  of  a 
pendulum.  When  the  pendulum  is  at  rest  in  its  lowest  position  it  does  not 
possess  any  energy,  for  it  has  no  power  of  setting  either  itself  or  other  bodies 
in  motion  or  of  producing  in  them  any  kind  of  change.  In  order  to  set  the 
pendulum  oscillating,  work  must  be  done  upon  it,  and  it  thereafter  possesses 
an  amount  of  energy  corresponding  to  the  work  that  has  been  expended. 
When  it  has  reached  either  end  of  its  path,  the  pendulum  is  for  an  instant  at 
rest,  but  it  possesses  energy  by  virtue  of  its  position,  and  can  do  an  amount  of 
work  while  falling  to  its  lowest  position  which  is  represented  by  the  product 
of  its  weight  into  the  vertical  height  through  which  its  centre  of  gravity  de- 
scends. When  at  the  middle  of  its  path  the  pendulum  is  passing  through  its 
position  of  equilibrium  and  has  no  power  of  doing  work  by  falling  lower  ; 
but  it  now  possesses  energy  by  virtue  of  the  velocity  which  it  has  gained,  and 
this  energy  is  able  to  carry  it  up  on  the  second  side  of  its  lowest  position  to 
a  height  equal  to  that  from  which  it  has  descended  on  the  first  side.  By  the 
time  it  reaches  this  position  the  pendulum  has  lost  all  its  velocity,  but  it  has 
regained  the  power  of  falling  :  this,  in  its  turn,  is  lost  as  the  pendulum  returns 
again  to  its  lowest  position,  but  at  the  same  time  it  regains  its  previous 
velocity.  Thus  during  every  quarter  of  an  oscillation,  the  energy  of  the 
pendulum  changes  from  potential  energy  of  position,  into  actual  energy  or 
energy  of  motion,  or  vice  versa. 

A  more  complex  case  of  the  transformation  of  energy  is  afforded  by  a 
thermo-electric  pile,  the  terminals  of  which  are  connected  by  a  conducting 
wire  :  the  application  of  energy  in  the  form  of  heat  to  one  face  of  the  pile 
gives  rise  to  an  electric  current  in  the  wire,  which,  in  its  turn,  reproduces 
heat,  or  by  proper  arrangements  can  be  made  to  produce  chemical,  magnetic, 
or  mechanical  effects,  such  as  those  described  below  in  the  chapters  on 
Electricity. 

It  has  also  been  found  that  the  transformations  of  energy  always  take 
place  according  to  fixed  proportions.     For  instance,  when  coal  or  any  other 
combustible  is  burned,  its  chemical  energy,  or   power  of  combining  with  j 
oxygen,  vanishes,  and  heat  or  thermal  energy  is  produced,  and  the  quantity 
of  heat  produced  by  the  combustion  of  a  given  amount  of  coal  is  fixed  and  I 
invariable.     If  the  combustion  take  place  under  the  boiler  of  a  steam-engine,  : 
mechanical  work  can  be  obtained  by  the  expenditure  of  part  of  the  heat  pro- 
duced, and  here  again  the  quantitative  relation  between  the  heat  expended 
and  the  work  gained  in  place  of  it  is  perfectly  constant. 


-66]  Conservation  of  Energy.  49 

66.  Conservation  of  Energy. — Another  result  of  great  importance  which 
has  been  arrived  at  by  experiment  is  that  the  total  amount  of  energy  possessed 
by  any  system  of  bodies  is  unaltered  by  any  transformations  arising  from  the 
action  of  one  part  of  the  system  upon  another,  and  can  only  be  increased  or 
diminished  by  effects  produced  on  the  system  by  external  agents.  In  this 
statement  it  is  of  course  understood  that  in  reckoning  the  sum  of  the  energy 
of  various  kinds  which  the  system  may  possess,  those  amounts  of  the 
different  forms  of  energy  which  are  mutually  convertible  into  each  other  are 
taken  as  being  numerically  equal ;  or,  what  comes  virtually  to  the  same 
thing,  the  total  energy  of  the  system  is  supposed  to  be  reduced — either  ac- 
tually, or  by  calculation  from  the  known  ratio  of  transformation  of  the  various 
forms  of  energy — to  energy  of  some  one  kind  ;  then  the  statement  is  equivalent 
to  this  :  that  the  total  energy  of  any  one  form  to  which  the  energy  of  a  given 
system  of  bodies  is  reducible  is  unalterable  so  long  as  the  system  is  not  acted 
on  from  without.  Practically  it  is  always  possible,  in  one  way  or  another,  to 
convert  the  whole  of  the  energy  possessed  by  any  body  or  system  of  bodies 
into  heat,  but  it  cannot  be  all  converted  without  loss  into  any  other  form  of 
energy  ;  hence  the  principle  stated  at  the  beginning  of  this  article  can  be 
enunciated  in  the  closest  conformity  with  the  direct  results  of  experiment,  by 
saying  that,  so  long  as  any  system  of  bodies  is  not  acted  on  from  without, 
the  total  quantity  of  heat  that  can  be  obtained  from  it  is  unalterable  by  any 
changes  which  may  go  on  within  the  system  itself.  For  instance,  a  quantity 
of  air  compressed  into  the  reservoir  of  an  air-gun  possesses  energy  which  is 
represented  partly  by  the  heat  which  gives  to  it  its  actual  temperature  above 
the  absolute  zero  (460),  and  partly  by  the  work  which  the  air  can  do  in  expand- 
ing. This  latter  portion  can  be  converted  into  heat  in  various  ways  ;  as,  for 
example,  by  allowing  the  air  to  escape  through  a  system  of  capillary  tubes, 
so  fine  that  the  air  issues  from  them  without  any  sensible  velocity.  If,  how- 
ever, the  expanding  air  be  employed  to  propel  a  bullet  from  the  gun,  it 
produces  considerably  less  heat  than  in  the  case  previously  supposed,  the 
deficiency  being  represented  for  a  time  by  the  energy'  of  the  moving  bullet, 
but  reappearing  in  the  form  of  heat  in  the  friction  of  the  bullet  against  the 
air,  and,  when  the  motion  of  the  bullet  is  destroyed,  by  striking  against  an 
inelastic  obstacle  at  the  same  level  as  the  gun.  But  whatever  the  mode  and 
however  numerous  the  intermediate  steps  by  which  the  energy  of  the  com- 
pressed air  is  converted  into  heat,  the  total  quantity  of  heat  finally  obtainable 
from  it  is  the  same. 


Gravitation  and  Molecular  Attraction.  [67- 


BOOK   II. 

GRAVITATION   AND   MOLECULAR   ATTRACTION. 


CHAPTER    I. 
GRAVITY.      CENTRE  OF  GRAVITY.      THE   BALANCE. 

67.  Universal  Attraction;  its  Laws. —  Universal  attraction  is  a  force  in 
virtue  of  which  the  material  particles  of  all  bodies  tend  incessantly  to  ap- 
proach each  other ;  it  is  a  mutual  action,  however,  which  all  bodies,  at  rest 
or  in  motion,  exert  upon  one  another,  no  matter  how  great  or  how  small  the 
space  between  them  may  be,  or  whether  this  space  be  occupied  or  unoccu- 
pied by  other  matter. 

A  vague  hypothesis  of  the  tendency  of  the  matter  of  the  earth  and  stars 
to  a  common  centre  was  adopted  even  by  Democritus  and  Epicurus.  Kepler 
assumed  the  existence  of  a  mutual  attraction  between  the  sun,  the  earth,  and 
the  other  planets.  Bacon,  Galileo,  and  Hooke  also  recognised  the  existence 
of  universal  attraction.  But  Newton  was  the  first  who  established  the  law, 
and  the  universality  of  gravitation. 

Since  Newton's  time  the  attraction  of  matter  by  matter  was  experiment- 
ally established  by  Cavendish.  This  eminent  English  physicist  succeeded 
by  means  of  a  delicate  torsion  balance  (90)  in  rendering  visible  the  attraction 
between  a  large  leaden  and  a  small  copper  ball. 

The  attraction  between  any  two  bodies  is  the  resultant  of  the  attractions 
of  each  molecule  of  the  one  upon  every  molecule  of  the  other  according  to 
the  law  of  Newton,  which  may  be  thus  expressed  :  the  attraction  between 
two  material  particles  is  directly  proportional  to  the  product  of  their  masses 
and  inversely  proportional  to  the  square  of  their  distajices  asunder.  To 
illustrate  this,  we  may  take  the  case  of  two  spheres  which,  owing  to  their 
symmetry,  attract  each  other  just  as  if  their  masses  were  concentrated  in 
their  centres.  If  without  other  alteration  the  mass  of  one  sphere  were 
doubled,  tripled,  &c.,  the  attraction  between  them  would  be  doubled,  tripled, 
&c.  If,  however,  the  mass  of  one  sphere  being  doubled,  that  of  the  other 
were  increased  three  times,  the  distance  between  their  centres  remaining  the 
same,  the  attraction  would  be  increased  six  times.  Lastly,  if,  without  alter- 
ing their  masses,  the  distance  between  their  centres  were  increased  from  i  to 
2,  3,  4>  •  •  •  •  units,  the  attraction  would  be  diminished  to  the  4th, 


-68]  Terrestrial  Gravitation.  5 1 

9th,  1 6th,  ....  part  of  its  former  intensity.  In  short,  if  we  define  the 
unit  of  attraction  as  that  which  would  exist  between  two  units  of  mass 
whose  distance  asunder  was  the  unit  of  length,  the  attraction  of  two  mole- 
cules, having  the  masses  m  and  /«',  at  the  distance  r,  would  be  expressed  by 
ni  in' 
r2 

68.  Terrestrial  gravitation. — The  tendency  of  any  body  to  fall  towards 
the  earth  is  due  to  the  mutual  attraction  of  that  body  and  the  earth,  or  to 
terrestrial  gravitation,  and  is,  in  fact,  merely  a  particular  case  of  universal 
gravitation. 

At  any  point  of  the  earth's  surface,  the  direction  of  gravity — that  is,  the 
line  which  a  falling  body  describes — is  called  the  vertical  line.  The  vertical 
lines  drawn  at  different  points  of  the  earth's  surface  converge  very  nearly  to 
the  earth's  centre.  For  points  situated  on  the  same  meridian  the  angle  con- 
tained between  the  vertical  lines  equals  the  difference  between  the  latitudes 
of  those  points. 

The  directions  of  the  earth's  attraction  upon  neighbouring  bodies,  or  upon 
different  molecules  of  one  and  the  same  body,  must,  therefore,  be  considered 
as  parallel,  for  the  two  vertical  lines  form  the  sides  of  a  triangle  whose  vertex 
is  near  the  earth's  centre,  about  4,000  miles  distant,  and  whose  base  is  the 
small  distance  between  the  molecules  under  consideration. 

A  plane  or  line  is  said  to  be  horizontal  when  it  is  perpendicular  to  the 
vertical  line. 

The  vertical  line  at  any  point  of  the  globe  is  generally  determined  by  the 
phnnb-line  (fig.  41),  -which  consists  of  a  weight  attached  to  the  end  of  a  string. 
It  is  evident  that  the  weight  cannot  be  in  equilibrium,  un- 
less the  direction  of  the  earth's  attraction  upon  it  passes 
through  the  point  of  support,  and  therefore  coincides  with 
that  of  the  string.  .  .  . 

The  horizontal  plane  is  also  determined  with  great 
ease,  since  it  coincides,  as  will  be  afterwards  shown,  with 
the  Imel  surface  of  every  liquid  when  in  a  state  of  equili- 
brium. 

When  the  mean  figure  of  the  earth  has  been  approxi- 
mately determined,  it  becomes  possible  to  compare  the 
direction  of  the  plumb-line  at  any  place  with  that  of  the 
normal  to  the  mean  figure  at  that  place.  When  any  differ- 
ence in  these  directions  can  be  detected,  it  constitutes  a  9 
deviation  of  the  plumb-line,  and  is  due  to  the  attraction  of  Flg-  4I< 

some  great  mass  of  matter  in  the  neighbourhood,  swch  as  a  mountain. 
Thus,  in  the  case  of  the  mountain  of  Schehallien,  in  Perthshire,  it  was  found 
by  Dr.  Maskelyne  that  the  angle  between  the  directions  of  two  plumb-lines, 
one  at  a  station  to  the  north,  and  the  other  to  the  south,  of  the  mountain, 
was  greater  by  1 1"6  than  the  angle  between  the  normals  of  the  mean  surface 
of  the  earth  at  those  points  ;  in  o.ther  words,  each  plumb-line  was  deflected 
by  about  6"  towards  the  mountain.  By  calculating  the  volume  and  mass  of 
the  mountain,  it  was  inferred  from  this  observation  that  the  mean  density  of 
the  mountain  was  to  that  of  the  earth  in  the  ratio  of  5  :  9,  and  that  the  mean 
density  of  the.  earth  is  about  five  times. that  of. water — a  result  agreeing 

D    2  ^^? 

rtp*  or  TH*^<$\ 

IUII7BRSITT1 


Gravitation  and  Molecular  A  ttraction. 


[68- 


pretty  closely  with  that  deduced  from  Cavendish's  experiments  referred  to  in 
the  last  article. 

69.  Centre  of  gravity,  its  experimental  determination. — Into  what- 
ever position  a  body  may  be  turned  with  respect  to  the  earth,  there  is  a 
certain  point,  invariably  situated  with  respect  to  the  body,  through  which 
the  resultant  of  the  attracting  forces  between  the  earth  and  its  several  mole- 
cules always  passes.  This  point  is  called  the  centre  of  gravity  ;  it  may  be 
within  or  without  the  body,  according  to  the  form  of  the  latter  ;  its  existence, 
however,  is  easily  established  by  the  following  considerations  :  Let  m  m'  m" 


Fig.  42. 


Fig.  43- 


m"'.  .  .  (fig.  42)  be  molecules  of  any  body.  The  earth's  attraction  upon 
these  molecules  will  constitute  a  system  of  parallel  forces,  having  a  common 
vertical  direction,  whose  resultant,  according  to  (36)  will  be  found  by  seek- 
ing first  the  resultant  of  the  forces  which  act  on  any  two  molecules,  m  and 
m\  then  that  of  this  resultant,  and  a  third  force  acting  on  ;«",  and  so  on 
until  we  arrive  at  the  final  resultant,  W,  representing  the  weight  of  the  body, 
and  applied  at  a  certain  point,  G.  If  the  body  be  now  turned  into  the 
position  shown  in  fig.  43,  the  molecules  ;;/,  ?/z',  m".  .  ,  will  continue  to  be 
acted  on  by  the  same  forces  as  before,  the  resultant  of  the  forces  on  m  and 
m'  will  still  pass  through  the  same  point  o  in  the  line  mm',  the  following  re- 
sultant will  again  pass  through  the  same  point  o'  in  om",  and  so  on  up  to  the 
final  resultant  P,  which  will  still  pass  through  the  same  point  G,  which  is 
the  centre  of  gravity. 

To  find  the  centre  of  gravity  of  a  body  is  a  purely  geometrical  problem  ; 
in  many  cases,  however,  it  can  be  at  once  determined.  For  instance,  the 
centre  of  gravity  of  a  right  line  of  uniform  density  is  the  point  which  bisects 
its  length ;  in  the  circle  and  sphere  it  coincides  with  the  geometrical  centre ; 
in  cylindrical  bars  it  is  the  middle  point  of  the  axis.  The  centre  of  gravity 
of  a  plane  triangle  ts  in  the  line  which  joins  any  vertex  with  the  middle  of  the 
opposite  side,  and  at  a  distance  from  the  vertex  equal  to  two-thirds  of  this 
line :  in  a  cone  or  pyramid  it  is  in  the  line  which  joins  the  vertex  with  the 
centre  of  gravity  of  the  base,  and  at  a  distance  from  the  vertex  equal  to  three- 
fourths  of  this  line.  These  rules,  it  must  be  remembered,  presuppose  that 
the  several  bodies  are  of  uniform  density. 

In  order  to  determine  experimentally  the  centre  of  gravity  of  a  body,  it 
is  suspended  by  a  string  in  two  different  positions,  as  shown  in  figs.  44  and 
45  ;  the  point  where  the  directions  AB  and  CD  of  the  string  in  the  two  ex- 
periments intersect  each  other  is  the  centre  of  gravity  required.  For  the 


-71] 


Different  States  of  Equilibrium. 


53 


Fig.  44. 


Fig.  45- 


resultant  of  the  earth's  attraction  being  a  vertical  force  applied  at  the  centre 
of  gravity,  the  body  can  only  be  in  equilibrium  when  this  point  lies  vertically 
under  the  point  of  suspension  ;  that  is,  in  the  prolongation  of  the  suspended 
string.  But  the  centre  of  gravity, 
being  in  AB  as  well  as  in  CD,  must 
coincide  with  the  point  of  intersec- 
tion of  these  two  lines. 

70.  Equilibrium      of      heavy 
bodies. — Since  the  action  of  gravity 
upon  a  body   reduces   itself  to   a 
single  vertical  force  applied  at  the 
centre  of  gravity  and  directed  to- 
wards  the    earth's    centre,   equili- 
brium will  be  established  only  when 
this  resultant  is   balanced   by  the 
resultant  of  other  forces  and  resist- 
ances acting  on   the  body  at  the 
fixed  point  through  which  it  passes. 

When  only  one  point  of  the 
body  is  fixed,  it  will  be  in  equili- 
brium if  the  vertical  line  through  its  centre  of  gravity  passes  through  the  fixed 
point.  If  more  than  one  point  is  supported,  the  body  will  be  in  equilibrium, 
if  a  vertical  line  through  the  centre  of  gravity  passes  through  a  point  within 
the  polygon  formed  by  joining  the  points  of  support. 

The  Leaning  Tower  of  Pisa  continues  to  stand  because  the  vertical  line 
drawn  through  its  centre  of  gravity  passes  within  its  base. 

It  is  easier  to  stand  on  our  feet  than  on  stilts,  because  in  the  latter  case 
the  smallest  motion  is  sufficient  to  cause  the  vertical  line  through  the  centre 
of  gravity  of  our  bodies  to  pass  outside  the  supporting  base,  which  is  here 
reduced  to  a  mere  line  joining  the  feet  of  the  stilts.  Again,  it  is  impossible 
to  stand  on  one  leg  if  we  keep  one  side  of  the  foot  and  head  close  to  a  vertical 
wall,  because  the  latter  prevents  us  from  throwing  the  body's  centre  of  gravity 
vertically  above  the  supporting  base. 

71.  Different  states  of  equilibrium. — Although  a  body  supported  by  a 
fixed  point  is  in  equilibrium  whenever  its  centre  of  gravity  is  in  the  vertical 
line  through  that  point,  the  fact  that  the  centre  of  gravity  tends  incessantly 
to  occupy  the  lowest  possible  position  leads  us  to  distinguish  between  three 
states  of  equilibrium — stable,  unstable,  neutral. 

A  body  is  said  to  be  in  stable  equilibrium  if  it  tends  to  return  to  its  first 
position  after  the  equilibrium  has  been  slightly  disturbed.  Every  body  is  in 
this  state  when  its  position  is  such  that  the  slightest  alteration  of  the  same 
elev*ates  its  centre  of  gravity ;  for  the  centre  of  gravity  will  descend  again 
when  permitted,  and  after  a  few  oscillations  the  body  will  return  to  its 
original  position. 

The  pendulum  of  a  clock  continually  oscillates  about  its  position  of  stable 
equilibrium,  and  an  egg  on  a  level  table  is  in  this  state  when  its  long  axis 
is  horizontal.  We  have  another  illustration  in  the  toy  represented  in  the 
adjoining  fig.  46.  A  small  figure  cut  in  ivory  is  made  to  stand  on  one  foot 
at  the  top  of  a  pedestal  by  being  loaded  with  two  leaden  balls,  a,  b,  placed 


54 


Gravitation  and  Molecular  A  ttraction. 


[71- 


sufficiently  low  to  throw  the   centre   of  gravity,  g,  of  the  whole  compound 
body  below  the  foot  of  the  figure.     After  being  disturbed  the  little  figure 
oscillates  like  a  pendulum,  having  its  point  of  suspen- 
sion at  the  toe,  and  its  centre  of  gravity  at  a  lower 
point,  g. 

A  body  is  said  to  be  in  unstable  equilibrium  when, 
after  the  slightest  disturbance,  it  tends  to  depart  still 
more  from  its  original  position.  A  body  is  in  this  state 
when  its  centre  of  gravity  is  vertically  above  the  point 
of  support,  or  higher  than  it  would  be  in  any  adjacent 


Fig.  46. 

position  of  the  body.  An.  egg  standing  on  its  end,  or  a  stick  balanced  upright 
on  the  finger,  is  in  this  state. 

Lastly,  if  in  any  adjacent  position  a  body  still  remains  in  equilibrium,  its 
state  of  equilibrium  is  said  to  be  neutral.  In  this  case  an  alteration  in  the 
position  of  the  body  neither  raises  nor  lowers  its  centre  of  gravity.  A  perfect 
sphere  resting  on  a  horizontal  plane  is  in  this  state. 

Fig.  47  represents  three  cones,  A,  B,  C,  placed  respectively  in  stable, 
unstable,  and  neutral  equilibrium  upon  a  horizontal  plane.  The  letter  g  in 
each  shows  the  position  of  the  centre  of  gravity. 

72.  The  balance. — The  balance  is  an  instrument  for  determining  the 
relative  weights  or  masses  of  bodies.  There  are  many  varieties. 

The  ordinary  balance  (fig.  48)  consists  of  a  lever  of  the  first  kind,  called 
the  beam,  AB,  with  its  fulcrum  in  the  middle  ;  at  the  extremities  of  the  beam 
are  suspended  two  scale  pans,  C  and  D,  one  intended  to  receive  the  object  to 
be  weighed,  and  the  other  the  counterpoise.  The  fulcrum  consists  of  a  steel 
prism,  n,  commonly  called  a  knife  edge,  which  passes  through  the  beam,  and 
rests  with  its  sharp  edge,  or  axis  of  suspension,  upon  two  supports  ;  these  are 
formed  of  agate,  in  order  to  diminish  the  friction.  A  needle  or  pointer  is 
fixed  to  the  beam,  and  oscillates  with  it  in  front  of  the  graduated  arc,  a  ; 
when  the  beam  is  perfectly  horizontal  the  needle  points  to  the  zero  of  the 
graduated  arc. 

Since  by  (40)  two  equal  forces  in  a  lever  of  the  first  kind  cannot  be  in 
equilibrium  unless  their  leverages  are  equal,  the  length  of  the  arms  ?zA  and 
«B  ought  to  remain  equal  during  the  process  of  weighing.  To  secure  this 
the  scales  are  suspended  from  hooks,  whose  curved  parts  have  sharp  edges, 
and  rest  on  similar  edges  at  the  ends  of  the  beam.  In  this  manner  the 
scales  are  in  effect  supported  on  mere  points,  which  remain  unmoved  during 
the  oscillations  of  the  beam.  This  mode  of  suspension  is  represented  in 
fig.  48. 


-73] 


Conditions  to  be  satisfied  by  a  Balance. 


55 


73.  Conditions  to  be  satisfied  by  a  balance. — A  good  balance  ought 
to  satisfy  the  following  conditions  : — 

5.  The  tiuo  arms  of  the  beam  ought  to  be  precisely  equal,  otherwise, 
according  to  the  principle  of  the  lever,  unequal  weights  will  be  required  to 
produce  equilibrium.  To  test  whether  the  arms  of  the  beam  are  equal, 
weights  are  placed  in  the  two  scales  until  the  beam  becomes  horizontal ; 
the  contents  of  the  scales  being  then  interchanged,  the  beam  will  remain 


B 


Fig.  48. 

horizontal  if  its  arms  are  equal,  but  if  not,  it  will  descend  on  the  side  of  the 
longer  arm. 

ii.  The  balance  ought  to  be  in  equilibrium  'when  the  scales  are  empty,  for 
otherwise  unequal  weights  must  be  placed  in  the  scales  in  order  to  produce 
equilibrium.  It  must  be  borne  in  mind,  however,  that  the  arms  are  not 
necessarily  equal,  even  if  the  beam  remains  horizontal  when  the  scales  are 
empty  ;  for  this  result  might  also  be  produced  by  giving  to  the  longer  arm 
the  lighter  scale. 

iii.  The  beam  being  horizontal,  its  centre  of  gravity  ought  to  be  in  the  same 


56  Gravitation  and  M'olecular  Attraction.  [73- 

vertical  line  with  the  edge  of  the  fulcrum,  and  a  little  below  the  latter,  for 
otherwise  the  beam  would  not  be  in  stable  equilibrium  (71). 

The  effect  of  changing  the  position  of  the  centre  of  gravity  may  be  shown 
by  means  of  a  beam  (fig.  49),  whose  fulcrum  being  the  nut  of  a  screw,  a,  can 
be  raised  or  lowered  by  turning  the  screw-head,  b. 

When  the  fulcrum  is  at  the  top  of  the  groove  c,  in  which  it  slides,  the 
centre  of  gravity  of  the  beam  is  below  its  edge,  and  the  latter  oscillates  freely 


Fig.  49. 

about  a  position  of  stable  equilibrium.  By  gradually  lowering  the  fulcrum 
its  edge  may  be  made  to  pass  through  the  centre  of  gravity  of  the  beam  when 
the  latter  is  in  neutral  equilibrium  ;  that  is  to  say,  it  no  longer  oscillates,  but 
remains  in  equilibrium  in  all  positions.  When  the  fulcrum  is  lowered  still 
more,  the  centre  of  gravity  passes  above  its  edge,  the  beam  is  in  a  state  of 
unstable  equilibrium,  and  is  overturned  by  the  least  displacement. 

74.  Delicacy  of  the  balance. — A  balance  is  said  to  be  delicate  when  a 
very  small  difference  between  the  weights  in  the  scales  causes  a  perceptible 
deflection  of  the  pointer. 

Let  A  and  B  (figs.  50  and  51)  be  the  points  from  which  the  scale  pans  are 
suspended,  and  C  the  axis  of  suspension  of  the  beam.  A,  B,  and  C  are 


Fig.  50. 

supposed  to  be  in  the  same  straight  line,  according  to  the  usual  arrangement. 
Suppose  weights  P  and  Q  to  be  in  the  pans,  suspended  from  A  and  B  re- 
spectively, and  let  G  be  the  centre  of  gravity  of  the  beam  ;  then  the  beam 
will  come  to  rest  in  the  position  shown  in  the  figure,  where  the  line  DCN  is 
vertical,  and  ECG  is  the  direction  of  the  pointer.  According  to  the  above 
statement,  the  greater  the  angle  ECD  for  a  given  difference  between  P  and  O, 
the  greater  is  the  delicacy  of  the  balance.  Draw  GN  at  right  angles  to  CG. 
Let  W  be  the  weight  of  the  beam,  then  from  the  properties  of  the  lever  it 
follows  that  measuring  moments  with  respect  to  C,  the  moment  of  P  equals 
the  sum  of  the  moments  of  Q  and  W,  a  condition  which  at  once  leads  to  the 
relation 

(P-Q)  AC  =  WxGN 


-75] 


Physical  and  Chemical  Balances. 


Now  it  is  clear  that  for  a  given  value  of  CG  the  angle  GCN  (that  is,  ECD, 
which  measures  the  delicacy)  is  great  as  GN  is  greater  :  and  from  the 
formula  it  is  clear  that  for  a  given  value  of  P  — Q  we  shall  have  GN  greater 
as  AC  is  greater,  and  as  \V  is  less.  Again,  for  a  given  value  of  GN  the  angle 
GCX  is  greater  as  CG  is  less.  Hence  the  means  of  rendering  a  balance 
delicate  are  : — 

i.  To  make  the  arms  of  the  balance  long. 

ii.  To  make  the  weight  of  the  beam  as  small  as  is  consistent  with  its 
rigidity. 

iii.  To  bring  tJte  centre  of  gravity  of  the  beam  a  very  little  below  the 
point  of  support. 

Moreover,  since  friction  will  always  oppose  the  action  of  the  force  that 
tends  to  preponderate,  the  balance  will  be  rendered  more  delicate  by  diminish- 


Fig.  52- 

ing  friction.  To  secure  this  advantage  the  edges  from  w^hich  the  beam  and 
scales  are  suspended  are  made  as  sharp  and  as  hard  as  possible,  and  the 
supports  on  which  they  rest  are  very  smooth  and  hard.  This  is  effected  by 
the  use  of  agate  knife  edges.  And,  further,  the  pointer  is  made  long,  since 
its  elongation  renders  a  given  deflection  more  perceptible  by  increasing  the 
arc  which  its  end  describes. 

75.  Physical  and  cbemical  balances. — Fig.  52  represents  one  of  the 
accurate  balances  ordinarily  used  for  chemical  analysis.  Its  sensitiveness  is 
such  that  when  charged  with  a  kilogramme  (1,000  grms.)  in  each  scale  an 
excess  of  a  milligramme  (y^oth  °f  a  §rm-)  m  either  scale  produces  a  very 
perceptible  deflection  of  the  index. 

In  order  to  protect  the  balance  from  air  currents,  dust,  and  moisture, 
it  is  always,  even  when  weighing,  surrounded  by  a  glass  case,  whose  front 

D3 


58  Gravitation  and  Molecular  Attraction.  [75- 

slides  up  and  down,  to  enable  the  operator  to  introduce  the  objects  to  be 
weighed.  Where  extreme  accuracy  is  desired  the  case  is  constructed  so 
that  the  space  may  be  exhausted  and  the  weighing  made  in  vacua. 

In  order  to  preserve  the  edge  of  the  fulcrum  as  much  as  possible,  the  whole 
beam,  BB,  with  its  fulcrum  K,  can  be  raised  from  the  support  on  which  the 
latter  rests  by  simply  turning  the  button  O  outside  the  case. 

The  horizontality  of  the  beam  is  determined  by  means  of  a  long  index, 
which  points  downwards  to  a  graduated  arc  near  the  foot  of  the  supporting 
pillar.  Lastly,  the  button  C  serves  to  alter  the  sensitiveness  of  the  balance  ; 
by  turning  it,  the  centre  of  gravity  of  the  beam  can  be  made  to  approach 
or  recede  from  the  fulcrum  (73). 

76.  Method  of  double  weighing. — Even  if  a  balance  be  not  perfectly 
accurate,  the  true  weight  of  a  body  may  still  be  determined  by  its  means.  To 
do  so,  the  body  to  be  weighed  is  placed  in  one  scale,  and  shot  or  sand  poured 
into  the  other  until  equilibrium  is  produced  ;  the  body  is  then  replaced 
by  known  weights  until  equilibrium  is  re-established.  The  sum  of  these 
weights  will  necessarily  be  equal  to  the  weight  of  the  body,  for,  acting  under 
precisely  the  same  circumstances,  both  have  produced  precisely  the  same 
effect. 

The  exact  weight  of  a  body  may  also  be  determined  by  placing  it  suc- 
cessively in  the  two  pans  of  a  balance,  and  then  deducing  its  true  weight. 

For,  having  placed  in  one  pan  the  body  to  be  weighed,  whose  true  weight 
is  x,  and  in  the  other  the  weight  p,  required  to  balance  it,  let  a  and  b  be 
the  arms  of  levers  corresponding  to  x  and  p.  Then  from  the  principle  of 
the  lever  (40)  we  have  ax=pb.  Similarly  if/!  is  the  weight  when  the 
body  is  placed  in  the  other  pan,  then  bx  =  apr  Hence  abx*  =  abpp^  from 
which  x  •= 


-77] 


Laws  of  Falling  Bodies. 


59 


LAWS   OF   FALLING   BODIES. 


CHAPTER    II. 

INTENSITY  OF  TERRESTRIAL  GRAVITY. 
PENDULUM. 


THE 


77.  Laws  of  falling  bodies. — Since  a  body  falls  to  the  ground  in  conse- 
quence of  the  earth's  attraction  on  each  of  its  molecules,  it  follows  that 
everything  else  being  the  same,  all  bodies,  great  and 
small,  light  and  heavy,  ought  to  fall  with  equal 
rapidity,  and  a  lump  of  sand  without  cohesion  should, 
during  its  fall,  retain  its  original  form  as  perfectly 
as  if  it  were  compact  stone.  The  fact  that  a  stone 
falls  more  rapidly  than  a  feather  is  due  solely  to  the 
unequal  resistances  opposed  by  the  air  to  the  descent 
of  these  bodies;  in  a  vacuum  all  bodies  fall  iL'ith 
equal  rapidity.  To  demonstrate  this  by  experiment 
a  glass  tube  about  two  yards  long  (fig.  53)  may  be 
taken,  having  one  of  its  ends  completely  closed, 
and  a  brass  cock  fixed  to  the  other.  After  having 
introduced  bodies  of  different  weights  and  densities 
(pieces  of  lead,  paper,  feather,  &c.)  into  the  tube, 
the  air  is  withdrawn  from  it  by  an  air-pump,  and 
the  cock  closed.  If  the  tube  be  now  suddenly  re- 
versed, all  the  bodies  will  fall  equally  quickly.  On 
introducing  a  little  air  and  again  inverting  the  tube, 
the  lighter  bodies  become  slightly  retarded,  and  this 
retardation  increases  with  the  quantity  of  air  intro- 
duced. 

The  resistance  opposed  by  the  air  to  falling  bodies 
is  especially  remarkable  in  the  case  of  liquids.  The 
Staubbach  in  Switzerland  is  a  good  illustration  ;  an 
immense  mass  of  water  is  seen  falling  over  a  high 
precipice,  but  before  reaching  the  bottom  it  is 
shattered  by  the  air  into  the  finest  mist.  In  a 
vacuum,  however,  liquids  fall  like  solids  without 
separation  of  their  molecules.  The  water-hammer 
illustrates  this  :  the  instrument  consists  of  a  thick 
glass  tube  about  a  foot  long,  half  filled  with  water, 
the  air  having  been  expelled  by  ebullition  previous  to 
closing  one  extremity  with  the  blow-pipe.  When 
such  a  tube  is  suddenly  inverted,  the  water  falls  in 
one  undivided  mass  against  the  other  extremity  of 
the  tube,  and  produces  a  sharp  dry  sound,  resem- 
bling that  which  accompanies  the  shock  of  two  solid 
bodies.  Fig-  53- 


6o 


Gravitation  and  Molecular  A  ttraction. 


[77- 


From  Newton's  law  (67)  it  follows  that  when  a  body  falls  to  the  earth 
the  force  of  attraction  which  causes  it  to  do  so  increases  as  the  body 

approaches  the  earth.  Unless  the 
height  from  which  the  body  falls, 
however,  be  very  great,  this  in- 
crease will  be  altogether  inappre- 
ciable, and  the  force  in  question 
may  be  considered  as  constant 
and  continuous.  If  the  resistance 
of  the  air  were  removed,  therefore, 
the  motion  of  all  bodies  falling  to 
the  earth  would  be  uniformly  ac- 
celerated, and  would  obey  the 
laws  already  explained  (49). 

78.  At  woods  machine. — 
Several  instruments  have  been 
invented  for  illustrating  and  ex- 
perimentally verifying  the  laws  of 
falling  bodies.  Galileo,  who  dis- 
covered these  laws  in  the  early 
part  of  the  seventeenth  century, 
illustrated  them  by  means  of 
bodies  falling  down  inclined 
planes.  The  great  object  of  all 
such  instruments  is  to  diminish 
the  rapidity  of  the  fall  of  bodies 
without  altering  the  character  of 
their  motion,  for  by  this  means 
their  motion  may  not  only  be 
better  observed,  but  it  will  be  less 
modified  by  the  resistance  of  the 
air  (48). 

The  most  convenient  instru- 
ment of  this  kind  is  that  invented 
by  Atwood  at  the  end  of  the  last 
century,  and  represented  in  fig. 
54.  It  consists  of  a  stout  pillar  of 
wood,  about  2|  yards  high,  at  the 
top  of  which  is  a  brass  pulley, 
whose  axle  rests  and  turns  upon 
four  other  wheels,  called  friction 
wheels,  inasmuch  as  they  serve  to 
diminish  friction.  Two  equal 
weights,  M  and  M',  are  attached 
to  the  extremities  of  a  fine  silk 
thread,  which  passes  round  the 
pulley  ;  a  time-piece,  H,  fixed  to 


Fig.  54- 


the  pillar,  is  regulated  by  a  seconds  pendulum,  P,  in  the  usual  way ;  that  is 
to  say,  the  oscillations  of  the  pendulum  are  communicated  to  a  ratchet, 


-78]  Atwood's  Mac/line.  6 1 

whose  two  teeth,  as  seen  in  the  figure,  fit  into  those  of  the  ratchet  wheel. 
The  axle  of  this  wheel  gives  motion  to  the  seconds  hand  of  the  dial,  and 
also  to  an  eccentric  behind  the  dial,  as  shown  at  E  by  a  separate  figure. 
This  eccentric  plays  against  the  extremity  of  a  lever  D,  which  it  pushes 
until  the  latter  no  longer  supports  the  small  plate,  z,  and  thus  the  weight  M, 
which  at  first  rested  on  this  plate,  is  suddenly  exposed  to  the  free  action  of 
gravity.  The  eccentric  is  so  constructed  that  the  little  plate  z  falls  pre- 
cisely when  the  hand  of  the  dial  points  to  zero. 

The  weights  M  and  M',  being  equal,  hold  each  other  in  equilibrium  ; 
the  weight  M,  however,  is  made  to  descend  slowly  by  putting  a  small  bar  or 
overweight  ;;/  upon  it ;  and  to  measure  the  spaces  which  it  describes,  the  rod 
or  scale,  Q,  is  divided  into  feet  and  inches,  commencing  from  the  plate  z. 
To  complete  the  instrument,  there  are  a  number  of  plates,  A,  A',  C,  C',  and 
a  number  of  rings,  B,  B',  which  may  be  fixed  by  screws  at  any  part  of  the 
scale.  The  plates  arrest  the  descending  weight  M,  the  rings  only  arrest  the 
bar  or  overweight  ?«,  which  was  the  cause  of  motion,  so  that  after  passing 
through  them,  the  weight  M,  in  consequence  of  its  inertia,  will  move  on 
uniformly  with  the  velocity  it  had  acquired  on  reaching  the  ring.  The 
several  parts  of  the  apparatus  being  described,  a  few  words  will  suffice  to 
explain  the  method  of  experimenting. 

Let  the  hand  of  the  dial  be  placed  behind  the  zero  point,  the  lever  D 
adjusted  to  support  the  plate  z',  on  \vhich  the  weight  M  with  its  overweight 
m  rests,  and  the  pendulum  put  in  motion.  As  soon  as  the  hand  of  the  dial 
points  to  zero  the  plate  i  will  fall,  the  weights  M  and  m  will  descend,  and  by 
a  little  attention  and  a  few  trials  it  will  be  easy  to  place  a  plate  A  so  that  M 
may  reach  it  exactly  as  the  dial  indicates  the  expiration  of  one  second.  To 
make  a  second  experiment,  let  the  weights  M  and  ///,  the  plate  z,  and  the 
lever  D,  be  placed  as  at  first ;  remove  the  plate  A,  and  in  its  place  put  a  ring, 
B,  so  as  to  arrest  the  overweight  m  just  when  the  weight  M  would  have 
reached  A  ;  on  putting  the  pendulum  in  motion  again  it  will  be  easy,  after  a 
few  trials,  to  put  a  plate,  C,  so  that  the  weight  M  may  fall  upon  it  precisely 
when  the  hands  of  the  dial  point  to  two  seconds.  Since  the  overweight  in 
in  this  experiment  was  arrested  by  the  ring  B  at  the  expiration  of  one  second, 
the  space  BC  was  described  by  M  in  one  second  purely  in  virtue  of  its  own 
inertia,  and  consequently  by  (25)  BC  will  indicate  the  velocity  of  the  falling 
mass  at  the  expiration  of  one  second. 

Proceeding  in  the  same  manner  as  before,  let  a  third  experiment  be  made 
in  order  to  ascertain  the  point  B'  at  which  the  weights  M  and  m  arrive  after 
the  lapse  of  two  seconds,  and  putting  a  ring  at  B',  ascertain  by  a  fourth  ex- 
periment the  point  C'  at  which  M  arrives  alone,  three  seconds  after  the 
descent  commenced  ;  B'C'  will  then  express  the  velocity  acquired  after  a 
descent  of  two  seconds.  In  a  similar  manner,  by  a  fifth  and  sixth  experiment, 
we  may  determine  the  space  OB"  described  in  three  seconds,  and  the  velo- 
city B"C"  acquired  during  those  three  seconds,  and  so  on  ;  we  shall  find 
that  B'C'  is  twice,  and  B"C"  three  times  as  great  as  BC — in  other  words, 
that  the  velocities  BC,  B'C',  B"C",  increase  in  the  same  proportion  as  the 
times  (i,  2,  3,  .  .  .  seconds)  employed  in  their  acquirement.  By  the  defi- 
nition (49),  therefore,  the  motion  is  uniformly  accelerated.  The  same  ex- 
periments will  also  serve  to  verify  and  illustrate  the  four  laws  of  uniformly 


62  Gravitation  and  Molecular  Attraction.  [78- 

accelerated  motion  as  enunciated  in  (49).  For  example,  the  spaces  OB, 
OB',  OB",  ....  described  from  a  state  of  rest  in  i,  2,  3,  ....  seconds 
will  be  found  to  be  proportional  to  the  numbers  i,  4,  9 ;  .  .  .  that  is  to  say, 
to  the  squares  of  those  numbers  of  seconds,  as  stated  in  the  third  law. 

Lastly,  if  the  overweight  m  be  changed,  the  acceleration  or  velocity  BC 
acquired  per  second  will  also  be  changed,  and  we  may  easily  verify  the 
assertion  in  (29),  that  force  is  proportional  to  the  product  of  the  mass  moved 
into  the  acceleration  produced  in  a  given  time.  For  instance,  assuming  the 
pulley  to  be  so  light  that  its  inertia  can  be  neglected,  if  m  weighed  half  an 
ounce,  and  M  and  M'  each  15^  ounces,  the  acceleration  BC  would  be  found 
to  be  six  inches  ;  whilst  if  in  weighed  i  ounce,  and  M  and  M'  each  63  .V 
ounces,  the  acceleration  BC  would  be  found  to  be  three  inches. 

Now  in  these  cases  the  forces  producing  motion,  that  is  the  overweights, 
are  in  the  ratio  of  i  :  2  ;  while  the  products  of  the  masses  and  the  accelera- 
tions are  in  the  ratio  of  (£  +  isf  +  I5f)  x  6  to  (i  +  63^  +  63^)  x  3  ;  that  is,  they 
are  also  in  the  ratio  of  i  :  2.  Now  the  same  result  is  obtained  in  whatever 
way  the  magnitudes  of  m,  M,  and  M'  are  varied,  and  consequently  in  all 
cases  the  ratio  of  the  forces  producing  motion  equals  the  ratio  of  the  mo- 
menta generated. 

79.  iviorin's  apparatus. — The  principle  of  this  apparatus,  the  original 
idea  of  which  is  due  to  General  Poncelet,  is  to  make  the  body  in  falling  trace 
its  own  path.  Figure  55  gives  a  view  of  the  whole  apparatus,  and  figure  56 
gives  the  details.  The  apparatus  consists  of  a  wooden  framework,  about 
7  feet  high,  which  holds  in  a  vertical  position  a  very  light  wooden  cylinder, 
M,  which  can  turn  freely  about  its  axis.  This  cylinder  is  coated  with  paper 
divided  into  squares  by  equidistant  horizontal  and  vertical  lines.  The  latter 
measure  the  path  traversed  by  the  body  falling  along  the  cylinder,  while  the 
horizontal  lines  are  intended  to  divide  the  duration  of  the  fall  into  equal  parts. 

The  falling  body  is  a  mass  of  iron,  P,  provided  with  a  pencil  which  is 
pressed  against  the  paper  by  a  small  spring.  The  iron  is  guided  in  its  fall 
by  two  light  iron  wires  which  pass  through  guide-holes  on  the  two  sides. 
The  top  of  this  mass  is  provided  with  a  tipper  which  catches  against  the  end 
of  a  bent  lever,  AC.  This  being  pulled  by  the  string  K  attached  at  A,  the 
weight  falls.  If  the  cylinder  M  were  fixed,  the  pencil  would  trace  a  straight 
line  on  it ;  but  if  the  cylinder  moves  uniformly,  the  pencil  traces  the  line 
mn,  which  serves  to  deduce  the  law  of  the  fall. 

The  cylinder  is  rotated  by  means  of  a  weight,  Q,  suspended  to  a  cord 
which  passes  round  the  axle  G.  At  the  end  of  this  is  a  toothed  wheel,  c, 
which  turns  two  endless  screws,  a  and  b,  one  of  which  turns  the  cylinder, 
and  the  other  two  vanes,  x  and  x1  (fig.  56).  At  the  other  end  is  a  ratchet 
wheel,  in  which  fits  the  end  of  a  lever,  B  ;  by  pulling  at  a  cord  fixed  to  the 
other  end  of  B,  the  wheel  is  liberated,  the  weight  Q  descends,  and  the  whole 
system  begins  to  turn.  The  motion  is  at  first  accelerated,  but  as  -the  air 
offers  a  resistance  to  the  vanes  (48),  which  increases  as  the  rotation  becomes 
more  rapid,  the  resistance  finally  equals  the  acceleration  which  gravity  tends 
to  impart.  From  this  time  the  motion  becomes  uniform.  This  is  the  case 
when  the  weight  Q  has  traversed  about  three-quarters  its  course  ;  at  this 
moment  the  weight  P  is  detached  by  pulling  the  cord  K,  and  the  pencil  then 
traces  the  curve  mn. 


-80J 


The  Length  of  the  Compound  Pendulum. 


If,  by  means  of  this  curve,  we  examine  the  double  motion  of  the  pencil 
on  the  small  squares  which  divide  the  paper,  we  see  that,  for  displacements 
i,  2,  3,  ....  in  a  horizontal  direction,  the  displacements  are  I,  4,  9  .  .  .  . 
in  a  vertical  direction.  This  shows  that  the  paths  traversed  in  the  direction 
of  the  fall  are  directly  as  the  squares  of  the  lines  in  the  direction  of  the 
rotation,  which  verifies  the  second  law  of  falling  bodies. 


From  the  relation  which  exists  between  the  two  dimensions  of  the  curve 
mn.  it  is  concluded  that  this  curve  is  a  parabola. 

80.  The  length  of  the  compound  pendulum. — The  formula  deduced  in 
article  (55)  and  the  conclusions  which  follow  therefrom  refer  to  the  case  of  the 
simple  or  mathematical  pendulum  ;  that  is,  to  a  single  heavy  point  suspended 
by  a  thread  without  weight.  Such  a  pendulum  has  only  an  imaginary 


64  Gravitation  and  Molecular  Attraction.  [80-- 

existence,  and  any  pendulum  which  does  not  realise  these  conditions  is 
called  a  compound  or  physical  pendulum.  The  laws  for  the  time  of  vibra- 
tion of  a  compound  pendulum  are  the  same  as  those  which  regulate  the 
motion  of  the  simple  pendulum,  though  it  will  be  necessary  to  define  ac- 
curately what  is  meant  by  the  length  of  such  a  pendulum.  A  compound 
pendulum  being  formed  of  a  heavy  rod  terminated  by  a  greater  or  less  mass, 
it  follows  that  the  several  material  points  of  the  whole  system  will  strive  to 
perform  their  oscillations  in  different  times,  their  distances  from  the  axis  of 
suspension  being  different,  and  the  more  distant  points  requiring  a  longer 
time  to  complete  an  oscillation.  From  this,  and  from  the  fact  that  being 
points  of  the  same  body  they  must  all  oscillate  together,  it  follows  that  the 
motion  of  the  points  near  the  axis  of  suspension  will  be  retarded,  whilst  that 
of  the  more  distant  points  will  be  accelerated,  and  between  the  two  extremi- 
ties there  will  necessarily  be  a  series  of  points  whose  motion  will  be  neither 
accelerated  nor  retarded,  but  which  will  oscillate  precisely  as  if 
they  were  perfectly  free  and  unconnected  with  the  other  points  of 
the  system.  These  points,  being  equidistant  from  the  axis  of  sus- 
pension, constitute  a  parallel  axis  known  as  the  axis  of  oscillation  ; 
and  it  is  to  the  distance  between  these  two  axes  that  the  term 
length  of  the  compound  pendulum  is  applied  :  we  may  say,  there- 
fore, tha.t  the  length  of  a  compound  pendulum  is  that  of  the  simple 
pendulum  which  would  describe  its  oscillations  in  tJie  same 
time. 

Huyghens,  the  celebrated  Dutch  physicist,  discovered  that  the 
axes  of  suspension  and  oscillation  are  mutually  convertible  ;  that 
is  to  say,  the  time  of  oscillation  will  remain  unaltered  when  the 
pendulum  is  suspended  from  its  axis  of  oscillation.  This  enables  us 
to  determine  experimentally  the  length  of  the  compound  pendulum. 
For  this  purpose  the  reversible  pendulum  devised  by  Bohnenberger 
and  Kater  may  be  used.  One  form  of  this  (fig.  57)  is  a  rod  with 
the  knife-edges  a  and  b  turned  towards  each  other.  W  and  V  are 
lens-shaped  masses  the  relative  positions  of  which  may  be  varied. 
By  a  series  of  trials  a  position  can  be  found  such  that  the  number 
of  oscillations  of  the  pendulum  in  a  given  time  is  the  same 
whether  it  oscillates  about  the  axis  a  or  the  axis  b.  This  being 
so,  the  distance  ab  represents  the  length  /  of  a  simple  pendulum 
which  has  the  same  time  of  oscillation.  From  the  value  of  /,  thus 
obtained,  it  is  easy  to  determine  the  length  of  the  seconds  pen- 
dulum. 

The  length  of  the  seconds  pendulum — that  is  to  say,  of  the 
pendulum  which  makes  one  oscillation  in  a  second — varies,  of 
course,  with  the  intensity  of  gravity.  The  following  table  gives  its 
value  at  the  sea  level  at  various  places.  The  accelerative  effect  of 
gravity  at  these  places,  according  to  formula  (55),  is  obtained  in 
feet  and  metres,  by  multiplying  the  length  of  the  seconds  pendulum, 
reduced  to  feet  and  metres  respectively,  by  the  square  of  3-14159. 


-81] 


Verification  of  the  Laws  of  the  Pendulum. 


Latitude. 

Hammerfest    . 

7o°-4o/  N. 

Manchester     . 

53  '29 

Konigsberg     . 

54  -42 

Berlin      . 

52  -30 

Greenwich 

51  -29 

Paris 

48  -50 

New  York 

40  '43 

Washington    . 

38  '54 

Madras  . 

13  "4 

Ascension 

7-56 

St.  Thomas     . 

0*25 

Cape  of  Good  Hope 

33  '55  S. 

Length  of 

Acceleration  of  Gravity 

Pendulum 

in 

in  inches. 

feet. 

metres. 

39-1948 

32-2364 

9-8258 

39T472 

32T972 

9-8I32 

39-I507 

32-2002 

9-8I42 

39-I439 

32-1945 

9-8I24 

39-I398 

32-1912 

9-8II5 

39-I285 

32-I8I9 

9-8039 

39*1012 

32-1594 

9-8019 

39-0968 

32-1558 

9-8006 

39-0268 

32-0992 

97836 

39-0242 

32-0939 

97817 

39-0207 

32-0957 

97826 

39-0780 

32-1404 

97962 

Consequently,  \g  or  the  space  described  in  the  first  second  of  its  motion 
by  a  body  falling  in  vacua  from  a  state  of  rest  (49)  is 

16-0478  feet  or  4-891  metres  at  St.  Thomas, 
16-0956  „  „  4-905  „  at  London,  and 
16-1182  „  ,,4-913  „  at  Hammerfest. 

In  all  calculations,  which  are  used  for  the  sake  of  illustration,  we  may 
take  32  feet  or  9-8  metres  as  the  accelerative 
effect  due  to  gravity. 

From  observations  of  this  kind,  after  apply- 
ing the  necessary  corrections,  and  taking  into 
account  the  effect  of  rotation  (83),  the  form  of 
the  earth  can  be  deduced. 

8 1.  Verification  of  the  laws  of  the  pen- 
dulum.—  In  order  to  verify  the  laws  of  the 
simple  pendulum  (55)  we  are  compelled  to  em- 
ploy a  compound  one,  whose  construction  differs 
as  little  as  possible  from  that  of  the  former. 
For  this  purpose  a  small  sphere  of  a  very  dense 
substance,  such  as  lead  or  platinum,  is  sus- 
pended from  a  fixed  point  by  means  of  a  very 
fine  metal  wire.  A  pendulum  thus  formed  os- 
cillates almost  like  a  simple  pendulum,  whose 
length  is  equal  to  the  distance  of  the  centre  of 
the  sphere  from  the  point  of  suspension. 

In  order  to  verify  the  isochronism  of  small 
oscillations,  it  is  merely  necessary  to  count  the 
number  of  oscillations  made  in  equal  times,  as 
the  amplitudes  of  these  oscillations  diminish 
from  3  degrees  to  a  fraction  of  a  degree  ;  this 
number  is  found  to  be  constant. 

That  the  time  of  vibration  is  proportional 
to  the  square  root  of  the  length  is  verified 


Fig.  58. 


by  causing  pendulums,  whose  lengths  are  as  the  numbers  i,  4,  9,  .  .  .  .  to 
oscillate  simultaneously.  The  corresponding  numbers  of  oscillations  in  a  given 


66 


Gravitation  and  Molecular  Attraction. 


[81- 


time  are  then  found  to  be  proportional  to  the  fractions,  i,  £,  f,  £c., 

which  shows  that  the  times  of  oscillation  increase   as   the   numbers    i,    2, 

3, &c. 

By  taking  several  pendulums  of  exactly  equal  length,  B,  C,  D  (fig.  58), 
but  with  spheres  of  different  substances — lead,  copper,  ivory — it  is  found  that, 
neglecting  the  resistance  of  the  air,  these  pendulums  oscillate  in  equal  times, 
thereby  showing  that  the  accelerative  effect  of  gravity  on  all  bodies  is  the 
same  at  the  same  place. 

By  means  of  an  arrangement  resembling  the  above,  Newton  verified  the 
fact  that  the  masses  of  bodies  are  determined  by  the  balance  ;  which,  it  will 
be  remarked,  lies  at  the  foundation  of  the  measure  of  force  (29).  For 
it  will  be  seen  on  comparing  (54)  and  (55)  with  (50)  that  the  law  of  the 
time  of  a  small  oscillation  is  obtained  on  the  supposition  that  the  force  of 
gravity  on  all  bodies  is  represented  by  M^-,  in  which  M  is  determined  by  the 
balance.  In  order  to  verify  this,  he  had  made  two  round  equal  wooden  boxes  ; 
he  filled  one  with  wood,  and  as  nearly  as  possible  in  the  centre  of  oscillation 
of  the  other  he  placed  an  equal  weight  of  gold.  He  then  suspended  the 
boxes  by  threads  eleven  feet  long,  so  that  they  formed  pendulums  exactly 
equal  so  far  as  weight,  figure,  and  resistance  of  the  air  were  concerned.  Their 
oscillations  were  performed  in  exactly  the  same  time.  The  same  results  were 
obtained  when  other  substances  were  used,  such  as  silver,  lead,  glass,  sand, 
salt,  wood,  water,  corn.  Now  all  these  bodies  had  equal  weights,  and  if  the 
inference,  that  therefore  they  had  equal  masses,  had  been  erroneous,  by  so 
much  as  the  one-thousandth  part  of  the  whole,  the  experiment  would  have 
detected  it. 

82.  Application  of  the  pendulum  to  clocks. — The  regulation  of  the 
motion  of  clocks  is  effected  by  means  of  pendulums,  that  of  watches  by 
balance-springs.  Pendulums  were  first  applied  to 
this  purpose  by  Huyghens  in  1658,  and  in  the  same 
year  Hooke  applied  a  spiral  spring  to  the  balance 
of  a  watch.  The  manner  of  employing  the  pendu- 
lum is  shown  in  fig.  59.  The  pendulum  rod  passing 
between  the  prongs  of  a  fork  a  communicates  its 
motion  to  a  rod  b,  which  oscillates  on  a  horizontal 
axis  o.  To  this  axis  is  fixed  a  piece  mn  called  an 
escapement  or  crutch,  terminated  by  two  projections 
or  pallets,  which  work  alternately  with  the  teeth  of 
the  escapement  wheel  k.  This  wheel  being  acted 
on  by  the  weight  tends  to  move  continuously,  let  us 
say,  in  the  direction  indicated  by  the  arrow-head. 
Now  if  the  pendulum  is  at  rest,  the  wheel  is  held  at 
rest  by  the  pallet  m,  and  with  it  the  whole  of  the 
clockwork  and  the  weight.  If,  however,  the  pen- 
dulum moves  and  takes  the  position  shown  by  the 
dotted  line,  m  is  raised,  the  wheel  escapes  from  the 
confinement  in  which  it  was  held  by  the  pallet,  the 
weight  descends,  and  causes  the  wheel  to  turn  until 
its  motion  is  arrested  by  the  other  pallet  n  ;  which 
in  consequence  of  the  motion  of  the  pendulum  will  be  brought  into  contact 


Fig.  59- 


-83]  Intensity  of  Terrestrial  Gravitation.  67 

with  another  tooth  of  the  escapement  wheel.  In  this  manner  the  descent  of 
the  weight  is  alternately  permitted  and  arrested — or,  in  a  word,  regulated — 
by  the  pendulum.  By  means  of  a  proper  train  of  wheehvork  the  motion  of 
the  escapement  is  communicated  to  the  hands  of  the  clock ;  and  consequently 
their  motion,  also,  is  regulated  by  the  pendulum. 

The  pendulum  has  also  been  .used  for  measuring  great  velocities.  A  large 
block  of  wood  weighing  from  3  to  5  tons  is  coated  with  iron  ;  against  this 
arrangement,  which  is  known  as  a  ballistic-pendulum,  a  shot  is  fired,  and  the 
deflection  thereby  produced  is  observed.  From  the  laws  of  the  impact  of 
inelastic  bodies,  and  from  those  of  the  pendulum,  the  velocity  of  the  ball  may 
be  calculated  from  the  amount  of  this  deflection. 

The  gun  may  also  be  fastened  to  a  pendulum  arrangement  ;  and,  when 
fired,  the  reaction  causes  an  angular  velocity,  from  which  the  pressure  of  the 
enclosed  gases  can  be  deduced,  and  therefrom  the  initial  velocity  of  the 
shot. 

83.  Causes  which  modify  the  intensity  of  terrestrial  gravitation. — 
The  intensity  of  the  force  of  gravity — that  is,  the  value  of  g — is  not  the  same 
in  all  parts  of  the  earth.  It  is  modified  by  several  causes,  of  which  the  form 
of  the  earth  and  its  rotation  are  the  most  important. 

i.  The  attraction  which  the  earth  exerts  upon  a  body  at  its  surface  is  the 
sum  of  the  partial  attractions  which  each  part  of  the  earth  exerts  upon  that 
body,  and  the  resultant  of  all  these  attractions  may  be  considered  to  act  from 
a  single  point,  the  centre.  Hence,  if  the  earth  were  a  perfect  sphere,  a  given 
body  would  be  equally  attracted  at  any  part  of  the  earth's  surface.  The 
attraction  would,  however,  vary  with  the  height  above  the  surface.  For  small 
alterations  of  level  the  differences  would  be  inappreciable  ;  but  for  greater 
heights  and  in  accurate  measurements  observations  of  the  value  of  g  must 
be  reduced  to  the  sea  level.  The  attraction  of  gravitation  being  inversely 
as  the  square  of  the  distance  from  the  centre  (67)  we  shall  have 

£  '•  St  =  T^I  "•  TF> — TV*  where  g  is  the  value  of  the  acceleration  of  gravity  at 
K       (K  +  n) 

the  sea  level,  g,  its  value  at  any  height  //,  and  R  is  the  radius  of  the  earth. 
From  this,  seeing  that  h  is  very  small  compared  with  R,  and  that  therefore 
its  square  may  be  neglected,  we  get  by  simple  algebraical  transformation 

g  =      - 

r   1^ 

R 

But  even  at  the  sea  level  the  force  of  gravity  varies  in  different  parts  in 
consequence  of  the  form  of  the  earth.  The  earth  is  not  a  true  sphere  but 
an  ellipsoid,  the  major  axis  of  which  is  12,754,796  metres,  and  the  minor 
12,712,160  metres.  The  distance,  therefore,  at  the  centre  being  greater  at 
the  equator  than  at  the  Poles,  and  as  the  attraction  on  a  body  is  inversely 
as  the  square  of  these  distances,  calculation  shows  that  the  attraction  due  to 
this  cause  is  p^th  greater  at  the  Poles  than  at  the  equator.  This  is  what 
would  be  true  if,  other  things  being  the  same,  the  earth  were  at  rest. 

ii.  In  consequence  of  the  earth's  rotation,  the  force  of  gravity  is  further 
modified.  If  we  imagine  a  body  relatively  at  rest  on  the  equator,  it  really 
shares  the  earth's  rotation,  and  describes,  in  the  course  of  one  day,  a  circle 
whose  centre  and  radius  are  the  centre  and  radius  of  the  earth.  Now  since 


68 


Gravitation  and  Molecular  A  (traction. 


[83- 


a  body  in  motion  tends  by  reason  of  its  inertia  to  move  in  a  straight  line,  it 
follows  that  to  make  it  move  in  a  circle,  a  force  must  be  employed  at  each 
instant  to  deflect  it  from  the  tangent  (53).  Consequently,  a  certain  portion 
of  the  earth's  attraction  must  be  employed  in  keeping  the  above  body  on  the 
surface  of  the  earth,  and  only  the  remainder  is  sensible  as  weight  or  accele- 
rating force.  It  appears  from  calculation  that  on  the  equator  the  -^^  part 
of  the  earth's  attraction  on  any  body  is  thus  employed,  so  that  the  magnitude 
of  g  at  the  equator  is  less  by  the  gihth  part  of  what  it  would  be  were  the  earth 
at  rest. 

iii.  As  the  body  goes  nearer  the  Poles  the  force  of  gravity  is  less  and  less 
diminished  by  the  effect  of  centrifugal  force.     For  in  any  given  latitude  it 
will  describe  a  circle  coinciding  with  the  parallel  of  latitude  in  which  it  is 
placed  ;  but  as  the  radii  of  these  circles  diminish,  so 
does  the  centrifugal  force  until  the  Pole,  where  the. 
radius  is  null.    Further,  on  the  equator  the  centrifugal  ; 
force  is  directly  opposed  to  gravitation  ;  in  any  other  ; 
latitude  only  a  component  of  the  whole  force  is  thus  i 
employed.     This  is  seen  in  figure  60,  in  which  PP' 
represents  the  axis  of  rotation  of  the  earth  and  EE'  | 
the  equator.     At  any  given  point  E  on  the  equator  the 
centrifugal  force  is  directed  along  CE,  and  acts  wholly  \ 
in  diminishing  the  intensity  of  gravitation  ;  but  on  any 
other  point,  <z,  nearer  the  Pole,  the  centrifugal  force 
acting  on  a  right  line  ab  at  right  angles  to  the  axis  PP',  while  gravity  acts  \ 
along  #C,  gravity  is  no  longer  directly  diminished  by  centrifugal  force,  but 
only  by  its  component  ad^  which  is  less  the  nearer  a  is  to  the  Pole. 

The  combined  effect  of  these  two  causes — the  flattening  of  the  earth  at 
the  Poles,  and  the  centrifugal  force — is  to  make  the  attraction  of  gravitation 
at  the  equator  less  by  about  the  ^  part  of  its  value  at  the  Poles. 


-85]  Cohesion.  69 


CHAPTER   III. 

MOLECULAR   FORCES. 

84.  nature  of  molecular  forces. — The  various  phenomena  which  bodies 
present  show  that  their  molecules  are  under  the  influence  of  two  contrary 
forces,  one  of  which  tends  to  bring  them  together,  and  the  other  to  separate 
them  from  each  other.     The  first  force,  which  is  called  molecular  attraction, 
varies  in  one  and  the  same  body  with  the  distance  only.     The  second  force 
is  due  to  the  vis  viva  or  moving  force,  which  the  molecules  possess.    It  is  the 
mutual  relation  between  these  forces,  the  preponderance  of  the  one  or  the 
other,  which  determines  the  molecular  state  of  a  body  (4) — whether  it  be 
solid,  liquid,  or  gaseous. 

Molecular  attraction  is  only  exerted  at  infinitely  small  distances.  Its  effect 
is  inappreciable  when  the  distance  between  the  molecules  is  appreciable. 

According  to  the  manner  in  which  it  is  regarded,  molecular  attraction  is 
designated  by  the  terms,  cohesion,  affinity,  or  adhesion. 

85.  Cohesion. — Cohesion  is  the  force  which  unites  adjacent  molecules  of 
the  same  nature  ;  for  example,  two  molecules  of  water,  or  two  molecules  of 
iron.     Cohesion  is  strongly  exerted  in  solids,  less  strongly  in  liquids,  and 
scarcely  at  all  in  gases.    Its  strength  decreases  as  the  temperature  increases, 
because  then  the  vis  viva  of  the  molecules   increases.     Hence   it   is   that 
when  solid  bodies  are  heated  they  first  liquefy,  and  are  ultimately  converted 
into  the  gaseous  state,  provided  that  heat  produces  in  them  no  chemical 
change. 

Cohesion  varies  not  only  with  the  nature  of  bodies,  but  also  with  the 
arrangement  of  their  molecules  ;  for  example,  the  difference  between  tempered 
and  untempered  steel  is  due  to  a  difference  in  the  molecular  arrangement 
produced  by  tempering.  Many  of  the  properties  of  bodies,  such  as  tenacity, 
hardness,  and  ductility,  are  due  to  the  modifications  which  this  force  under- 
goes. 

In  large  masses  of  liquids,  the  force  of  gravity  overcomes  that  of  cohesion. 
Hence  liquids  acted  upon  by  the  former  force  have  no  special  shape  ;  they 
take  that  of  the  vessel  in  which  they  are  contained.  But  in  smaller  masses 
cohesion  gets  the  upper  hand,  and  liquids  present  then  the  spheroidal  form. 
This  is  seen  in  the  drops  of  dew  on  the  leaves  of  plants  ;  it  is  also  seen  when 
a  liquid  is  placed  on  a  solid  which  it  does  not  moisten  ;  as,  for  example, 
mercury  upon  wood.  The  experiment  may  also  be  made  with  water,  by 
sprinkling  upon  the  surface  of  the  wood  some  light  powder  such  as  lycopodium 
or  lampblack,  and  then  dropping  some  water  on  it.  The  following  pretty 
experiment  is  an  illustration  of  the  force  of  cohesion  causing  a  liquid  to  assume 
the  spheroidal  form.  A  saturated  solution  of  sulphate  of  zinc  is  placed  in  a 


Gravitation  and  Molecular  Attraction. 


[85- 


narrow-necked  bottle,  and  a  few  drops  of  bisulphide  of  carbon,  coloured  with 
iodine,  made  to  float  on  the  surface.  If  pure  water  be  now  carefully  added, 
so  as  to  rest  on  the  surface  of  the  sulphate  of  zinc  solution  the  bisulphide 
collects  in  the  form  of  a  flattened  spheroid,  which  presents  the  appearance 
of  blown  coloured  glass,  and  is  larger  than  the  neck  of  the  bottle,  provided 
a  sufficient  quantity  has  been  taken. 

The  force  of  cohesion  of  liquids  may  be  measured  as  follows.  A  plane, 
perfectly  smooth  disc  D  is  suspended  horizontally  to  one  scale  pan  p  of  a  deli- 
cate balance,  and  is  accurately  equipoised.  A  some- 
what wide  vessel  of  liquid  is  placed  below,  and  the 
position  of  the  disc  regulated  by  means  of  the  slid- 
ing screw  s  until  it  just  touches  the  liquid.  Weights 
are  then  carefully  added  to  the  other  scale  pan  until 
the  disc  is  detached  from  the  liquid.  In  this  way  it 
has  been  found  that  the  weights  required  to  detach 
the  disc  vary  with  the  nature  of  the  liquid  ;  with 
a  disc  of  118  mm.  in  diameter  the  numbers  for 
water,  alcohol,  and  turpentine  were  59-4,  31,  and  34 
grammes  respectively. 

The  results  were  the  same  whether  the  disc 
was  of  glass,  of  copper,  or  of  other  metals,  and 
they  thus  only  depend  on  the  nature  of  the  liquid. 
It  is  a  measure  of  the  cohesion  of  the  liquid,  for  a 
layer  remains  adhering  to  the  disc ;  hence  the 
weight  on  the  other  side  does  not  separate  the  disc 
from  the  liquid,  but  separates  the  particles  of  liquid 
from  each  other. 

86.  Affinity. — Chemical  affinity,  or  chemical  at- 
traction, is  the  force  which  is  exerted  between  mole- 
cules not  of  the  same  kind.  Thus,  in  water,  which 
i  is  composed  of  oxygen  and  hydrogen,  it  is  affinity 
~  which  unites  these  elements,  but  it  is  cohesion 
which  binds  together  two  molecules  of  water.  In 
compound  bodies  cohesion  and  affinity  operate  simultaneously,  while  in  simple 
bodies  or  elements  cohesion  has  alone  to  be  considered. 

To  affinity  are  due  all  the  phenomena  of  combustion,  and  of  chemical 
combination  and  decomposition. 

The  causes  which  tend  to  weaken  cohesion  are  most  favourable  to  affinity  ; 
for  instance,  the  action  of  affinity  between  substances  is  facilitated  by  their 
division,  and  still  more  by  reducing  them  to  a  liquid  or  gaseous  state.  It  is 
most  powerfully  exerted  by  a  body  in  its  nascent  state — that  is,  the  state  in 
which  the  body  exists  at  the  moment  it  is  disengaged  from  a  compound  ;  the 
body  is  then  free,  and  ready  to  obey  the  feeblest  affinity.  An  increase  of 
temperature  modifies  affinity  differently  under  different  circumstances.  In 
some  cases,  by  diminishing  cohesion,  and  increasing  the  distance  between 
the  molecules,  heat  promotes  combination.  Sulphur  and  oxygen,  which  at 
the  ordinary  temperature  are  without  action  on  each  other,  combine  to  form 
sulphurous  acid  when  the  temperature  is  raised  :  in  other  cases  heat  tends 
to  decompose  compounds  by  imparting  to  their  elements  an  unequal  expan- 
sibility. Thus  it  is  that  many  metallic  oxides,  as  for  example  those  of 


Fig.  61. 


-87]  Adhesion.  71 

silver  and  mercury,  are  decomposed,  by  the  action  of  heat,  into  gas  and 
metal. 

87.  Adhesion. — The  molecular  attraction  exerted  between  the  surfaces  of 
bodies  in  contact  is  called  adhesion. 

i.  Adhesion  takes  place  between  solids.  If  two  leaden  bullets  are  cut 
with  a  penknife  so  as  to  form  two  equal  and  brightly  polished  surfaces,  and 
the  two  faces  are  pressed  and  turned  against  each  other,  until  they  are  in  the 
closest  contact,  they  adhere  so  strongly  as  to  require  a  force  of  more  than 
loo  grammes  to  separate  them.  The  same  experiment  may  be  made  with 
two  equal  pieces  of  glass  which  are  polished  and  made  perfectly  plane. 
When  they  are  pressed  one  against  the  other,  the  adhesion  is  so  powerful 
that  they  cannot  be  separated  without  breaking.  As  the  experiment  succeeds 
/;/  vacua,  it  cannot  be  due  to  atmospheric  pressure,  but  must  be  attributed  to 
a  reciprocal  action  between  the  two  surfaces.  The  attraction  also  increases 
as  the  contact  is  prolonged,  and  is  greater  in  proportion  as  the  contact  is  closer. 

In  the  operation  of  gluing  the  adhesion  is  complete,  for  the  pores  and 
crevices  of  the  fresh  surfaces  being  filled  with  liquid  glue,  so  that  there  is  no 
empty  space  on  drying,  wood  and  glue  form  one  compact  whole.  In  some 
cases  the  adhesion  of  the  cement  is  so  powerful  that  the  mass  breaks  more 
readily  at  other  places  than  at  the  cemented  parts. 

There  is  no  real  difference  between  adhesion  and  cohesion  ;  thus,  when 
two  freshly  cut  surfaces  of  caoutchouc  are  pressed  together,  they  adhere  with 
considerable  force,  and  ultimately  form  one  compact  solid  mass. 

ii.  Adhesion  also  takes  place  between  solids  and  liquids.  If  we  dip  a  glass 
rod  into  water,  on  withdrawing  it  a  drop  will  be  found  to  collect  at  its  lower 
extremity,  and  remain  suspended  there.  As  the  weight  of  the  drop  tends  to 
detach  it,  there  must  necessarily  be  some  force  superior  to  this  weight  which 
maintains  it  there  ;  this  force  is  the  force  of  adhesion. 

The  adhesion  between  liquids  and  solids  is  more  powerful  than  that  be- 
tween solids.  Thus,  if  in  the  above  experiment  a  thin  layer  of  oil  is  inter"- 
posed  between  the  plates  they  adhere  firmly,  but  when  pulled  asunder  each 
plate  is  moistened  by  the  oil,  thus  showing  that  in  separating  the  plates  the 
cohesion  of  the  plates  is  overcome,  but  not  the  adhesion  of  the  oil  to  the 
metal.  Alcohol  adheres  more  firmly  to  glass  than  water.  A  layer  of  water 
on  a  glass  plate  is  displaced  by  a  drop  of  alcohol  brought  on  it. 

iii.  The  force  of  adhesion  operates,  lastly,  between  solids  and  gases. 
'If  a  glass  or  metal  plate  be  immersed  in  water,  bubbles  will  be  found  to 
appear  on  the  surface.  As  air  cannot  penetrate  into  the  pores  of  the  plate, 
the  bubbles  could  not  arise  from  the  air  which  had  been  expelled.  It  is 
solely  due  to  the  layer  of  air  which  covered  the  plate,  and  moistened  it  like 
a  liquid.  In  many  cases  when  gases  are  separated  in  the  nascent  state 
•on  the  surface  of  metals — as  in  electrolysis — the  layer  of  gas  which  covers 
the  plate  has  such  a  density  that  it  can  produce  chemical  actions  more  power- 
"ful  than  those  which  it  can  bring  about  in  the  free  state. 

The  collection  of  dust  on  walls,  writing  and  drawing  with  chalks  and 
pencils,  depend  on  the  adhesion  of  solids.  Yet  these  are  easily  rubbed  out, 
for  the  adhesion  is  only  to  the  surface  layer.  In  writing  with  ink,  and  in  water- 
colour  painting,  the  liquid  penetrates  into  the  pores,  taking  the  solid  with  it 
which  is  left  behind  as  the  liquid  evaporates,  and  hence  the  adhesion  of  such 
writing  and  painting  is  more  complete. 


Gravitation  and  Molecular  Attraction. 


[88- 


CHAPTER    IV. 

PROPERTIES  PECULIAR  TO  SOLIDS. 

88.  Various  special  properties. — After  having  described  the  principal 
properties  common  to  solids,  liquids,  and  gases,  we  shall  discuss  the  properties 
peculiar  to  solids.     They  are,  elasticity  of  traction,  elasticity  of  torsion,  elas- 
ticity of  flexure,  tenacity,  ductility,  and  Jiardness. 

89.  Elasticity  of  traction. — Elasticity,  as  a  general  property  of  matter, 
has  been  already  mentioned  (17),  but  simply  in  reference  to  the  elasticity 
developed  by  pressure  ;  in  solids  it  may  also  be  called  into  play  by  traction, 
by  torsion,  and  by  flexure.     The  definitions  there  given  require  some  exten- 
sion.    In  ordinary  life  we  consider 
those    bodies     as     highly    elastic, 
which,    like    caoutchouc,    undergo 
considerable  change  on  the  appli-i 
cation  of  only  a  small  force.     Yet 
the  force  of  elasticity  is  greatest  in 
many  bodies,   such  as  iron,  whicH 
do  not  seem  to  be  very  elastic.     Fon 
by  force  of  elasticity  is  understood 
the  force  with  which  the  displaced 
particles    tend   to   revert   to    thei 
original  position,  and  which  force 
equivalent  to  that  which  has  brough 
about  the  change.    Considered  fron 
this  point  of  view,  gases  have  th 
least   force   of  elasticity  ;    that 
liquids  is  considerably  greater,  an 
is,  indeed,  greater  than  that  of  man 
solids.    Thus,  the  force  of  elasticit 
of  mercury  is  greater  than  that 
caoutchouc,  glass,  wood,  and  ston< 
It  is,  however,  less  than  that  of  th 
other  metals,  with  the  exception 
lead. 

This  seems  discordant  with  o 
dinan-  ideas  about  elasticity  ;  bi 
it  must  be  remembered  that  tho« 
bodies  which,  by  the  exertion  of  a  small  force,  undergo  a  considerab 
change,  generally  have  also  the  property  of  undergoing  this  change  withoi 
losing  the  property  of  reverting  completely  to  their  original  state.  The 


-89]  Elasticity  \of  Traction.  73 

have  a  wide  //;;;//  of  elasticity  (17).  Those  bodies  which  require  great  force 
to  effect  a  change  are  also,  for  the  most  part,  those  on  which  the  exertion 
of  a  force  produces  a  permanent  alteration  ;  when  the  force  is  no  longer 
exerted,  they  do  not  completely  revert  to  their  original  state. 

In  order  to  study  the  laws  of  the  elasticity  of  traction,  Savart  used  the 
apparatus  represented  in  fig.  62.  It  consists  of  a  wooden  support  from 
which  are  suspended  the  rods  or  wires  taken  for  experiment.  At  the  lower 
extremity  there  is  a  scale  pan,  and  on  the  wire  two  points,  A  and  B,  are 
marked,  the  distance  between  which  is  measured  by  means  of  the  catlieto- 
>efore  the  weights  are  added. 

The  cathctometer  consists  of  a  strong  brass  support,  K,  divided  into  milli- 
metres, and  which  can  be  adjusted  in  a  vertical  position  by  means  of  levelling 
screws  and  the  plumb  line.  A  small  telescope,  exactly  at  right  angles  to  the 
scale,  can  be  moved  up  and  down,  and  is  provided  with  a  vernier  which 
measures  fiftieths  of  a  millimetre.  By  fixing  the  telescope  successively  on 
the  two  points  A  and  B,  as  represented  in  the  figure,  the  distance  between 
these  points  is  obtained  on  the  graduated  scale.  Placing  then  weights  in 
the  pan,  and  measuring  again  the  distance  from  A  to  B,  the  elongation  is 
obtained 

By  experiments  of  this  kind  it  has  been  ascertained  that  for  elasticity  of 
traction  or  pressure  — 

The  altcratioji  in  length,  within  the  limits  of  elasticity,  is  in  proportion 
to  the  length  and  to  the  load  acting  on  the  body,  and  is  inversely  as  the  section. 

It  depends,  moreover,  on  the  specific  elasticity  ;  that  is,  on  the  material  of 
the  body.  If  this  coefficient  be  denoted  by  E,  and  if  the  length,  section, 
and  load  are  respectively  designated  by  /,  s,  and  P,  then  for  the  alteration  in 
length,  <?,  we  have 


If  in  the  above  expression  the  sectional  area  be  a  square  millimetre,  and 
P  be  one  kilogramme,  then 

e  =  E/,  from  which  E  =  t, 

which  expresses  by  what  fraction  the  length  of  a  bar  a  square  millimetre  in 
~>n  is  altered  by  a  load  of  a  kilogramme.  This  is  called  the  coefficient  of 
-•city  ;  it  is  a  very  small  fraction,  and  it  is  therefore  desirable  to  use  its 

reciprocal,  that  is  I  or  /A,  as  the  modulus  of  elasticity  ;  or  the  weight  in  kilo- 

mes  which  applied  to  a  bar  would  elongate  it  by  its  own  length,  assum- 
ing it  to  be  perfectly  elastic.      This  cannot  be  observed,  for  no  body  is 
perfectly  elastic,  but  it  may  be  calculated  from  any  accurate  observations 
by  means  of  the  above  formula. 

The  following  are  the  best  values  for  some  of  the  principal  substances  :  — 
Steel  .....     21,000     Lead          .....     1,800 

Wrought  Iron     .         .         .     19,000     Wood        .....     1,100 

Copper       ....     12,400     Whalebone        ....        700 

Brass  .....       9,000     Ice     ......        236^ 

Zinc    .....       8,700     Glass          .....          90 

Silver          ....       7,400 


74 


Gravitation  and  Molecular  Attraction. 


[89- 


Thus,  to  double  the  length  of  a  wrought-iron  wire  a  square  millimetre  in 
section,  would  (if  this  were  possible)  require  a  weight  of  19,000  kilogrammes  ; 
but  a  weight  of  1 5  kilogrammes  produces  a  permanent  alteration  in  length 
of  j^th,  and  this  is  the  limit  of  elasticity.  The  weight  which  when  applied 
to  a  body  of  the  unit  of  section  just  brings  about  an  appreciable  permanent 
change  is  a  measure  of  the  limit  of  elasticity.  Whalebone,  on  the  contrary, 
has  only  a  modulus  of  700,  and  experiences  a  permanent  change  by  a  weight 
of  5  kilogrammes  ;  its  limit  is,  therefore,  relatively  greater  than  that  of  iron. 
Steel  has  a  high  modulus,  along  with  a  wide  limit. 

Both  calculation  and  experiment  show  that  when  bodies  are  lengthened 
by  traction  their  volume  increases. 

When  weights  are  placed  on  a  bar,  the  amount  by  which  it  is  shortened, 
or  the  coefficient  of  contraction,  is  equal  to  the  elongation  which  it  would  ex- 
perience if  the  same  weights  were  suspended  to  it,  and  is  represented  by  the 
above  numbers. 

The  influence  of  temperature  on  the  elasticity  of  iron,  copper,  and  brass 
was  investigated  by  Kohlrausch  and  Loomis.  They  found  that  the  alteration 
in  the  coefficient  of  elasticity  by  heat  is  the  same  as  that  which  heat  produces 
in  the  coefficient  of  expansions  and  in  the  refractive  power ;  it  is  also  much 
the  same  as  the  change  in  the  permanent  magnetism,  and  in  the  specific  heat, 
while  it  is  less  than  the  alteration  in  the  conductivity  for  electricity. 

90:  Elasticity  of  Torsion. — The  laws  of  the  torsion  of  wires  were  deter- 
mined by  Coulomb,  by  means  of  an  apparatus  called  the  torsion  balance 
(fig.  63).  It  consists  of  a  metal  wire,  clasped 
at  its  upper  extremity  in  a  support,  A,  and 
holding  at  the  other  extremity  a  metal  sphere, 
B,  to  which  is  affixed  an  index,  C.  Immedi- 
ately below  this  there  is  a  graduated  circle,  CD. 
If  the  needle  is  turned  from  its  position  of  equi- 
librium through  a  certain  angle,  which  is  the 
angle  of  torsion,  the  force  necessary  to  produce 
this  effect  is  the  force  of  torsion.  When,  after 
"this  deflection,  the  sphere  is  left  to  itself,  the 
reaction  of  torsion  produces  its  effect,  the  wire 
untwists  itself,  and  the  sphere  rotates  about  its 
vertical  axis  "with  increasing  rapidity  until  it 
reaches  its  position  of  equilibrium.  It  does  not, 
however,  rest  there  ;  in  virtue  of  its  inertia  it 
passes  this  position,  and  the  wire  undergoes  a 
torsion  in  the  opposite  direction.  The  equi- 
librium being  again  destroyed,  the  wire  again 
tends  to  untwist  itself,  the  same  alterations  are 
again  produced,  and  the  needle  does  not  rest  at 
zero  of  the  scale  until  after  a  certain  number  of 
oscillations  about  this  point  have  been  completed. 

By  means  of  this  apparatus  Coulomb  found  that  when  the  amplitude  of 
the  oscillations  is  within  certain  limits,  the  oscillations  are  subject  to  the 
following  laws  : 

I.   The  oscj Uations  are  very  nearly  isochronous. 


'Fig.  63. 


-91]  Elasticity-  of  Flexure.  7  5 

II.  For  the  same  wire,  the  angle  of  torsion  is  proportional  to  the  moment 
of  the  force  of  torsion. 

III.  With  the  same  force  of  torsion,  and  with  wires  of  the  same  diameter, 
the  angles  of  torsion  are  proportional  to  the  lengths  of  the  wires. 

IV.  The  same  force  of  torsion  being  applied  to  wires  of  the  same  length, 
the  angles  of  torsion  are  inversely  proportional  to  the  fourth  powers  of  the 
diameters. 

Wertheim  has  examined  the  elasticity  of  torsion  in  the  case  of  stout  rods 
by  means  of  a  different  apparatus,  and  finds  that  it  is  also  subject  to  these 
laws.  He  has  further  found  that,  all  dimensions  being  the  same,  different 
substances  undergo  different  degrees  of  torsion,  and  each  substance  has  its 

own  coefficient  of  torsion,  which  is  denoted  by  =. 

The  laws  of  torsion  may  be  enunciated  in  the  formula  w=  1    —  •    in 

T  r^ 

which  w  is  the  angle  of  torsion,  F  the  moment  of  the  force  of  torsion,  /  the 
length  of  the  wire,  r  its  diameter,  and  -  the  specific  torsion-coefficient. 

91.  Elasticity  of  flexure.  —  A  solid,  when  cut  into  a  thin  plate,  and  fixed 
at  one  of  its  extremities,  after  having  been  more  or  less  bent,  strives  to  return 
to  its  original  position  when  left  to  itself.  This  property  is  the  elasticity  of 
flexure,  and  is  very  distinct  in  steel,  caoutchouc,  wood,  and  paper. 

If  a  rectangular  bar  A  B  be  clamped  at  one  end  and  loaded  at  the  other 
(fig.  64),  the  flexure  e  is  represented  by  the  formula 


V 


where  W  is  the  load,  /  the  length  of  the  bar,  b  its  breadth,  h  its  thick- 
ness, and  p  the  modulus  of  elasticity. 

The  elasticity  of  flexure  is  applied  in  a  vast  variety  of  instances— for 
example,  in  bows,  watch  springs,  carriage  springs  ;  in  spring  balances  it  is 
used  to  determine  weights, 
in  dynamometers  to    de-  A< 

termine  the  force  of  agents  -JttS^  -^  [T^B 

in  prime  movers  ;  and,  as 
existing  in  wool,  hair,  and 
feathers,  it  is  applied  to 
domestic  uses  in  cushions 
and  mattresses. 

Whatever  be  the  kind 
of  elasticity,  there  is,  as 
has  been  already  said,  a 
limit  to  it — that  is,  there 
is  a  molecular  displace- 
ment, beyond  which 
bodies  are  broken,  or  at 
any  rate  do  not  regain  their  primitive  form.  This  limit  is  affected  by 
various  causes.  The  elasticity  of  many  metals  is  increased  by  Jiardening, 
whether  by  cold,  by  means  of  the  draw-plate,  by  rolling,  or  by  hammering. 

E  2 


76  Gravitation  and  Molecular  Attraction.  [91- 

Some  substances,  such  as  steel,  cast  iron,  and  glass,  become  both  harder 
and  more  elastic  by  tempering  (95). 

Elasticity,  on  the  other  hand,  is  diminished  by  annealing,  which  consists 
in  raising  the  body  to  a  temperature  lower  than  that  necessary  for  tempering, 
and  allowing  it  to  cool  slowly.  It  is  by  this  means  that  the  elasticity  of 
springs  may  be  regulated  at  pleasure.  Glass,  when  it  is  heated,  undergoes 
a  true  tempering  in  being  rapidly  cooled,  and  hence,  in  order  to  lessen  the 
fragility  of  glass  objects,  they  are  reheated  in  a  furnace,  and  are  carefully 
allowed  to  cool  slowly,  so  that  the  particles  have  time  to  assume  their  most 
stable  position  (95). 

92.  Tenacity. —  Tenacity  is  the  resistance  which  a  body  opposes  to  the 
total  separation  of  its  parts.  According  to  the  manner  in  which  the  external 
force  acts,  we  may  have  various  kinds  of  tenacity  :  tenacity  in  the  ordinary 
sense,  or  resistance  to  traction  ;  relative  tenacity,  or  resistance  to  fracture  ; 
reactive  tenacity,  or  resistance  to  crushing  ;  sheering  tenacity,  or  resistance 
to  displacement  of  particles  in  a  lateral  direction  ;  and  torsional  tenacity,  or 
resistance  to  twisting.  Ordinary  tenacity  is  determined  in  different  bodies 
by  forming  them  into  cylindrical  or  prismatic  wires,  and  ascertaining  the 
weight  necessary  to  break  them. 

Mere  increase  in  length  does  not  influence  the  breaking  weight,  for  the 
weight  acts  in  the  direction  of  the  length,  and  stretches  all  parts  as  if  it  had 
been  directly  applied  to  them. 

Tenacity  is  directly  proportional  to  the  breaking  weight,  and  inversely 
proportional  to  the  area  of  a  transverse  section  of  the  wire. 

Tenacity  diminishes  with  the  duration  of  the  traction.  A  small  force 
continuously  applied  for  a  long  time  will  often  break  a  wire,  which  would  not 
at  once  be  broken  by  a  larger  weight. 

Not  only  does  tenacity  vary  with  different  substances,  but  it  also  varies 
with  the  form  of  the  body.  Thus,  with  the  same  sectional  area,  a  cylinder 
has  greater  tenacity  than  a  prism.  The  quantity  of  matter  being  the  same, 
a  hollow  cylinder  has  greater  tenacity  than  a  solid  one  ;  and  the  tenacity  of 
this  hollow  cylinder  is  greatest  when  the  external  radius  is  to  the  internal 
one  in  the  ratio  of  1 1  to  5. 

The  shape  has  also  the  same  influence  on  the  resistance  to  crushing  as 
it  has  on  the  resistance  to  traction.  A  hollow  cylinder  with  the  same  mass, 
and  the  same  weight,  offers  a  greater  resistance  than  a  solid  cylinder.  Thus 
it  is  that  the  bones  of  animals,  the  feathers  of  birds,  the  stems  of  corn  and 
other  plants,  offer  greater  resistance  than  if  they  were  solid,  the  mass  re- 
maining the  same. 

Tenacity,  like  elasticity,  is  different  in  different  directions  in  bodies.  In 
wood,  for  example,  both  the  tenacity  and  the  elasticity  are  greater  in  the 
direction  of  the  fibres  than  in  a  transverse  direction.  And  this  difference 
obtains  in  general  in  all  bodies,  the  texture  of  which  is  not  the  same  in  all 
directions. 

Wires  by  being  worked  acquire  greater  tenacity  on  the  surface,  and 
have  therefore  a  higher  coefficient,  than  even  somewhat  thicker  rods  of 
the  same  material.  A  strand  of  wires  is  stronger  than  a  rod  of  the  same 
section. 

Wertheim  found  the  following  numbers  representing  the  weight  in  kilo- 


-93]  Hardness.  77 

grammes  for  the  limit  of  elasticity  and  for  the  tenacity  of  wires,  I  mm.  in 
diameter. 

The  table  shows  that  of  all  metals  cast  steel  has  the  greatest  tenacity. 
Yet  it  is  exceeded  by  fibres  of  unspun  silk,  a  thread  of  which  i  square  milli- 
metre  in  section  can  carry  a  load  of  500  kilogrammes.  Single  fibres  of  cotton 
can  support  a  weight  of  100  to  300  grammes  • 


300  gramm 
<k    \tfW- 


that  is  millions  of  times  their 


Lead. 
Tin  . 
Gold. 

Silver 


Zinc 


Copper 


Platinum 


Iron 


Steel 


Cast  Steel 


j  drawn 
( annealed 
1  drawn 
(annealed 
!  drawn 
( annealed 
i  drawn 
\  annealed 
i  drawn 
( annealed 
( drawn 
(annealed 
I  drawn 
I  annealed 
i  drawn 
(annealed 
I  drawn 
(annealed 
I  drawn 
{annealed 


Limit  of  Elasticity. 
Kilogrammes. 
0-25 
0'20 


0-20 
I3-50 

3-00 

11-25 

275 
075 

I -00 
12*00 

3-00 

26-00 

14-50 

32-5 

5-0 

42-5 

15-0 

55-6 
5-0 


Tenacity. 
Kilogrammes. 

2-07 
I -80 

2-45 

170 
27-00 
1 0-08 
29-00 

1 6'02 
1 2 -80 

40-30 

30'54 
34-10 
23-50 

6no 
46-88 
70-00 
40-00 
80-00 
6575 


In  this  table  the  bodies  are  supposed  to  be  at  the  ordinary  temperature. 
At  higher  temperatures  the  tenacity  rapidly  decreases.  Seguin  made  some 
experiments  on  this  point  with  iron  and  copper,  and  obtained  the  following 
values  for  the  tenacity,  in  kilogrammes,  of  millimetre  wire  at  different  tem- 
peratures : — 

Iron         .         .  at  10°,  60  ;  at  370°,  54  ;  at  500°,  37  ; 
Copper   .         .        „      21  ;         „          77  ;       „        o. 

93.  Ductility. — Ductility  is  the  property  in  virtue  of  which  a  great 
number  of  bodies  change  their  forms  by  the  action  of  traction  or  pressure. 

With  certain  bodies,  such  as  clay,  wax,  £c.,  the  application  of  a  very 
little  force  is  sufficient  to  produce  a  change  ;  with  others,  such  as  the  resins 
and  glass,  the  aid  of  heat  is  needed,  while  with  the  metals  more  powerful 
agents  must  be  used,  such  as  percussion,  the  draw-plate,  or  the  rolling-mill. 

Malleability  is  that  modification  of  ductility  wnich  is  exhibited  by  ham- 
mering. The  most  malleable  metal  is  gold,  which  has  been  bfeaten  into 
leaves  about  the  smooth  °f  an  mcn  thick. 

The  most  ductile  metal  is  platinum.  Wollaston  obtained  a  wire  of  it 
0-00003  of  an  inch  in  diameter.  This  he  effected  by  covering  with  silver  a 
platinum  wire  o-oi  of  an  inch  in  diameter,  so  as  to  obtain  a  cylinder  0-2  inch 


78  Gravitation  and  Molecular  Attraction.  [93- 

in  diameter  only,  the  axis  of  which  was  of  platinum.  This  was  then  drawn 
out  in  the  form  of  wire  as  fine  as  possible  ;  the  two  metals  were  equally  ex- 
tended. When  this  wire  was  afterwards  boiled  with  dilute  nitric  acid  the 
silver  was  dissolved,  and  the  platinum  wire  left  intact.  The  wire  was  so  fine 
that  a  mile  of  it  would  have  only  weighed  1-25  of  a  grain. 

94.  Hardness. — Hardness  is  the  resistance  which  bodies  offer  to  being 
scratched  or  worn  by  others.     It  is  only  a  relative  property,  for  a  body  which 
is  hard  in  reference  to  one  body  may  be  soft  in  reference  to  others.     The  re- 
lative hardness  of  two  bodies  is  ascertained  by  trying  which  of  them  will 
scratch  the  other.     Diamond  is  the  hardest  of  all  bodies,  for  it  scratches  all, 
and  is  not  scratched  by  any.     The  hardness  of  a  body  is  expressed  by  re- 
ferring it  to  a  scale  of  hardness  :  that  usually  adopted  is — 

1.  Talc  5.  Apatite  8.  Topaz 

2.  Rock  salt  6.  Felspar  9.  Corundum 

3.  Calcspar  7.  Quartz  10.  Diamond 

4.  Fluorspar 

Thus,  the  hardness  of  a  body  which  would  scratch  felspar,  but  would  be 
scratched  by  quartz,  would  be  expressed  by  the  number  6-5. 

The  pure  metals  are  softer  than  their  alloys.  Hence  it  is  that,  for  jewel- 
lery and  coinage,  gold  and  silver  are  alloyed  with  copper  to  increase  their 
hardness. 

The  hardness  of  a  body  has  no  relation  to  its  resistance  to  compression. 
Glass  and  diamond  are  much  harder  than  wood,  but  the  latter  offers  far 
greater  resistance  to  the  blow  of  a  hammer.  Hard  bodies  are  often  used 
for  polishing  powders  ;  for  example,  emery,  pumice,  and  tripoli.  Diamond 
being  the  hardest  of  all  bodies,  can  only  be  -ground  by  means  of  its  own 
powder. 

A  body  which  moves  with  great  velocity  can  cut  into  bodies  which  are 
harder  than  itself.  Thus  a  disc  of  wrought  iron  rotating  with  a  velocity 
of  1 1  metres  in  a  second  was  cut  by  a  steel  graver ;  while  when  it  rotated 
with  a  velocity  of  20  metres,  the  edge  of  the  disc  could  cut  the  graver,  and 
with  a  velocity  of  50  to  100  metres,  it  could  even  cut  into  agate  and  quartz. 

95.  Temper. — By  sudden  cooling  after  they  have  been  raised  to  a  high 
temperature,  many  bodies  acquire  great  hardness.     This  operation  is  called 
tempering.     All  cutting  instruments  are  made  of  tempered  steel.     There  are, 
however,  some  few  bodies  upon  which  tempering  produces  quite  a  contrary 
effect.     An  alloy  of  one  part  of  tin  and  four  parts  of  copper,  called  tamtam 
metal,  is  ductile  and  malleable  when  rapidly  cooled,  but  hard  and  brittle  as 
glass  when  cooled  slowly. 


-98]  Compressibility  of  Liquids.  79 


BOOK    III. 

ON     LIQUIDS. 
CHAPTER    I. 

HYDROSTATICS. 

96.  Object  of  "Hydrostatics. — The  science  of  hydrostatics  treats  of  the 
conditions  of  the  equilibrium  of  liquids,  and  of  the  pressures  they  exert, 
whether  within  their  own  mass  or  on  the  sides  of  the  vessels  in  which  they 
are  contained. 

The  science  which  treats  of  the  motion  of  liquids  is  hydrodynamics,  and 
the  application  of  the  principles  of  this  science  to  conducting  and  raising 
water  in  pipes  is  known  by  the  name  of  hydraulics. 

97.  General  characters  of  liquids. —  It  has  been  already  seen  (4)  that 
liquids  are  bodies  whose  molecules  are  displaced  by  the  slightest  force. 
Their  fluidity,  however,  is  not  perfect  ;  their  particles  always  adhere  slightly 
to  each  other,  and  when  a  thread  of  liquid  moves,  it  attempts  to  drag  the 
adjacent  stationary  particles  with  it,  and  conversely  is  held  back  by  them. 
This  property  is  called  viscosity. 

Gases  also  possess  fluidity,  but  in  a  higher  degree  than  liquids.  The 
distinction  between  the  two  forms  of  matter  is  that  liquids  are  almost  incom- 
pressible and  are  comparatively  inexpansible,  while  gases  are  eminently 
compressible  and  expand  spontaneously. 

The  fluidity  of  liquids  is  seen  in  the  readiness  with  which  they  take  all 
sorts  of  shapes.  Their  compressibility  is  established  by  the  following  expe- 
riment. 

98.  Compressibility  of  liquids. — From  the  experiment  of  the  Florentine 
Academicians  (13),  liquids  were  for  a  long  time  regarded  as  being  completely 
incompressible.     Since  then,  researches  have  been  made  on  this  subject  by 
various  physicists,  which  have  shown  that  liquids  are  really  compressible. 

The  apparatus  used  for  measuring  the  compressibility  of  liquids  has  been 
named  the  piezometer  (nufa,  I  compress,  pfrpov,  measure).  That  shown  in 
fig.  65  consists  of  a  strong  glass  cylinder,  with  very  thick  sides,  and  an 
internal  diameter  of  about  3^  inches.  The  base  of  the  cylinder  is  firmly 
cemented  into  a  wooden  foot,  and  on  its  upper  part  is  fitted  a  metallic  cylin- 
der closed  by  a  cap  which  can  be  unscrewed.  In  this  cap  there  is  a  funnel, 


8o 


On  Liquids. 


[98- 


R,  for  introducing  water  into  the  cylinder,  and  a  small  barrel  hermetically 
closed  by  a  piston,  which  is  moved  by  a  screw,  P. 

In  the  inside  of  the  apparatus  there  is  a  glass  vessel,  A,  containing  the 
liquid  to  be  compressed.  The  upper  part  of  this  vessel  terminates  in  a 
capillary  tube,  which  dips  under  mercury,  O.  This  tube  has  been  previously 
divided  into  parts  of  equal  capacity,  and  it  has  been  determined  how  many 
of  these  parts  the  vessel  A  contains.  The  latter  is  ascertained  by  finding  the 
weight,  P,  of  the  mercury  which  the  reservoir, 
A,  contains,  and  the  weight,  /,  of  the  mercury 
contained  in  a  certain  number  of  divisions,  ;z,  of 
the  capillary  tube.  If  N  be  the  number  of 
divisions  of  the  small  tube  contained  in  the 


A 


whole  reservoir,  we  have 


N     P 


— ,  from  which  the 
P 
There   is   further   a 


value   of  N    is   obtained. 

manometer.  This  is  a  glass  tube,  B,  containing 
air,  closed  at  one  end,  and  the  other  end  of 
which  dips  under  mercury.  When  there  is  no 
pressure  on  the  water  in  the  cylinder,  the  tube 
B  is  completely  full  of  air ;  but  when  the  water 
within  the  cylinder  is  compressed  by  means  of 
the  screw  P,  the  pressure  is  transmitted  to  the 
mercury,  which  rises  in  the  tube,  compressing 
the  air  which  it  contains.  A  graduated  scale 
fixed  on  the  side  of  the  tube  shows  the  reduction 
of  volume,  and  this  reduction  of  volume  indicates 
the  pressure  exerted  on  the  liquid  in  the  cylin- 
der, as  will  be  seen  in  speaking  of  the  mano- 
meter (177). 

In  making  the  experiment,  the  vessel  A  is 
filled  with  the  liquid  to  be  compressed,  and  the 
end  dipped  under  the  mercury.  By  means  of 
the  funnel  R  the -cylinder  is  entirely  filled  with 
water.  The  screw  P  being  then  turned  the 
piston  moves  downwards,  and  the  pressure  exerted  upon  the  water  is  trans- 
mitted to  the  mercuiy  and  the  air ;  in  consequence  of  which  the  mercury 
rises  in  the  tube  B,  and  also  in  the  capillary  tube.  The  ascent  of  mercury 
in  the  capillary  tube  shows  that  the  liquid  in  the  vessel  A  has  diminished  in 
volume,  and  gives  the  amount  of  its  compression,  for  the  capacity  of  the 
whole  vessel  A  in  terms  of  the  graduated  divisions  on  the  capillary  tube  has 
been  previously  determined. 

In  his  first  experiments,  Oersted  assumed  that  the  capacity  of  the  vessel 
A  remained  the  same,  its  sides  being  compressed  both  internally  and  exter- 
nally by  the  liquid.  But  mathematical  analysis  proves  that  this  capacity 
diminishes  in  consequence  of  the  external  and  internal  pressures.  Colladon 
and  Sturm  have  made  some  experiments  allowing  for  this  change  of  capacity, 
and  have  found  that  for  a  pressure  equal  to  that  of  the  atmosphere,  mercury 
experiences  a  compression  of  0-000005  parts  of  its  original  volume,  water  a 
compression  of  0-00005,  and  ether  a  compression  of  0-000133  parts  of  its 


Fig.  65. 


-99] 


Equality  of  Pressures.     Pascal's  Law. 


81 


original  bulk.  The  compressibility  of  sea  water  is  only  about  0*000044  :  it  is 
not  materially  denser  even  at  great  depths  ;  thus  at  the  depth  of  a  mile  its 
density  would  only  be  about  T|oth  the  greater.  The  compressibility  is  greater 
the  higher  the  original  temperature  ;  thus  that  of  ether  at  14°  is  one-fourth 
greater  than  its  compressibility  at  o°. 

For  water  and  mercury  it  was  also  found  that  within  certain  limits  the 
decrease  of  volume  is  proportional  to  the  pressure. 

Whatever  be  the  pressure  to  which  a  liquid  has  been  subjected,  experi- 
ment shows  that  as  soon  as  the  pressure  is  removed  the  liquid  regains  its 
original  volume,  from  which  it  is  concluded  that  liquids  are  perfectly  elastic. 
99.  Equality  of  pressures.  Pascal's  law. — By  considering  liquids  as 
perfectly  fluid,  and  assuming  them  to  be  uninfluenced  by  the  action  of  gravity, 
the  following  law  has  been  established.  It  is  often  called  Pascal's  law,  for 
it  was  first  enunciated  by  him. 

Pressure  exerted  anywhere  upon  a  mass  of  liquid  is  transmitted  undi- 
minished  in  all  directions,  and  acts  with  the  same  force  on  all  equal  surfaces, 
and  in  a  direction  at  right  angles  to  those  surfaces. 

To  get  a  clearer  idea  of  the  truth  of  this  principle,  let  us  conceive  a  vessel 
of  any  given  form  in  the  sides  of  which  are  placed  various  cylindrical  aper- 
tures, all  of  the  same  size,  and  closed  by  movable 
pistons.     Let  us,  further,  imagine  this  vessel  to  be 
filled  with  liquid  and  unaffected  by  the  action  of 
gravity  ;  the  pistons  will,   obviously,  have  no  ten- 
dency to  move.      If  now  upon  the  piston  A  (fig. 
66;.  which  has  a  surface  a,  a  weight  of  P  pounds 
be  placed,    it   will   be   pressed   inwards,   and  the 
pressure  will  be  transmitted  to  the  internal  faces 
of  each  of  the  pistons,  B,  C,  D,  and  E,  which  will 
each  be  forced   outwards  by  a  pressure  P,   their 
surfaces   being   equal   to  that   of  the  first  piston. 
Since  each  of  the  pistons  undergoes  a  pressure  P, 
equal  to  that  on  A,  let  us  suppose  two  of  the  pis- 
tons united  so  as  to  constitute  a  surface  2#,  it  will  have  to  support  a  pres- 
sure 2  P.     Similarly,  if  the  piston  were  equal  to  3*2,  it  would  experience  a 
pressure  of  3?  ;  and  if  its  area 
were  100  or  1,000  times  that  of 
(i,  it  would  sustain  a  pressure  of 
100  or  1,000  times  P.     In  other 
words,  the  pressure  on  any  part 
of   the    internal    walls    of   the 
vessel  would  be  proportional  to 
the  surface. 

The  principle  of  the  equality 
of  pressure  is  assumed  as  a 
consequence  of%  the  constitution  yig.  6?. 

of  fluids.     By  the  following  ex- 
periment it  can  be  shown  that  pressure  is  transmitted  in  all  directions, 
although  it  cannot  be  shown  that  it  is  equally  transmitted.     A  cylinder 
provided  with  a  piston  is  fitted  into  a  hollow  sphere  (fig.  67),  in  which 

E3 


Fig.  66. 


82 


On  Liquids. 


[99- 


small  cylindrical  jets  are  placed  perpendicular  to  the  sides.  The  sphere 
and  the  cylinder  being  both  filled  with  water,  when  the  piston  is  moved 
the  liquid  spouts  forth  from  all  the  orifices,  and  not  merely  from  that  which 
is  opposite  to  the  piston. 

The  reason  why  a  satisfactory  quantitative  experimental  demonstration 
of  the  principle  of  the  equality  of  pressure  cannot  be  given  is,  that  the 
influence  of  the  weight  of  the  liquid  and  of  the  friction  of  the  pistons  cannot 
be  eliminated. 

Yet  an  approximate  verification  may  be  effected  by  the  experiment 
represented  in  fig.  68.  Two  cylinders  of  different  diameters  are  joined  by  a 
tube  and  filled  with  water.  On  the  surface  of  the  liquid  are  two  pistons  P 
and  p,  which  hermetically  close  the  cylinders,  but  move  without  friction. 

Let  the  area  of  the  large  piston  be,  for 
instance,  thirty  times  that  of  the 
smaller  one.  That  being  assumed,  let 
a  weight,  say  of  two  pounds,  be  placed 
upon  the  small  piston  ;  this  pressure 
will  be  transmitted  to  the  water  and 
to  the  large  piston,  and  as  this  pres- 
sure amounts  to  two  pounds  on  each 
portion  of  its  surface  equal  to  that  of 
the  small  piston,  the  large  piston  must 
be  exposed  to  an  upward  pressure 
thirty  times  as  much,  or  of  sixty  pounds.  If  now  this  weight  be  placed 
upon  the  large  piston,  both  will  remain  in  equilibrium  ;  but  if  the  weight  is 
greater  or  less,  this  is  no  longer  the  case.  If  S  and  s  are  the  areas  of  the 
large  and  small  piston  respectively,  and  P  and  p  the  corresponding  loads, 

then,  ?  =  ?. ;  whence  P  =  &. 
ps  s 

It  is  important  to  observe  that  in  speaking  of  the  transmission  of  pres- 
sures to  the  sides  of  the  containing  vessel,  these  pressures  must  always  be 
supposed  to  be  perpendicular  to  the  sides  ;  for  any  oblique  pressure  may  be 
decomposed  into  two  others,  one  at  right  angles  to  the  side,  and  the  other 
acting  parallel  with  the  side  ;  but  as  the  latter  has  no  action  on  the  side,  the 
perpendicular  pressure  is  the  only  one  to  be  considered. 


Fig.  68. 


PRESSURE  PRODUCED   IN   LIQUIDS  BY  GRAVITY. 

loo.  Vertical  downward  pressure  ;  its  laws.— Any  given  liquid  being" 
in  a  state  of  rest  in  a  vessel,  if  we  suppose  it  to  be  divided  into  horizontal 
layers  of  the  same  density,  it  is  evident  that  each  layer  supports  the  weight 
of  those  above  it.  Gravity,  therefore,  produces  internal  pressures  in  the 
mass  of  a  liquid  which  vary  at  different  points.  These  pressures  are 
submitted  to  the  following  general  laws  :— 

I.  The  pressure  in  each  layer  is  proportional  to  the  depth. 

II.  With  different  liquids  and  the  same  depth,  the  pressure  is  propor- 
tional to  the  density  of  the  liquid. 

III.  The  pressure  is  the  same  at  all  points  of  t  lie  same  horizontal  layer,. 


-102] 


Pressure  produced  itt  Liquids  by  Gravity. 


The  first  two  laws  are  self-evident ;  the  third  necessarily  follows  from 
the  first  and  from  Pascal's  principle. 

Meyer  has  found,  by  direct  experiments,  that  pressures  are  transmitted 
through  liquids  contained  in  tubes,  with  the  same  velocity  as  that  with  which 
sound  travels  under  the  same  circumstances. 

101.  Vertical  upward  pressure.— The  pressure  which  the  upper  layers 
of  a  liquid  exert  on  the  lower  layers  causes  them  to  exert  an  equal  reaction 
in  an  upward  direction,  a  necessary  consequence  of  the  principle  of  trans- 
mission of  pressure  in  all  directions.     This  upward  pressure  is  termed  the 
buoyancy  of  liquids  ;  it  is  very  sensible  when  the  hand  is  plunged  into  a 
liquid,  more  especially  one  of  great  density,  like  mercury. 

The  following  experiment  (fig.  69)  serves  to  exhibit  the  upward  pressure 
of  liquids.  A  large  open  glass  tube  A,  one  end  of  which  is  ground,  is  fitted 
with  a  ground-glass  disc,  O,  or  still  better  with  a 
thin  card  or  piece  of  mica,  the  weight  of  which  may 
be  neglected.  To  the  disc  is  fitted  a  string,  C,  by 
which  it  can  be  held  agairist  the  bottom  of  the  tube. 
The  whole  is  then  immersed  in  water,  and  now  the 
disc  does  not  fall,  although  no  longer  held  by  the 
string  ;  it  is  consequently  kept  in  its  position  by 
the  upward  pressure  of  the  water.  If  water  be  now 
slowly  poured  into  the  tube,  the  disc  will  only  sink 
when  the  height  of  the  water  inside  the  tube  is  equal 
to  the  height  outside.  It  follows  thence  that  the 
upward  pressure  on  the  disc  is  equal  to  the  pressure 
of  a  column  of  water,  the  base  of  which  is  the  in- 
ternal section  of  the  tube  A,  and  the  height  the 
distance  from  the  disc  to  the  upper  surface  of  the 
liquid.  Hence  the  upward  pres stir e  of  liquids  at  any  point  is  governed  by 
the  same  laws  as  the  downward  pressure. 

1 02.  Pressure    is    independent    of  the    sbape    of  the    vessel. — The 
pressure  exerted  by  a  liquid,  in  virtue  of  its  weight,  on  any  portion  of  the 
liquid,  or  on  the  sides  of  the  vessel  in  which  it  is  contained,  depends  on  the 
depth  and  density  of  the  liquid,  but  is  independent  of  the  shape  of  the  vessel 
and  of  the  quantity  of  the  liquid. 

This  principle,  which  follows  from  the  law  of  the  equality  of  pressure, 
may  be  experimentally  demonstrated  by  many  forms  of  apparatus.  The 
following  is  the  one  most  frequently  used,  and  is  due  to  Haldat.  It  consists 
of  a  bent  tube,  ABC  (fig.  70),  at  one  end  of  which,  A,  is  fitted  a  stop-cock,  in 
which  can  be  screwed  two  vessels,  M  and  P,  of  the  same  height,  but  different 
in  shape  and  capacity,  the  first  being  conical,  and  the  other  nearly  cylin- 
drical. Mercury  is  poured  into  the  tube,  ABC,  until  its  level  nearly 
reaches  A.  The  vessel  M  is  then  screwed  on  and  filled  with  water.  The 
pressure  of  the  water  acting  on  the  mercury  causes  it  to  rise  in  the  tube 
C,  and  its  height  may  be  marked  by  means  of  a  little  collar,  #,  which  slides 
up  and  down  the  tube.  The  level  of  the  water  in  M  is  also  marked  by  means 
of  the  movable  rod  o.  When  this  is  done,  M  is  emptied  by  means  of  the 
stop-cock,  unscrewed,  and  replaced  by  P.  When  water  is  now  poured  in 
this,  the  mercury,  which  had  resumed  its  original  level  in  the  tube  ABC, 


Fig.  69. 


On  Liquids. 


[102- 


again  rises  in  C,  and  when  the  water  in  P  has  the  same  height  as  it  had  in 
M,  which  is  indicated  by  the  rod  o,  the  mercury  will  have  risen  to  the 
•height  it  had  before,  which  is  marked  by  the  collar  a.  Hence  the  pressure 
on  the  mercury  in  both  cases  is  the  same.  This  pressure  is  therefore  inde- 
pendent of  the  shape  of  the  vessels,  and,  consequently,  also  of  the  quantity 


Fig.  70. 

of  liquid.     The  base  of  the  vessel  is  obviously  the  same  in  both  cases  ;  it  is 
the  surface  of  the  mercury  in  the  interior  of  the  tube  A. 

Another  mode  of  demonstrating  this  principle  is  by  means  of  an  apparatus 
devised  by  Masson.  In  this  (fig.  71)  the  pressure  of  the  water  contained  in 
the  vessel  M  is  not  exerted  upon  the  column  of  mercury,  as  in  that  of 
Haldat,  but  on  a  small  disc  or  stop  a,  which  closes  a  tubulure  £,  on  which  is 
screwed  the  vessel  M.  The  disc  is  not  fixed  to  the  tubulure,  but  is  sustained 
by  a  thread  attached  to  the  end  of  a  scale-beam.  At  the  other  end  is  a  pan 
in  which  weights  can  be  placed  until  they  counterbalance  the  pressure 
exerted  by  the  water  on  the  stop.  The  vessel  M  being  emptied  is  unscrewed, 
and  replaced  by  the  narrow  tube  O.  This  being  filled  to  the  same  height 
as  the  large  vessel,  which  is  observed  by  means  of  the  mark  <?,  it  will  be 
observed  that  to  keep  the  disc  in  its  place  just  the  same  weight  must  be 
placed  in  the  pan  as  before,  which  leads,  therefore,  to  the  same  conclusion 
as  does  Haldat's  experiment.  The  same  result  is  obtained  if,  instead  of  the 
vertical  tube  P,  the  oblique  tube  Q  be  screwed  to  the  tubulure. 

From  a  consideration  of  these  principles  it  will  be  readily  seen  that  a 
very  small  quantity  of  water  can  produce  considerable  pressures.  Let  us 
imagine  any  vessel — a  cask,  for  example — filled  with  water  and  with  a  long 
narrow  tube  tightly  fitted  into  the  side.  If  water  is  poured  into  the  tube, 
there  will  be  a  pressure  on  the  bottom  of  the  cask  equal  to  the  weight  of  a 
column  of  water  whose  base  is  the  bottom  itself,  and  whose  height  is  equal 


-103] 


Pressure  on  the  ^Sides  of  Vessels. 


85 


to  that  of  the  water  in  the  tube.  The  pressure  may  be  made  as  great  as  we 
please  ;  by  means  of  a  narrow  thread  of  water  forty  feet  high,  Pascal  suc- 
ceeded in  bursting  a  very  solidly  constructed  cask. 

The  toy  known  as  the  hydrostatic  bellows  depends  on  the  same  principle, 
and  we  shall  shortly  see  a  most  important  application  of  it  in  the  hydraulic 
press. 

From  the  principle  just  laid  down,  the  pressures  produced  at  the  bottom 
of  the  sea  may  be  calculated.  It  will  be  presently  demonstrated  that  the 
pressure  of  the  atmosphere  is  equal  to  that  of  a  column  of  sea-water  about 


Fig.  71. 

thirty-three  feet  high.  At  sea  the  lead  has  frequently  descended  to  a  depth 
of  thirteen  thousand  feet ;  at  the  bottom  of  some  seas,  therefore,  there  must 
be  a  pressure  of  four  hundred  atmospheres. 

103.  Pressure  on  the  sides  of  vessels. — Since  the  pressure  caused  by 
gravity  in  the  mass  of  a  liquid  is  transmitted  in  every  direction,  according  to 
the  general  law  of  the  transmission  of  fluid  pressure,  it  follows  that  at  every 
point  of  the  side  of  any  vessel  a  pressure  is  exerted,  at  right  angles  to  the 
side,  which  we  will  suppose  to  be  plane.  The  resultant  of  all  these 
pressures  is  the  total  pressure  on  the  sides.  But  since  these  pressures  in- 
crease in  proportion  to  the  depth,  and  also  in  proportion  to  the  horizontal 
extent  of  their  side,  their  resultant  can  only  be  obtained  by  calculation, 
which  shows  that  the  total  pressure  on  any  given  portion  of  the  side  is  equal 
to  the  weight  of  a  column  of  liquid,  which  has  this  portion  of  the  side  for  its 
base,  and  whose  height  is  the  vertical  distance  from  the  centre  of  gravity  of 
the  portion  to  the  surface  of  the  liquid.  If  the  side  of  a  vessel  is  a  curved 
surface  the  same  rule  gives  the  pressure  on  the  surface,  but  the  total  pres- 
sure is  no  longer  the  resultant  of  the  fluid  pressures. 

The  point  in  the  side  supposed  plane,  at  which  the  resultant  of  all  the 
pressure  is  applied,  is  called  the  centre  of  pressure,  and  is  always  below  the 


86  On  Liquids.  [103- 

centre  of  gravity  of  the  side.  For  if  the  pressures  exerted  at  different  parts 
of  the  plane  side  were  equal,  the  point  of  application  of  their  resultant,  the 
centre  of  pressure  would  obviously  coincide  with  the  centre  of  gravity  of  the 
side.  But  since  the  pressure  increases  with  the  depth,  the  centre  of  pressure 
is  necessarily  below  the  centre  of  gravity.  This  point  is  determined  by  cal- 
culation which  leads  to  the  following  results  : — 

i.  With  a  rectangular  side  whose  upper  edge  is  level  with  the  water,  the 
centre  of  pressure  is  at  two-thirds  of  the  line  which  joins  the  middle  of  the 
horizontal  sides  measured  from  the  top. 

ii.  With  a  triangular  side  whose  base  is  horizontal,  and  coincident  with 
the  level  of  the  water,  the  centre  of  pressure  is  at  the  middle  of  the  line 
which  joins  the  vertex  of  the  triangle  with  the  middle  of  the  base. 

iii.  With  a  triangular  side  whose  vertex  is  level  with  the  water,  the  centre 
of  pressure  is  in  the  line  joining  the  vertex  and  the  middle  of  the  base,  and 
at  three-fourths  of  the  distance  ^of  the  latter  from  the  vertex. 

104.  Hydrostatic  paradox. — We  have  already  seen  that  the  pressure  on 
the  bottom  of  a  vessel  depends  neither  on  the  form  of  the  vessel  nor  on  the 
quantity  of  the  liquid,  but  simply  on  the  height  of  the  liquid  above  the 
bottom.     But  the  pressure  thus  exerted  must  not  be  confounded  with  the 
pressure  which  the  vessel  itself  exerts  on  the  body  which  supports  it.     The 
latter  is  always  equal  to  the  cofnbined  weight  of  the  liquid  and  the  vessel  in 
which  it  is  contained,  while  the  former  may  be  either  smaller  or  greater  than 
this  weight  according  to  the  form  of  the  vessel.     This  fact  is  often  termed 
the  hydrostatic  paradox,  because  at  first  sight  it  appears  paradoxical. 

CD  (fig.  72)  is  a  vessel  composed  of  two  cylindrical  parts  of  unequal  dia- 
meters, and  filled  with  water  to  a.  From  what  has  been  said  before,  the 
bottom  of  the  vessel  CD  supports  the  same  pressure 
as  if  its  diameter  were  everywhere  the  same  as  that 
of  its  lower  part ;  and  it  would  at  first  sight  seem  that 
the  scale  MN  of  the  balance,  in  which  the  vessel  CD 
is  placed,  ought  to  show  the  same  weight  as  if  there 
had  been  placed  in  it  a  cylindrical  vessel  having  the 
same  height  of  water,  and  having  the  diameter  of  the 
part  D.  But  the  pressure  exerted  on  the  bottom  of 
the  vessel  is  not  all  transmitted  to  the  scale  MN  ;  for 
the  upward  pressure  upon  the  surface  no  of  the  vessel 
*  is  precisely  equal  to  the  weight  of  the  extra  quantity  of 
water  which  a  cylindrical  vessel  would  contain,  and 
balances  an  equal  portion  of  the  downward  pressure 
"'rig"  72""  on;;/.  Consequently,  the  pressure  on  the  plate  MN  is 

simply  equal  to  the  weight  of  the  vessel  CD  and  of  the 
water  which  it  contains. 

CONDITIONS   OF  THE   EQUILIBRIUM   OF   LIQUIDS. 

105.  Equilibrium  of  a  liquid  in  a  single  vessel. —  In  order  that  a  liquid 
may  remain  at  rest  in  a  vessel  of  any  given  form,  it  must  satisfy  the  two 
following  conditions  : — 

I.  Its  surface  must  be  everywhere  perpendicular  to  the  resultant  of  the 
forces  which  act  on  the  molecules  of  the  liquid. 


-106] 


Conditions  of  the  Equilibrium  of  Liquids. 


II.  Every  molecule  of  the  mass  of  the  liquid  must  be  subject  in  every 
direction  to  equal  and  contrary  pressures. 

The  second  condition  is  self-evident ;  for  if,  in  two  opposite  directions, 
the  pressures  exerted  on  any  given  molecule  were  not  equal  and  contrary, 
the  molecule  would  be  moved  in  the  direction  of  the  greater  pressure,  and 
there  would  be  no  equilibrium,  Thus  the  second  condition  follows  from  the 
principle  of  the  equality  of  pressures,  and  from  the  reaction  which  all  pres- 
sure causes  on  the  mass  of  liquids. 

To  prove  the  first  condition,  let  us  suppose  that  mp  is  the  resultant  of  all 
the  forces  acting  upon  any  molecule  m  on  the  surface  (fig.  73),  and  that  this 
surface  is  inclined  in  reference  to  the  force  mp. 
The  latter  can  consequently  be  decomposed  into 
two  forces,  mq  and  mf;  the  one  perpendicular  to 
the  surface  of  the  liquid  and  the  other  to  the 
direction  mp*  Now  the  first  force,  mq,  would  be 
destroyed  by  the  resistance  of  the  liquid,  while 
the  second  would  move  the  molecule  in  the  direc-  Fig.  73. 

tion  mf,  which  shows  that  the  equilibrium  is  impossible. 

If  gravity  be  the  force  acting  on  the  liquid,  the  direction  mp  is  vertical  ; 
hence,  if  the  liquid  is  contained  in  a  basin  or  vessel  of  small  extent,  the  sur- 
face ought  to  be  plane  and  horizontal  (68),  because  then  the  direction  of 
gravity  is  the  same  in  ever}7  point.  But  the  case  is  different  with  liquid  sur- 
faces of  greater  extent,  like  the  ocean.  The  surface  will  be  perpendicular  to 
the  direction  of  gravity  :  but  as  this  changes  from  one  point  to  another, 
and  always  tends  towards  a  point  near  the  centre  of  the  earth,  it  follows  that 
the  direction  of  the  surface  of  the  ocean  will  change  also,  and  assume  a 
nearly  spherical  form. 

1 06.  Equilibrium  of  the  same  liquid  in  several  communicating 
vessels.— When  several  vessels  of  any  given  form  communicate  with  each 
other,  there  will  be  equilibrium  when  the  liquid  in  each  vessel  satisfies  the 
two  preceding  conditions  (105),  and 
further,  ivhen  the  surfaces  of  the  li- 
quids in  all  the  vessels  are  in  the  same 
horizontal  plane. 

In  the  vessels  ABCD  (fig.  74), 
which  communicate  with  each  other, 
let  us  consider  any  transverse  section 
of  the  tube  mn  ;  the  liquid  can  only 
remain  in  equilibrium  as  long  as  the 
pressures  which  this  section  supports 
from  ///  in  the  direction  of  n,  and  from 
n  in  the  direction  of  m,  are  equal  and 
opposite.  Now.  it  has  been  already 
proved  that  these  pressures  are  respec- 
tively equal  to  the  weight  of  a  column 
of  water,  whose  base  is  the  supposed 


Fig.  74- 


section,  and  whose  height  is  the  distance  from  the  centre  of  gravity  of  this 
section  to  the  surface  of  the  liquid.  If  we  conceive,  then,  a  horizontal  plane, 
mn,  drawn  through  the  centre  of  gravity  of  this  section,  it  will  be  seen  that 


88 


On  Liquids. 


[106- 


there  will  only  be  equilibrium  as  long  as  the  height  of  the  liquid  above  this 
plane  is  the  same  in  each  vessel,  which  demonstrates  the  principle  enunciated. 

107.  Equilibrium  of  superposed  liquids. — In  order  that  there  should 
be  equilibrium  when  several  heterogeneous  liquids  are  superposed  in  the 
same  vessel,  each  of  them  must  satisfy  the  conditions  necessary  for  a  single 
liquid  (105)  ;  and  further,  there  will  be  stable  equilibrium  only  when  the 
liquids  are  arranged  in  the  order  of  their  decreasing  densities  from  the 
bottom  upwards. 

The  last  condition  is  experimentally  demonstrated  by  means  of  the  phial 
of  four  elements.  This  consists  of  a  long  narrow  bottle  containing  mercury, 
water  saturated  with  carbonate  of  potass,  alcohol  coloured  red,  and  petroleum. 
When  the  phial  is  shaken  the  liquids  mix,  but  when  it  is  allowed  to  rest  they 
separate  ;  the  mercury  sinks  to  the  bottom,  then  comes  the  water,  then  the 
alcohol,  and  then  the  petroleum.  This  is  the  order  of  the  decreasing  densi- 
ties of  the  bodies.  The  water  is  saturated  with  carbonate  of  potass  to  pre- 
vent its  mixing  with  the  alcohol. 

This  separation  of  the  liquids  is  due  to  the  same  cause  as  that  which 
enables  solid  bodies  to  float  on  the  surface  of  a  liquid  of  greater  density 
than  their  own.  It  is  also  on  this  account  that  fresh  water,  at  the  mouths 
of  rivers,  floats  for  a  long  time  on  the  denser  salt  water  of  the  sea  ;  and  it  is 
for  the  same  reason  that  cream,  which  is  lighter  than  milk,  rises  to  the  surface. 

1 08.  Equilibrium     of     two     different     liquids     in     communicating 
vessels. — When  two  liquids  of  different  densities,  which  do  not  mix,  are 
contained  in  two  communicating  vessels,  they  will  be  in  equilibrium  when, 
in  addition  to  the  preceding  principles,  they  are  subject  to  the  following  : 
that  the  heights  above  the  horizontal  surface  of  contact  of  two  columns  of 
liquid  in  equilibrium  are  in  the  inverse  ratio  of  their  densities. 

To  show  this  experimentally,  mercury  is  poured  into  a  bent  glass  tube, 
mn,  fixed  against  an  upright  wooden  support  (fig.  75),  and  then  water  is 

poured  into  one  of  the  legs,  AB.  The 
column  of  water,  AB,  pressing  on  the 
mercury  at  B,  lowers  its  level  in  the  leg  AB, 
and  raises  it  in  the  other  by  a  quantity,  CD  ; 
so  that  if,  when  equilibrium  is  established, 
we  imagine  a  horizontal  plane,  BC,  to  pass 
through  B,  the  column  of  water  in  AB  will 
balance  the  column  of  mercury  CD.  If  the 
heights  of  these  two  columns  are  then 
measured,  by  means  of  the  scales,  it  will  be 
found  that  the  height  of  the  column  of  water 
is  about  131  times  that  of  the  height  of  the 
column  of  mercury.  We  shall  presently  see 
that  the  density  of  mercury  is  about  13! 
times  that  of  water,  from  which  it  follows 
that  the  heights  are  inversely  as  the  den- 
sities. 

It  may  be  added  that   the    equilibrium 

cannot  exist  unless  there  is  a  sufficient  quantity  of  the  heavier  liquid  for  part 
of  it  to  remain  in  both  legs  of  the  tube. 


Fig.  75- 


-109] 


Hydraulic  Press. 


The  preceding  principle  may  be  deduced  by  a  very  simple  calculation. 
Let  d  and  d'  be  the  densities  of  water  and  mercury,  and  h  and  h'  their  re- 
spective heights,  and  let  g  be  the  force  of  gravity.  The  pressure  on  B  will 
be  proportional  to  the  density  of  the  liquid,  to  its  height,  and  to  the  force  of 
gravity  ;  on  the  whole,  therefore,  to  the  product  dhg.  Similarly  the  pres- 
sure at  C  will  be  proportional  to  d'h'g.  But  in  order  to  produce  equilibrium, 
dhg  must  be  equal  to  d'h'g,  or  dh  =  dh'.  This  is  nothing  more  than  an 
algebraical  expression  of  the  above  principle  ;  for  since  the  two  products 
must  always  be  equal,  cf  must  be  as  many  times  greater  than  d,  as  h'  is  less 
than  h. 

In  this  manner  the  density  of  a  liquid  may  be  determined.  Suppose  one 
of  the  branches  contained  water  and  the  other  oil,  and  their  heights  were, 
respectively,  15  inches  for  the  oil  and  14  inches  for  the  water.  The  density 
of  water  being  taken  as  unity,  and  that  of  oil  being  called  x,  we  shall  have 


15  x  x 


14  x  i  ;  whence  x=      =  0-933. 


APPLICATIONS   OF  THE  PRECEDING   HYDROSTATIC  PRINCIPLES. 

109.  Hydraulic  press.  —  The  law  of  the,  equality  of  pressure  has  received 
a  most  important  application  in  the  hydraulic  press,  a  machine  by  which 


Fig.  76. 

enormous  pressures  may  be  produced.     Its  principle  is  due  to  Pascal,  but  it 
was  first  constructed  by  Bramah  in  1796. 

It  consists  of  a  cylinder,  B,  with  very  strong   thick  sides    (fig.  76),  in 


On  Liquids. 


[109- 


which  there  is  a  cast-iron  ram,  P,  working  water-tight  in  the  collar  of  the 
cylinder.  On  the  ram  P  there  is  a  cast-iron  plate  on  which  the  substance 
to  be  pressed  is  placed.  Four  strong  columns  serve  to  support  and  fix  a 
second  plate  O. 

By  means  of  a  leaden  pipe  K,  the  cylinder,  B,  which  is  filled  with  water, 
communicates  with  a  small  force-pump,  A,  which  works  by  means  of  a  lever, 
M.  When  the  piston  of  this  pump/  ascends,  a  vacuum  is  produced  and  the 
water  rises  in  the  tube  a,  at  the  end  of  which  there  is  a  rose,  to  prevent  the 
entrance  of  foreign  matters.  When  the  piston/  descends,  it  drives  the  water 
into  the  cylinder  by  the  tube  K. 

Fig.  77  represents  a  section,  on  a  larger  scale,  of  the  system  of  valves 
necessary  in  working  the  apparatus.  The  valve  o,  below  the  piston  /,  opens 


when  the  piston  rises,  and  closes  when  it  descends.  The  valve  0,  during 
this  descent,  is  opened  by  the  pressure  of  the  water  which  passes  by  the  pipe 
K.  The  valve  /  is  a  safety  valve,  held  by  a  weight  which  acts  on  it  by  means 
of  a  lever.  By  weighting  the  latter  to  a  greater  or  less  extent  the  pressure 
can  be  regulated,  for  as  soon  as  there  is  an  upward  pressure  greater  than 
that  of  the  weight  upon  it,  it  opens  and  water  escapes.  A  screw  r  serves  to 
relieve  the  pressure,  for  when  it  is  opened  it  affords  a  passage  for  the  efflux 
of  the  water  in  the  cylinder  B. 

A  most  important  part  is  the  leather  collar,  ;z,  the  invention  of  which  by 
Bramah  removed  the  difficulties  which  had  been  experienced  in  making  the 
large  ram  work  water-tight  when  submitted  to 
great  pressures.  It  consists  of  a  circular  piece 
of  stout  leather,  fig.  78,  saturated  with  oil  so  as 
to  be  impervious  to  water,  in  the  centre  of  which 
a  circular  hole  is  cut.  This  piece  is  bent  so 
that  a  section  of  it  represents  a  reversed  U,  and 
is  fitted  into  a  groove  n  made  in  the  neck  of  the 
cylinder.  This  collar  being  concave  downwards, 

in  proportion  as  the  pressure  increases,  it  fits  the  more  tightly  against  the 
ram  P  on  one  side  and  the  neck  of  the  cylinder  on  the  other,  and  quite 
prevents  any  escape  of  water. 

The  pressure  which  can  be  obtained  by  this  press  depends  on  the  relation 


-110]  Water 

of  the  piston  P  to  that  of  the  piston  p.  If  the  former  has  a  transverse  section 
fifty  or  a  hundred  times  as  large  as  the  latter,  the  upward  pressure  on  the 
large  piston  will  be  fifty  or  a  hundred  times  that  exerted  upon  the  small  one. 
By  means  of  the  lever  M  an  additional  advantage  is  obtained.  If  the 
distance  from  the  fulcrum  to  the  point  where  the  power  is  applied  is  five  times 
the  distance  from  the  fulcrum  to  the  piston  p,  the  pressure  on  p  will  be  five 
times  the  power.  Thus,  if  a  man  acts  on  M  with  a  force  of  sixty  pounds, 
the  force  transmitted  by  the  piston/  will  be  300  pounds,  and  the  force  which 
tends  to  raise  the  piston  P  will  be  30,000  pounds,  supposing  the  section  of  P 
is  a  hundred  times  that  of/. 

The  hydraulic  press  is  used  in  all  cases  in  which  great  pressures  are  re- 
quired. It  is  used  in  pressing  cloth  and  paper,  in  extracting  the  juice  of  beet- 
root, in  compressing  hay  and  cotton,  in  expressing  oil  from  seeds,  and  in 
bending  iron  plates  ;  it  also  serves  to  test  the  strength  of  cannon,  of  steam 
boilers,  and  of  chain  cables.  The  parts  composing  the  tubular  bridge  which 
spans  the  Menai  Straits  were  raised  by  means  of  an  hydraulic  press.  The 
cylinder  of  this  machine,  the  largest  which  has  ever  been  constructed,  was 
nine  feet  long,  and  twenty-two  inches  in  internal  diameter ;  it  was  capable 
of  raising  a  weight  of  two  thousand  tons. 

The  principle  of  the  hydraulic  press  is  advantageously  employed  in  cases 
in  which  great  power  is  only  required  at  intervals,  such  as  in  opening  dock 
gates,  in  lifts  in  hotels,  warehouses,  and  the  like.  In  these  cases  an  accu- 
mulator is  used.  The  piston  P  is  loaded  with  very  great  weights,  and  water 
is  forced  into  the  cylinder  B  by  powerful  pumps.  From  the  bottom  of  this 
cylinder  a  tube  conducts  water  to  any  place  where  the  power  is  to  be  applied, 
and  the  flow  of  even  small  quantities  of  water  can  perform  a  great  amount 
of  work. 

Suppose,  for  instance,  the  area  of  the  piston  P  is  four  square  feet,  and 
that  it  has  a  load  of  100  tons  ;  that  represents  a  pressure  of  over  370  pounds 
on  the  square  inch,  or  more  than  25  atmospheres.  When  the  large  piston 
sinks  through  the  —th  of  an  inch  about  a  pint  of  water  will  flow  out,  and 
this  represents  a  work  of  about  1,100  foot-pounds. 

1 10.  Water  level. — The  water  level  is  an  application  of  the  conditions 


Fig.  79. 

of  equilibrium  in  communicating  vessels.     It  consists  of  a  metal  tube  bent 
at  both  ends,  in  which  are  fitted  glass  tubes  D  and  E  (fig.  79).     It  is  placed 


On  Liquids. 


[110- 


on  a  tripod,  and  water  poured  in  until  it  rises  in  both  legs.  When  the  liquid 
is  at  rest,  the  level  of  the  water  in  both  tubes  is  the  same  ;  that  is,  they  are 
both  in  the  same  horizontal  plane. 

This  instrument  is  used  in  levelling,  or  ascertaining  how  much  one  point 
is  higher  than  another.  If,  for  example,  it  is  desired  to  find  the  difference 
between  the  heights  of  B  and  A,  a  levelling-staff  is  fixed  on  the  latter  place. 
This  staff  consists  of  a  rule  formed  of  two  sliding  pieces  of  wood,  and  sup- 
porting a  piece  of  tin  plate  M,  in  the  centre  of  which  there  is  a  mark.  This 
staff  being  held  vertically  at  A,  an  observer  looks  at  it  through  the  level 
along  the  surfaces  D  and  E,  and  directs  the  holder  to  raise  or  lower  the  slide 
until  the  mark  is  in  the  prolongation  of  the  line  DE.  The  height  AM  is 
then  measured,  and  subtracting  it  from  the  height  of  the  level,  the  height  of 
the  point  A  above  B  is  obtained. 

in.  Spirit  level. — The  spirit  level  is  both  more  delicate  and  more  ac- 
curate than  the  water  level.  It  consists  of  a  glass  tube,  AB  (fig.  80),  very 

slightly    curved  ;    that  is, 

Fis-  8o-  the  tube,  instead  of  being 

a  true  cylinder  as  it  seems 
to  be,  is  in  fact  slightly 
curved  in  such  a  manner 
that  its  axis  is  an  arc  of  a 
circle  of  very  large  radius. 
It  is  filled  with  spirit  with 
the  exception  of  a  bubble 
of  air,  which  tends  to 
occupy  the  highest  part. 
The  tube  is  placed  in  a 
brass  case,  CD  (fig.  Si), 


Fig.  81. 


which  is  so  arranged  that  when  it  is  in  a  perfectly  horizontal  position  the 
bubble  of  air  is  exactly  between  the  two  points  marked  in  the  case. 

To  take  levels  with  this  apparatus,  it  is  fixed  on  a  telescope,  which  can 
consequently  be  placed  in  a  horizontal  position. 

112.  Artesian  wells. — All  natural  collections  of  water  exemplify  the 
tendency  of  water  to  find  its  level.  Thus,  a  group  of  lakes,  such  as  the 
great  lakes  of  North  America,  may  be  regarded  as  a  number  of  vessels  in 
communication,  and  consequently  the  waters  tend  to  maintain  the  same 
level  in  all.  This,  too,  is  the  case  with  the  source  of  a  river  and  the  sea, 
and,  as  the  latter  is  on  the  lower  level,  the  river  continually  flows  down  to 
the  sea  along  its  bed,  which  is,  in  fact,  the  means  of  communication  between 
the  two. 

Perhaps  the  most  striking  instance  of  this  class  of  natural  phenomena  is 
that  of  artesian  wells.  These  wells  derive  their  name  from  the  province 
of  Artois,  where  it  has  long  been  customary  to  dig  them,  and  from  whence 
their  use  in  other  parts  of  France  and  Europe  was  derived.  It  seems,  how- 
ever, that  at  a  very  remote  period  wells  of  the  same  kind  were  dug  in  China 
and  Egypt. 

To  understand  the  theory  of  these  wells,  it  must  be  premised  that  the 
strata  composing  the  earth's  crust  are  of  two  kinds  :  the  one  permeable  to 
water,  such  as  sand,  gravel,  &c.  ;  the  other  impermeable^  such  as  clay.  Let 


-113] 


Bodies  Immersed  in  Liquids. 


93 


us  suppose,  then,  a  geographical  basin  of  greater  or  less  extent,  in  which  the 
two  impermeable  layers  AB,  CD  (fig.  82),  enclose  between  them  a  permeable 
layer  KK.  The  rain-water  falling  on  the  part  of  this  layer  which  comes  to 
the  surface,  which  is  called  the  outcrop,  will  filter  through  it,  and  following 
the  natural  fall  of  the  ground  will  collect  in  the  hollow  of  the  basin,  whence 
it  cannot  escape  owing  to  the  impermeable  strata  above  and  below  it.  If, 
now,  a  vertical  hole,  I,  be  sunk  down  to  the  water-bearing  stratum,  the 
water  striving  to  regain  its  level  will  spout  out  to  a  height  which  depends  on 
the  difference  between  the  levels  of  the  outcrop  and  of  the  point  at  which 
the  perforation  is  made. 

The  waters  which  feed  artesian  wells  often  come  from  a  distance  of 
sixty  or  seventy  miles.     The  depth  varies  in  different  places.     The  well  at 


Fig.  82. 

Crenelle  is  1,800  feet  deep  ;  it  gives  656  gallons  of  water  in  a  minute,  and 
is  one  of  the  deepest  and  most  abundant  which  has  been  made.  The 
temperature  of  the  water  is  27°  C.  t  follows  from  the  law  of  the  in- 
crease of  temperature  with  the  increasing  depth  below  the  surface  of  the 
ground,  that,  if  this  well  were  210  feet  deeper,  the  water  would  have  all 
the  year  round  a  temperature  of  32°  C.  ;  that  is,  the  ordinary  temperature  of 
baths. 


BODIES    IMMERSED    IN    LIQUIDS. 

113.  Pressure  supported  by  a  body  immersed  in  a  liquid. — When  a 
solid  is  immersed  in  a  liquid,  every  portion  of  its  surface  is  submitted  to  a 
perpendicular  pressure  which  increases  with  the  depth.  If  we  imagine  all 
these  pressures  decomposed  into  horizontal  and  vertical  pressures,  the'  first 
set  are  in  equilibrium.  The  vertical  pressures  are  obviously  unequal,  and 
will  tend  to  move  the  body  upwards. 

Let  us  imagine  a  cube  immersed  in  a  mass  of  water  (fig.  83),  and  that 
four  of  its  edges  are  vertical.  The  pressures  upon  the  four  vertical  faces  being 
clearly  in  equilibrium,  we  need  only  consider  the  pressures  exerted  on  the 
horizontal  faces  A  and  B.  The  first  is  pressed  downwards  by  a  column  of 
water,  whose  base  is  the,  face  A,  and  whose  height  is  AD,  the  lower  face  B 


94  On  Liquids.  [113- 

is  pressed  upwards  by  the  weight  of  a  column  of  water  whose  base  is  the 
face  itself,  and  whose  height  is  BD  (101).  The  cube,  therefore,  is  urged 
upwards  by  a  force  equal  to  the  difference  between 
these  two  pressures,  which  latter  is  manifestly  equal 
to  the  weight  of  a  column  of  water  having  the  same 
base  and  the  same  height  as  this  cube.  Consequently 
this  upward  pressure  is  equal  to  the  weight  of  the 
'volume  of  water  displaced  by  the  immersed  body. 

We  shall  readily  see  from  the  following  reason- 
ing that  every  body  immersed  in  a  liquid  is  pressed 
upwards  by  a  force  equal  to  the  weight  of  the  dis- 
placed liquid.  In  a  liquid  at  rest,  let  us  suppose  a 
portion  of  it  of  any  given  shape,  regular  or  irregular, 
to  become  solidified,  without  either  increase  or  de- 
crease of  volume.  The  liquid  thus  solidified  will 
remain  at  rest,  and  therefore  must  be  acted  upon  by 
a  force  equal  to  its  weight,  and  acting  vertically  up- 
wards through  its  centre  of  gravity  ;  for  otherwise  motion  would  ensue.  If 
in  the  place  of  the  solidified  water  we  imagine  a  solid  of  another  substance  of 
exactly  the  same  volume  and  shape,  it  will  necessarily  receive  the  same  pres- 
sures from  the  surrounding  liquid  as  the  solidified  portion  did  ;  hence,  like 
the  latter,  it  will  sustain  the  pressure  of  a  force  acting  vertically  upwards 
through  the  centre  of  gravity  of  the  displaced  liquid,  and  equal  to  the  weight 
of  the  displaced  liquid.  If,  as  almost  invariably  happens,  the  liquid  is  of 
uniform  density,  the  centre  of  gravity  of  the  displaced  liquid  means  the  centre 
of  gravity  of  the  immersed  part  of  the  body  supposed  to  be  of  tiniform  density. 
This  distinction  is  sometimes  of  importance  ;  for  example,  if  a  sphere  is  com- 
posed of  a  hemisphere  of  iron  and  another  of  wood,  its  centre  of  gravity 
would  not  coincide  with  its  geometrical  centre ;  but  if  it  were  placed  .under 
water,  the  centre  of  gravity  of  the  displaced  water  would  be  at  the  geome- 
trical centre ;  that  is,  would  have  the  same  position  as  the  centre  of  gravity  of 
the  sphere  if  of  uniform  density. 

1 14.  Principle  of  Archimedes. — The  preceding  principles  prove  that 
every  body  immersed  in  a  liquid  is  submitted  to  the  action  of  two  forces  : 
gravity  which  tends  to  lower  it,  and  the  buoyancy  of  the  liquid  which  tends 
to  raise  it  with  a  force  equal  to  the  weight  of  the  liquid  displaced.  The 
weight  of  the  body  is  either  totally  or  partially  overcome  by  this  buoyancy, 
from  which  it  is  concluded  that  a  body  immersed  in  a  liquid  loses  a  part  of 
its  weight  equal  to  the  weight  of  the  displaced  liquid. 

This  principle,  which  is  the  basis  of  the  theory  of  immersed  and  floating 
bodies,  is  called  the  principle  of  Archimedes,  after  the  discoverer.  It  may 
be  shown  experimentally  by  means  of  the  hydrostatic  balance  (fig.  84).  This 
is  an  ordinary  balance,  each  pan  of  which  is  provided  with  a  hook  ;  the 
beam  can  be  raised  by  means  of  a  toothed  rack,  which  is  worked  by  a  little 
pinion,  C.  A  catch,  D,  holds  the  rack  when  it  has  been  raised.  The  beam 
being  raised,  a  hollow  brass  cylinder,  A,  is  suspended  to  one  of  the  pans, 
and  below  this  a  solid  cylinder,  B,  whose  volume  is  exactly  equal  to  the 
capacity  of  the  first  cylinder  ;  lastly,  an  equipoise  is  placed  in  the  other  pan. 
If  now  the  hollow  cylinder  A  be  filled  with  water  the  equilibrium  is  disturbed  ; 


_116]  Equilibrium  of  Floating  Bodies.  95 

but  if  at  the  same  time  the  beam  is  lowered  so  that  the  solid  cylinder  B  be- 
comes immersed  in  a  vessel  of  water  placed  beneath  it,  the  equilibrium  will 
be  restored.  By  being  immersed  in  water  the  cylinder  B  loses  a  portion  of 
its  weight  equal  to  that  of  the  water  in  the  cylinder  A.  Now  as  the  capacity 
of  the  cylinder  A  is  exactly  equal  to  the  volume  of  the  cylinder  B,  the  prin» 
ciple  which  has  been  before  laid  down  is  proved. 


Fig.  84. 

1 1 5.  Determination  of  the  volume  of  a  body. — The  principle  of  Archi- 
medes furnishes  a  method  for  obtaining  the  volume  of  a  body  of  any  shape, 
provided  it  is  not  soluble  in  water.     The  body  is  suspended  by  a  fine  thread 
to  the  hydrostatic  balance,  and  is  weighed  first  in  the  air,  and  then  in  dis- 
tilled water  at  4°  C.     The  loss  of  weight  is  the  weight  of  the  displaced  water, 
from  which  the  volume  of  the  displaced  water  is  readily  calculated.     But 
this  volume  is  manifestly  that  of  the  body  itself.     Suppose,  for  example,  155 
grammes  is  the  loss  of  weight.     This  is  consequently  the  weight  of  the  dis- 
placed water.     Now  it  is  known  that  a  gramme  is  the  weight  of  a  cubic 
centimetre  of  water  at  4°  ;  consequently,  the  volume  of  the  body  immersed 
is  155  cubic  centimetres. 

1 1 6.  Equilibrium  of  floating  bodies. — A  body  when  floating  is  acted 
on   by  two   forces,  namely  its   weight,   which   acts   vertically   downwards 


On  Liquids. 


[116- 


through  its  centre  of  gravity,  and  the  resultant  of  the  fluid  pressures,  which 
(113)  acts  vertically  upwards  through  the  centre  of  gravity  of  the  fluid 
displaced  ;  but  if  the  body  is  at  rest  these  two  forces  must  be  equal  and 
act  in  opposite  directions  ;  whence  follow  the  conditions  of  equilibrium, 
namely  : — 

i.  The  floating  body  must  displace  a  volume  of  liquid  whose  weight  equals 
that  of  the  body. 

ii.  The  centre  of  gravity  of  the  floating  body  must  be  in  the  same  vertical 
line  with  that  of  the  fluid  displaced. 

Thus  in  fig.  85,  if  C  is  the  centre  of  gravity  of  the  body  and  G  that  of 
the  displaced  fluid,  the  line  GC  must  be  vertical,  since  when  it  is  so  the 
weight  of  the  body  and  the  fluid  pressure  will  act  in  opposite  directions 
along  the  same  line,  and  will  be  in  equilibrium  if  equal.  It  is  convenient, 
with  reference  to  the  subject  of  the  present  article,  to  speak  of  the  line  CG 
produced  as  the  axis  of  the  body. 

Next  let  it  be  inquired  whether  the  equilibrium  be  stable  or  unstable. 
Suppose  the  body  to  be  turned  through  a  small  angle  (fig.  86),  so  that  the 

axis  takes  a  position 
inclined  to  the  vertical. 
The  centre  of  gravity 
of  the  displaced  fluid 
will  no  longer  be  G, 
but  some  other  point, 
G'.  And  since  the  fluid 
pressure  acts  vertically 
upwards  through  G', 
its  direction  will  cut 
the  axis  in  some  point 
M',  which  will  gener- 


Fig.  86. 


Fig.  87. 


Fig.  85. 

ally  have  different  positions  according  as  the  inclination  of  the  axis  to  the 
vertical  is  greater  or  smaller.  If  the  angle  is  indefinitely  small,  M'  will 
have  a  definite  position  M,  which  always  admits  of  determination,  and  is 
called  the  metacentre. 

If  we  suppose  M  to  be  above  C,  an  inspection  of  fig.  87  will  show  that 
when  the  body  has  received  an  indefinitely  small  displacement,  the  weight  of 
the  body  W,  and  the  resultant  of  the  fluid  pressures  R  tend  to  bring  the 
body  back  to  its  original  position  ;  that  is,  in  this  case  the  equilibrium  is 
stable  (71).  If,  on  the  contrary,  M  is  below  C,  the  forces  tend  to  cause  the 
axis  to  deviate  farther  from  the  vertical,  and  the  equilibrium  is  unstable. 
Hence  the  rule, 

iii.  The  equilibrium  of  a  floating  body  is  stable  or  unstable  according  as 
the  metacentre  is  above  or  below  the  centre  of  gravity. 

The  determination  of  the  metacentre  can  rarely  be  effected  except  by 
means  of  a  somewhat  difficult  mathematical  process.  When,  however,  the 
form  of  the  immersed  part  of  a  body  is  spherical  it  can  be  readily  determined, 
for  since  the  fluid  pressure  at  each  point  converges  to  the  centre,  and  con- 
tinues to  do  so  when  the  body  is  slightly  displaced,  their  resultant  must  in 
all  cases  pass  through  the  centre,  which  is  therefore  the  metacentre.  To 
illustrate  this  :  let  a  spherical  body  float  on  the  surface  of  a  liquid  (fig.  88), 


:,„ 

<    then, 


Cartesian  Diver. 


97 


en,  its  centre  of  gravity  and  the  metacentre  both  coinciding  with  the 
!-  geometrical  centre  C,  its  equilibrium  is  neutral  (71).  Now  suppose  a  small 
j;  heavy  body  to  be  fastened  at  P,  the  summit  of  the 

vertical  diameter.     The  centre  of  gravity  will  now 

be  at  some  point  G  above  C.     Consequently,  the 

equilibrium  is  unstable,  and  the  sphere,  left  to  itself, 

will  instantly  turn  over  and  will  rest  when  P  is  the 

lower  end  of  a  vertical  diameter. 

On  investigating  the  position  of  the  metacentre 

of  a  cylinder,  it  is  found  that    when   the  ratio   of 

the  radius  to  the  height  is  greater  than  a  certain 

•  quantity,  the  position  of  stable  equilibrium  is  that 
in  which  the  axis  is  vertical  ;  but  if  it  be  less  than 

|  that  quantity,  the  equilibrium  is  stable  when  the  axis  is  horizontal.     For  this 

i  reason  the  stump  of  a  tree  floats  lengthwise,  but  a  thin  disc  of  wood  floats 

;   flat  on  the  water. 

Hence,  also,  if  it  is  required  to  make  a  cylinder  of  moderate  length  float 

;  with  its  axis  vertical,  it  is  necessary  to  load  it  at  the  lower  end.     By  so 
doing  its  centre  of  gravity  is  brought  below  the 
metacentre. 

The  determination  of  the  metacentre  and  of  the 

;  centre  of  gravity  is  of  great  importance  in  the  stow- 
age of  vessels,  for  on  their  relative  positions  the 

»  stability  depends. 

117.  Cartesian    diver — The   different    effects 
of  suspension,  immersion,  and  floating  are  repro- 

;  duced  by  means  of  a  well-known  hydrostatic  toy,  the 
Cartesian  diver  (fig.  89).  It  consists  of  a  glass 
cylinder  nearly  full  of  water,  on  the  top  of  which  a 
brass  cap,  provided  with  a  piston,  is  hermetically 

I  fitted.  In  the  liquid  there  is  a  little  porcelain 
figure  attached  to  a  hollow  glass  ball  «,  which  con- 
tains air  and  water,  and  floats  on  the  surface.  In 

I  the  lower  part  of  this  ball  there  is  a  little  hole  by 

I  which  water  can  enter  or  escape,  according  as  the 

•  air  in  the  interior  is  more  or  less  compressed.     The 
quantity  of  water  in  the  globe  is  such  that  very 

•  little   more  is  required  "to  make  it   sink.     If  the 
piston  be  slightly  lowered,  the  air  is  compressed, 
and  this  pressure  is  transmitted  to  the  water  of  the 

(  vessel  and  the  air  in  the  bulb.     The  consequence 

is,  that  a  small  quantity  of  water  penetrates  into  the 

bulb,  which  therefore  becomes  heavier  and  sinks. 

If  the  pressure  is  relieved,  the  air  in  the  bulb  expands,  expels  the  excess 

of  water  which  had  entered  it,  and  the  apparatus,  being  now  lighter,  rises 

to  the  surface.     The  experiment  may  also  be  made  by  replacing  the  brass 

:  cap   and   piston  by   a  cover  of  sheet  india-rubber,    wTiich  is  tightly  tied 

>  over  the  mouth  ;  when  this  is  pressed  by  the  hand  the  same  effects  are 

produced. 


Fig.  89. 


98  On  Liquids.  [118- 

1 1 8.  Swimming-bladder  of  fishes. — Most   fishes   have  an  air-bladder 
below  the  spine,  which  is  called  the  swimming-bladder.     The  fish  can  com- 
press or  dilate  this  at  pleasure  by  means  of  a  muscular  effort,  and  produce 
the  same  effects  as  those  just  described — that  is,  it  can  either  rise  or  sink  in 
water. 

119.  Swimming1. — The  human  body  is  lighter,  on  the  whole,  than  an 
equal  volume  of  water  :  it  consequently  floats  on  the  surface,  and  still  better 
in  sea-water,  which  is  heavier  than  fresh  water.     The  difficulty  in  swimming 
consists  not  so  much  in  floating,  as  in  keeping  the  head  above  water,  so  as 
to  breathe  freely.     In  man  the  head  is  heavier  than  the  lower  parts,  and 
consequently  tends  to  sink,  and  hence  swimming  is  an  art  which  requires  to 
be  learned.     With  quadrupeds,  on  the  contrary,  the  head  being  less  heavy 
than  the  posterior  parts  of  the  body,  remains  above  water  without  any  effort, 
and  these  animals  therefore  swim  naturally. 

SPECIFIC   GRAVITY— HYDROMETERS. 

1 20.  Determination    of  specific    gravities. — It  has  been  already  ex- 
plained (24)  that  the  specific  gravity  of  a  body,  whether  solid  or  liquid,  is  the 
number  which  expresses  the  relation  of  the  weight  of  a  given  volume  of  this 
body  to  the  weight  of  the  same  volume  of  distilled  water  at  a  temperature 
of  4°.     In  order,  therefore,  to  calculate  the  specific  gravity  of  a  body,  it  is 
sufficient  to  determine  its  weight  and  that  of  an  equal  volume  of  water,  and 
then  to  divide  the  first  weight  by  the  second  :  the  quotient  is  the  specific 
gravity  of  the  body. 

Three  methods  are  commonly  used  in  determining  the  specific  gravities 
of  solids  and  liquids.     These  are,  1st,  the  method  of  the  hydrostatic  balance ; 
2nd,  that  of  the  hydrometer  ;  and  3rd,  the  specific  gravity  flask.     All  three,  i 
however,  depend  on  the  same  principle — that  of  first  ascertaining  the  weight ; 
of  a  body,  and  then  that  of  an  equal  volume  of  water.     We  shall  first  apply , 
these  methods  to  determining  the  specific  gravity  of  solids,  and  then  to  the  • 
specific  gravity  of  liquids. 

121.  Specific  gravity  of  solids.- — i.  Hydrostatic  balance. — To  obtain  the; 
specific  gravity  of  a  solid  by  the  hydrostatic  balance  (fig.  84),  it  is  first, 
weighed  in  the  air,  and  is  then  suspended  to  the  hook  of  the  balance  and 
weighed  in  water  (fig.  90).  The  loss  of  weight  which  it  experiences  is, 
according  to  Archimedes'  principle,  the  weight  of  a  volume  of  water  equal 
to  its  own  volume  ;  consequently,  dividing  the  weight  in  air  by  the  loss  of. 
weight  in  water,  the  quotient  is  the  specific  gravity  required.  If  P  is  the 

weight  of  the  body  in  air,  P'  its  weight  in  water,  and  D  its  specific  gravity, 

p 
P  —  P'  being  the  weight  of  the  displaced  water,  we  have  D  =- f. 

It  may  be  observed  that  though  the  weighing  is  performed  in  air,  yet, 
strictly  speaking,  the  quantity  required  is  the  weight  of  the  body  in  vacuo  : 
and  when  great  accuracy  is  required,  it  is  necessary  to  apply  to  the  observed 
weights  a  correction  for  the  weights  of  the  unequal  volumes  of  air  displaced 
by  the  substance,  and  the  weights  in  the  other  scale  pan.  The  water  in 
which  bodies  are  weighed  is  supposed  to  be  distilled  water  at  the  standard 
temperature. 


_122]  Specific  Gravity  Bottle. 

ii.  Xicholsoris  hydrometer.— The  apparatus  consists  of  a  hollow  metal 

cylinder  B  (fig  91),  to  which  is  fixed   a   cone  C,  loaded  with  lead.     The 

object  of  the  latter  is   to 

bring  the  centre  of  gravity 

below   the   metacentre,  so 

that  the  cylinder  may  float 

with  its  axis  vertical.     At 

the  top  is  a  stem,  termi- 
nated by  a  pan,  in  which  is 

placed  the  substance  whose 

specific    gravity   is   to    be 

determined.     On  the  stem 

a    standard     point,    <?,     is 

marked. 

The   apparatus    stands 

partly  out  of  the  water,  and 

the  first  step  is  to  ascertain 

the  weight  which  must  be 

placed  in  the  pan  in  order 

to  make  the    hydrometer 

sink  to  the  standard  point  <?. 

Let    this    weight    be    125  Fig.  9*  Fig.  9i. 

grains,  and  let  sulphur  be 

the  substance  whose  specific  gravity  is  to  be  determined.     The  weights  are 

then  removed  from  the  pan,  and  replaced  by  a  piece  of  sulphur  which  weighs 
less  than  125  grains,  and  weights  added  until  the  hydrometer  is  again 
depressed  to  the  standard  o.  If,  for  instance,  it  has  been  necessary  to  add 
55  grains,  the  weight  of  the  sulphur  is  evidently  the  difference  between  125 
and  55  grains  ;  that  is,  70  grains.  Having  thus  determined  the  weight  of  the 
sulphur  in  air,  it  is  now  only  necessary  to  ascertain  the  weight  of  an  equal 
volume  of  water.  To  do  this,  the  piece  of  sulphur  is  placed  in  the  lower  pan 
C  at  m,  as  represented  in  the  figure.  The  whole  weight  is  not  changed,  never- 
theless the  hydrometer  no  longer  sinks  to  the  standard  ;  the  sulphur,  by  im- 
mersion, has  lost  a  part  of  its  weight  equal  to  that  of  the  water  displaced. 
Weights  are  added  to  the  upper  pan  until  the  hydrometer  sinks  again  to  the 
standard.  This  weight,  34-4  grains,  for  example,  represents  the  weight  of 
the  volume  of  water  displaced  ;  that  is,  of  the  volume  of  water  equal  to  the 
volume  of  the  sulphur.  It  is  only  necessary,  therefore,  to  divide  70  grains, 
the  weight  in  air,  by  34^4  grains,  and  the  quotient  2-03  is  the  specific 
gravity. 

If  the  body  in  question  is  lighter  than  water  it  tends  to  rise  to  the  surface, 
and  will  not  remain  on  the  lower  pan  C.  To  obviate  this,  a  small  movable 
cage  of  fine  wire  is  adjusted  so  as  to  prevent  the  ascent  of  the  body.  The 
experiment  is  in  other  respects  the  same. 

122.  Specific  gravity  bottle.  Pyknometer. — When  the  specific  gravity 
of  a  substance  in  a  state  of  powder  is  required,  it  can  be  found  most  conve- 
niently by  means  of  the  Pyknometer,  or  specific  gravity  bottle.  This  instru- 
ment is  a  bottle,  in  the  neck  of  which  is  fitted  a  thermometer  A,  an  enlarge- 
ment on  the  stem  being  carefully  ground  for  this  purpose  (fig.  92).  In  the 

F  2 


100 


On  Liqiiids. 


[122- 


30 


side  is  a  narrow  capillary  stem  widened  at  the  top  and  provided  with  a 
stopper,  as  shown  in  the  figure.  On  this  tube  is  a  mark  ;;/,  and  the 
thermometer  stopper  having  been  inserted,  at  each  weighing  the  bottle 

is  filled  with  water  exactly  to  this  mark. 
The  bottle  may  conveniently  have  dimen- 
sions such  that  when  the  thermometer 
stopper  is  inserted  and  the  liquid  filled  to 
the  mark  m,  it  represents  a  definite  volume. 
This  is  done  by  filling  the  bottle  when 
wholly  under  water,  and  putting  in  the 
stopper  while  it  is  immersed.  The  bottle 
and  the  tube  are  then  completely  filled, 
and  the  quantity  of  water  in  excess  is  re- 
moved by  blotting  paper.  To  find  the 
specific  gravity  proceed  as  follows  : — Hav- 
ing weighed  the  powder,  place  it  in  one 
of  the  scale  pans,  and  with  it  the  bottle 
filled  exactly  to  ;;z,  and  carefully  dried. 
Then  balance  it  by  placing  small  shot,  or 
sand,  in  the  other  pan.  Next,  remove  the 
bottle  and  pour  the  powder  into  it,  and,  as 
before,  fill  it  up  with  water  to  the  mark  a. 
On  replacing  the  bottle  in  the  scale  pan  it 
will  no  longer  balance  the  shot,  since  the 
powder  has  displaced  a  volume  of  water 
equal  to  its  own  volume.  Place  weights 
in  the  scale  pan  along  with  the  bottle 
until  they  balance  the  shot.  These  weights 
give  the  weight  of  the  water  displaced. 
Then  the  weight  of  the  powder,  and  the 
weight  of  an  equal  bulk  of  water  being 
known,  its  specific  gravity  is  determined 
as  before.  The  thermometer  gives  the 
temperature  at  which  the  determination 
is  made,  and  thus  renders  it  easy  to  make  a  correction  (125). 

It  is  important  in  this  determination  to  remove  the  layer  of  air  which 
adheres  to  the  powder,  and  unduly  increases  the  quantity  of  water  expelled. 
This  is  effected  by  placing  the  bottle  under  the  receiver  of  an  air-pump 
and  exhausting.  The  same  result  is  obtained  by  boiling  the  water  in  which 
the  powder  is  placed. 

123.  Bodies  soluble  in  water. — If  the  body,  whose  specific  gravity  is  to 
be  determined  by  any  of  these  methods,  is  soluble  in  water,  the  determination 
is  made  in  some  liquid  in  which  it  is  not  soluble,  such  as  oil  of  turpentine 
or  naphtha,  the  specific  gravity  of  which  is  known.  The  specific  gravity  is 
obtained  by  multiplying  the  number  obtained  in  the  experiment  by  the  specific 
gravity  of  the  liquid  used  for  the  determination. 

Suppose,  for  example,  a  determination  of  the  specific  gravity  of  potassium 
has  been  made  in  naphtha.  For  equal  volumes,  P  represents  the  weight  of 
the  potassium,  P'  that  of  the  naphtha,  and  P"  that  of  water  ;  consequently 


Fig.  92 


-124]  Specific  Gravity  of  Liquids.  101 

-t  will  be  the  specific  gravity  of  the  substance  in  reference  to  naphtha,  and 

f-^  the  specific  gravity  of  the  naphtha  in  reference  to  water.     The  product 

p 

of  these  two  fractions    -f  is  the  specific  gravity  of  the  substance  compared 

with  water. 

In  determining  the  specific  gravity  of  porous  substances,  they  are  var- 
nished before  being  immersed  in  water,  which  renders  them  impervious  to 
moisture  without  altering  their  volume. 

Specific  gravity  of  solids  at  zero  as  compared  'with  distilled  'water  at  4°  C. 

Platinum,  rolled     .         .         .  22-069  Statuary  marble     .         .         .  2-837 

„          cast        ,         .         .  20-337  Aluminium     ....  2*680 

Gold,  stamped        .         .         .   19-362  Rock  crystal  .         .         .         .2-653 

„      cast       .         .         .         .19-258  St.  Gobin  glass       .         .         .  2-488 

Lead,  cast       ....  11-352  China  porcelain      .         .         .  2-38 

Silver,  cast     ....   10-474  Sevres  porcelain     .         .         .2-14 

Bismuth,  cast          .         .         .     9-822  Native  sulphur       .         .         .  2-033 

Copper,  drawn  wire        .         ,     8*878      Ivory i"9i? 

„        cast  .                  ,        .     8788  Anthracite      ....  r8oo 

German  silver         .         .         .     8-432  Compact  coal          .         .         .  1-329 

Brass 8-383      Amber 1-078 

Steel,  not  hammered      .         .     7-816      Sodium 0-970 

Iron,  bar         ....     7-788  Melting  ice     .         .         .         .  0.930 

Iron,  cast        ....     7-207  Potassium       ....  0-865 

Tin,  east         ....     7-291      Beech 0*852 

Zinc,  cast        ....     6'86i      Oak 0-845 

Antimony,  cast       .         .         .6-712      Elm O'Soo 

Iodine    .....     4*950  Yellow  Pine    ....  0-657 

Heavy  spar    ....     4*430  Lithium           .         .         .  0-585 

Diamonds      .         .        3"53i  to  3-501  Common  poplar      .         .         .  0-389 

Flint  glass      ....     3*329      Cork 0-240 

In  this  table  the  woods  are  supposed  to  be  in  the  ordinary  air-dried 
condition. 

124.  specific  gravity  of  liquids. — i.  Method  of  tJie  hydrostatic  balance. — 
From  the  pan  of  the  hydrostatic  balance  a  body  is  suspended,  on  which  the 
liquid,  whose  specific  gravity  is  to  be  determined,  exerts  no  chemical  action  ; 
for  example,  a  ball  of  platinum.  This  is  then  successively  weighed  in  air, 
in  distilled  water,  and  in  the  liquid.  The  loss  of  weight  of  the  body  in  these 
two  liquids  is  noted.  They  represent  respectively  the  weights  of  equal  volumes 
of  water  and  of  the  given  liquid,  and  consequently  it  is  only  necessary  to 
divide  the  second  of  them  by  the  first  to  obtain  the  required  specific  gravity. 

Let  P  be  the  weight  of  the  platinum  ball  in  air,  P'  its  weight  in  water,  P' 
its  weight  in  the  given  liquid,  and  let  D  be  the  specific  gravity  sought.  The 
weight  of  the  water  displaced  by  the  platinum  is  P  —  P',  and  that  of  the 

second  liquid  is  P-  P",  from  which  we  get  D  =      ~"p7- 

ii.  Fahrenheit's  hydrometer. — This  instrument  (fig.  93)  resembles  Nichol- 
son's hydrometer,  but  it  is  made  of  glass,  so  as  to  be  used  in  all  liquids.  At 


102 


On  Liquids. 


[124- 


its  lower  extremity,  instead  of  a  pan,  it  is  loaded  with  a  small  bulb  containing 
mercury.     There  is  a  standard  mark  on  the  stem. 

The  weight  of  the  instrument  is  first  accurately  determined  in  air  ;  it 
is  then  placed  in  water,  and  weights  added  to  the  scale  pan  until  the  mark 
on  the  stem  is  level  with  the  water.  It  follows,  from  the  first  principle  of 
the  equilibrium  of  floating  bodies,  that  the 
weight  of  the  hydrometer,  together  with  the 
weight  in  the  scale  pan,  is  equal  to  the  weight 
of  the  volume  of  the  displaced  water.  In  the 
same  manner,  the  weight  of  an  equal  volume  of 
the  given  liquid  is  determined,  and  the  specific 
gravity  is  found  by  dividing  the  latter  weight  by 
the  former. 

Neither  Fahrenheit's  nor  Nicholson's  hydro- 
meters give  such  accurate  results  as  the  hydro- 
static balance. 

iii.  Specific  gravity  bottle.  —  This  has  been 
already  described  (122).  In  determining  the 
specific  gravity  of  a  liquid,  a  bottle  of  special 
construction  is  used  ;  it  consists  of  a  cylindrical 
reservoir  b  (fig.  94),  to  which  is  fused  a  capillary 
tube  <:,  and  to  this  again  a  wider  tube  a  closed 
with  a  stopper.  The  bottle  is  first  weighed  empty, 
and  then  successively  full  of  water  to  the  mark  c  on  the  capillary  stem  and 
of  the  given  liquid.  If  the  weight  of  the  bottle  be  subtracted  from  the  two 
weights  thus  obtained,  the  result  represents  the  weights  of  equal  volumes  of 
the  liquid,  and  of  water,  from  which  the  specific  gravity  is  obtained  by  division. 
125.  On  the  observation  of  temperature  in  ascertaining  specific 
gravities.  —  As  the  volume  of  a  body  increases  with  the  temperature,  and 
as  this  increase  varies  with  different  substances,  the  specific  gravity  of  any 
given  body  is  not  exactly  the  same  at  different  temperatures  ;  and,  con- 
sequently, a  certain  fixed  temperature  is  chosen  for  those  determinations. 
That  of  water,  for  example,  has  been  made  at  4°  C.,  for  at  this  point  it  has 
the  greatest  density.  The  specific  gravities  of  other  bodies  are  assumed  to 
be  taken  at  zero  ;  but,  as  this  is  not  always  possible,  certain  corrections  must 
be  made,  which  we  shall  consider  in  the  Book  on  Heat. 

Specific  gravities  of  liquids  at  zero,  compared  ivith  that  of  water  at  4°  C. 


Fig.  93- 


Fig.  94. 


as  unity. 


Mercury 

.   13-598 

Sea-  we 

Bromine 

.     2-960 

DistilL 

Sulphuric  acid 

.      1-841 

„ 

Chloroform     . 

•      I-525 

Claret 

Nitric  acid 

.      I  -420 

Olive  ( 

Bisulphide  of  carbon 

.      1-293 

Oil  of 

Glycerine 

,     £-260 

Oil  of 

Hydrochloric  acid  . 

I  -240 

Petrol< 

Blood     .... 

.      I  -060 

Absoli 

Milk   .         .             . 

.      1-032 

Ether 

126.  Use   of  tables   of 

specific 

gravity 

T  I-026 

water  at  4°  C. .         .     rooo 
„     at  o°  C.  .         .     0-999 

Q'994 

.     0-915 

rpentine     .         .         .     0-870 

non  .         .         .         .0-852 

nci  0-836 

alcohol    .         .         .     0-793 

0-713 

-Tables   of  specific  gravity 


-127]  Hydrometers  wit/invariable  Volume.  103 

admit  of  numerous  applications.  In  mineralogy  the  specific  gravity  of  a 
mineral  is  often  a  highly  distinctive  character.  By  means  of  tables  of 
specific  gravities  the  weight  of  a  body  may  be  calculated  when  its  volume  is 
known,  and  conversely  the  volume  when  its  weight  is  known. 

With  a  view  to  explaining  the  last-mentioned  use  of  these  tables,  it  will 
be  well  to  premise  a  statement  of  the  connection  existing  between  the  British 
units  of  length,  capacity,  and  weight.  It  will  manifestly  be  sufficient  for  this 
purpose  to  define  that  which  exists  between  the  yard,  gallon,  and  pound 
avoirdupois,  since  other  measures  stand  to  these  in  well-known  relations. 
The  yard,  consisting  of  36  inches,  may  be  regarded  as  the  primary  unit. 
Though  it  is  essentially  an  arbitrary  standard,  it  is  determined  by  this,  that 
the  simple  pendulum  which  makes  one  oscillation  in  a  mean  second,  at 
London  on  the  sea-level,  is  39-  13983  inches  long.  The  gallon  contains 
277-274  cubic  inches.  A  gallon  of  distilled  water  at  the  standard  tempera- 
ture weighs  10  pounds  avoirdupois  or  70,000  grains  troy  ;  or,  which  comes 
to  the  same  thing,  one  cubic  inch  of  water  weighs  252-5  grains. 

On  the  French  system  the  metre  is  a  primary  unit,  and  is  so  chosen  that 
10,000,000  metres  are  the  length  of  a  quadrant  of  the  meridian  from  either 
pole  to  the  equator.  The  metre  contains  10  decimetres,  or  100  centimetres, 
or  1,000  millimetres  ;  its  length  equals  i  '0936  yards.  The  unit  of  the  measure 
of  capacity  is  the  litre  or  cubic  decimetre.  The  unit  of  weight  is  the  gramme, 
which  is  the  weight  of  a  cubic  centimetre  of  distilled  water  at  4°  C.  The 
kilogramme  contains  1,000  grammes,  or  is  the  weight  of  a  decimetre  of  dis- 
tilled water  at  4°  C.  The  gramme  equals  15*443  grains. 

If  V  is  the  number  of  cubic  centimetres  (or  decimetres)  in  a  certain 
quantity  of  distilled  water  at  4°  C.,  and  P  its  weight  in  grammes  (or  kilo- 
grammes), it  is  plain  that  P  =  V.  Now  consider  a  substance  whose  specific 
gravity  is  D  ;  every  cubic  centimetre  of  this  substance  will  weigh  as  much 
as  D  cubic  centimetres  of  water,  and  therefore  V  centimetres  of  this  sub- 
stance will  weigh  as  much  as  DV  centimetres  of  water.  Hence  if  P  is 
the  weight  of  the  substance  in  grammes,  we  have  P  =  DV.  If,  however,  V 
is  the  volume  in  cubic  inches,  and  P  the  weight  in  grains,  we  shall  have 

P=252-5DV. 

As  an  example,  we  may  calculate  the  internal  diameter  of  a  glass  tube. 
Mercury  is  introduced,  and  the  length  and  weight  of  the  column  at  4°  C. 
are  accurately  determined.  As  the  column  is  cylindrical,  we  have  V  =  rrr2/, 
where  r  is  the  radius,  and  /  the  length  of  the  column  in  centimetres.  Hence 
if  D  is  the  specific  gravity  of  mercury,  and  P  the  weight  of  the  column  in 
grammes,  we  have  P=7rrVD,  and  therefore 


If  rand  /  are  in  inches  and  P  in  grains,  we  shall  have  P  =  252-5^/0, 
and  therefore 


V    2&'S*V 


In  a  similar  manner  the  diameter  of  very  fine  metal  wires  can  be  de- 
termined with  great  accuracy. 

127.  Hydrometers  with  variable  volume.  —  The  hydrometers  of  Nichol- 
son and  Fahrenheit  are  called  hydrometers  of  constant  volume,  but  variable 
weight,  because  they  are  always  immersed  to  the  same  extent,  but  carry 


IO4  On  Liquids.  [127- 

difFerent  weights.  There  are  also  hydrometers  of  variable  volume  but  of 
constant  weight.  These  instruments,  known  under  the  different  names  of 
acidometer,  alcoholometer,  lactometer,  and  saccharometer,  are  not  used  to 
determine  the  exact  specific  gravity  of  the  liquids,  but  to  show  whether  the 
acids,  alcohols,  milk,  solutions  of  sugar,  &c.,  under  investigation,  are  more 
or  less  concentrated. 

128.  Beaume's  hydrometer. — This,  which  was  the  first  of  these  instru- 
ments, may  serve  as  a  type  of  them.     It  consists  of  a  glass  tube  (fig.  95) 

loaded  at  the  bottom  with  mercury,  and  with  a  bulb 
blown  in  the  middle.  The  stem,  the  external  diameter 
of  which  is  as  regular  as  possible,  is  hollow,  and  the 
scale  is  marked  upon  it. 

The  graduation  of  the  instrument  differs  according 
as  the  liquid,  for  which  it  is  to  be  used,  is  heavier  or 
lighter  than  water.  In  the  first  case,  it  is  so  constructed 
that  it  sinks  in  water  nearly  to  the  top  of  the  stem,  to  a 
point  A,  which  is  marked  zero.  A  solution  of  fifteen 
parts  of  salt  in  eighty-five  parts  of  water  is  made,  and 
the  instruments  immersed  in  it.  It  sinks  to  a  certain 
point  on  the  stem,  B,  which  is  marked  1 5  ;  the  distance 
between  A  and  B  is  divided  into  15  equal  parts,  and 
the  graduation  continued  to  the  bottom  of  the  stem. 
Sometimes  the  graduation  is  on  a  piece  of  paper  inside 
the  stem. 

The  hydrometer  thus  graduated  only  serves  for 
liquids  of  a  greater  specific  gravity  than  water,  such  as  acids  and  saline  solu- 
tions. For  liquids  lighter  than  water  a  different  plan  must  be  adopted.  Beaume' 
took  for  zero  the  point  to  which  the  apparatus  sank  in  a  solution  of  10  parts  of 
salt  in  90  of  water,  and  for  10°  he  took  the  level  in  distilled  water.  This  dis- 
tance he  divided  into  10°,  and  continued  the  division  to  the  top  of  the  scale. 
The  graduation  of  these  hydrometers  is  entirely  conventional,  and  they 
give  neither  the  densities  of  the  liquids  nor  the  quantities  dissolved.  But 
they  are  very  useful  in  making  mixtures  or  solutions  in  given  proportions, 
the  results  they  give  being  sufficiently  near  in  the  majority  of  cases.  For 
instance,  it  is  found  that  a  well-made  syrup  marks  35  on  Beaume's  hydro- 
meter, from  which  a  manufacturer  can  readily  judge  whether  a  syrup  which 
is  being  evaporated  has  reached  the  proper  degree  of  concentration. 

129.  Oray-Xiussac's  alcoholometer. — This  instrument  is  used  to  deter- 
mine the  strength  of  spirituous  liquors  ;  that  is,  the  proportion  of  pure  alcohol 
which  they  contain.     It  differs  from  Beaumd's  hydrometer  in  the  graduation. 

Mixtures  of  absolute  alcohol  and  distilled  water  are  made  containing  5, 
10,  20,  30,  &c.,  per  cent,  of  the  former.  The  alcoholometer  is  so  constructed 
that,  when  placed  in  pure  distilled  water,  the  bottom  of  its  stem  is  level 
with  the  water,  and  this  point  is  zero.  It  is  next  placed  in  absolute  alcohol, 
which  marks  100°,  and  then  successively  in  mixtures  of  different  strengths, 
containing  10,  20,  30,  &c.,  per  cent.  The  divisions  thus  obtained  are  not 
exactly  equal,  but  their  difference  is  not  great,  and  they  are  subdivided  into 
ten  divisions,  each  of  which  marks  one  per  cent,  of  absolute  alcohol  in  a 
liquid.  Thus  a  brandy  in  which  the  alcoholometer  stood  at  48°  would  con- 
tain 48  per  cent,  of  absolute  alcohol,  and  the  rest  would  be  water. 


Fig.  95- 


Densimeter. 


10* 


All  these  determinations  are  made  at  15°  C.,  and  for  that  temperature 
only  are  the  indications  correct.  For,  other  things  being  the  same,  if  the 
temperature  rises,  the  liquid  expands,  and  the  alcoholometer  will  sink,  and 
the  contrary  if  the  temperature  fall.  To  obviate  this  error,  Gay-Lussac  con- 
structed a  table  which  for  each  percentage  of  alcohol  gives  the  reading  of 
the  instrument  for  each  degree  of  temperature  from  o°  up  to  30°.  When  the 
exact  analysis  pf  an  alcoholic  mixture  is  to  be  made,  the  temperature  of  the 
liquid  is  first  determined,  and  then  the  point  to  which  the  alcoholometer 
sinks  in  it.  The  number  in  the  table  corresponding  to  these  data  indicates 
the  percentage  of  alcohol.  From  its  giving  the  percentage  of  alcohol,  this 
is  often  called  the  centesimal  alcoholometer. 

130.  Salimeters. — Salimeters,  or    instruments    for   indicating   the   per-, 
centage  of  salt  contained  in  a  solution,  are  made  on  the  principle  of  the- 
centesimal  alcoholometer.     They  are  graduated  by  immersing  them  in  pure, 
water  which  gives  the  zero,  and  then  in  solutions  containing  different  percent: 
ages,  5,  10,  20,  &c.,  of  the  salt,  and  marking  on  the  scale  the  corresponding 
points.    These  instruments  are  open  to  the  objection  that  every  salt  requires 
a  special  instrument.     Thus   one  graduated   for  common,  salt  would  give, 
totally  false  indications  in  a  solution  of  nitre. 

Lactometers  and  vtnometers  are  similar  instruments,  and  are  used  for 
measuring  the  quantity  of  water  which  is  introduced  into  milk  or  wine  for 
the  purpose  of  adulteration.  But  their  use  is  limited,  because  the  density 
of  these  liquids  is  very  variable,  even  when,  they  are  perfectly  natural,  and 
an  apparent  fraud  may  be  really  due  to  a  bad  natural  quality  of  wine  or  of 
milk.  Urinometers,  which  are  of  extensive  use  in  medicine,  are  based  on. 
the  same  principle. 

131.  Densimeter. — The  densimeter  is  an  apparatus  for  indicating  the 
specific  gravity  of  a  liquid.     Rosseau's  densimeter  (fig.  96)  is  of  great  use, 
in  many  scientific  investigations,  in  determining  the 

specific  gravity  of  a  small  quantity  of  a  liquid.  It  has 
the  same  form  as  Beaume's  hydrometer,  but  on  the 
upper  part  of  the  stem  there  is  a  small  tube  AC,  in 
which  is  placed  the  substance  to  be  determined.  A 
mark  A  on  the  side  of  the  tube  indicates  a  measure  of 
a  cubic  centimetre. 

The  instrument  is  so  constructed  that  when  AC  is 
empty  it  sinks  in  distilled  water  to  a  point,  B,  just  at 
the  bottom  of  the  stem.    It  is  then  filled  with  distilled 
water  to  the  height  measured  on  the  tube  AC,  which 
indicates  a  cubic  centimetre,  and  the  point  to  which  it 
now  sinks  is  20°.     The  interval  between  o  and  20  is 
divided  into  20  equal  parts,  and  this  graduation  is       g 
continued  to  the  top    of  the  scale.      As   this    is    of       'm. 
uniform  bore,  each  division  corresponds  to  ~  gramme 
or  0-05. 

To  obtain  the  density  of  any  liquid,  bile  for  example,  the  tube  is  filled 
with  it  up  to  the  mark  A  ;  if  the  densimeter-sinks  to  20.^  divisions,  its  weight  is 
0-05  x  20-5  =  i  -025  ;  that  is  to  say,  that  with  equal  volumes,  the' weight  of  water 
being  i,  that  of  bile  is  1-025.  The  specific  gravity  of  bile  is  therefore  1-025. 

F3 


Fig.  96. 


io6 


On  Liquids, 


[132- 


CHAPTER    II. 

CAPILLARITY,   ENDOSMOSE,   EFFUSION,   ABSORPTION,   AND   IMBIBITION. 

132.  Capillary  phenomena. — When  solid  bodies  are  placed  in  contact 
with  liquids,  a  class  of  phenomena  is  produced  called  capillary  phenomena, 
because  they  are  best  seen  in  tubes  whose  diameters  are  comparable  with 
the  diameter  of  a  hair.  These  phenomena  are  treated  of  in  physics  under 
the  head  of  capillarity  or  capillary  attraction  ;  the  latter  expression  is  also 
applied  to  the  force  which  produces  the  phenomena. 

The  phenomena  of  capillarity  are  very  various,  but  may  all  be  referred 
to  the  mutual  attraction  of  the  liquid  molecules  for  each  other,  and  tp  the 
attraction  between  these  molecules  and  solid  bodies.  The  following  are 
some  of  these  phenomena  : — 

When  a  body  is  placed  in  a  liquid  which  wets  it — for  example,  a  glass 
rod  in  water — the  liquid,  as  if  not  subject  to  the  laws  of  gravitation,  is  raised 
upwards  against  the  sides  of  the  solid,  and  its  surface,  instead  of  being  hori- 
zontal, becomes  slightly  concave  (fig.  97).  If,  on  the  contrary,  the  solid  is 


Fig.  97.  Fig.  98.  Fig.  99.  Fig.  100. 

. 

one  which  is  not  moistened  by  the  liquid,  as  glass  by  mercury,  the  liquid  is 
depressed  against  the  sides  of  the  solid,  and  assumes  a  convex  shape,  as 
represented  in  fig.  98.  The  surface  of  the  liquid  exhibits  the  same  concavity 
or  convexity  against  the  sides  of  a  vessel  in  which  it  is  contained,  according 
as  the  sides  are  or  are  not  moistened  by  the  liquid. 

These  phenomena  are  much  more  apparent  when  a  tube  of  small 
diameter  is  placed  in  a  liquid.  And  according  as  the  tubes  are  or  are  not 
moistened  by  the  liquid,  an  ascent  or  a  depression  of  the  liquid  is  produced 
which  is  greater  in  proportion  as  the  diameter  is  less  (figs.  99  and  100). 

When  the  tubes  are  moistened  by  the  liquid,  its  surface  assumes  the 
form  of  a  concave  hemispherical  segment,  called  the  concave  meniscus 
(fig.  99) ;  when  the  tubes  are  not  moistened,  there  is  a  convex  meniscus 
(fig.  i oo). 

133.  Laws  of  the  ascent  and  depression  in  capillary  tubes. — The 
most  important  law  in  reference  to  capillarity  is  known  as  Juriris  law.  It 


-134]  Ascent  and  Depression  between  Surfaces.  107 

is  that  the  height  of  the  ascent  of  one  and  the  same  liquid  in  a  capillary  tube 
is  inversely  as  the  diameter  of  the  tube.  Thus,  if  water  rises  to  a  height  of 
30  mm.  in  a  tube  I  mm.  in  diameter,  it  will  only  rise  to  a  height  of  1 5  mm. 
in  a  tube  2  mm.  in  diameter,  but  to  a  height  of  300  mm.  in  a  tube  cri  mm. 
in  diameter.  This  law  has  been  verified  with  tubes  whose  diameters  ranged 
from  5  mm.  to  0*07  mm.  It  presupposes  that  the  liquid  has  previously 
moistened  the  tube. 

The  height  to  which  a  liquid  rises  in  a  tube,  diminishes  as  the  tempera- 
ture rises.  Thus  in  a  capillary  tube  in  which  water  stood  at  a  height  of 
307  mm.  at  o°,  it  stood  at  28-6  mm.  at  35°,  and  at  26  mm.  at  80°. 

Provided  the  liquid  moistens  the  tube,  neither  its  thickness  nor  its  nature 
has  any  influence  on  the  height  to  which  the  liquid  rises.  Thus  water  rises 
to  the  same  height  in  tubes  of  different  kinds  of  glass  and  of  rock  crystal, 
provided  the  diameters  are  the  same. 

The  nature  of  the  liquid  is  of  great  importance  ;  of  all  liquids  water 
rises  the  highest  ;  thus  in  a  glass  tube  i  -29  mm.  in  diameter,  the  heights  of 
water,  alcohol,  and  turpentine  were  respectively  23-16,  9-18,  and  9-85  milli- 
metres. 

In  regard  to  the  depression  of  liquids  in  tubes  which  they  do  not 
moisten,  Jurin's  law  has  not  been  found  to  hold  with  the  same  accuracy. 
The  reason  for  this  is  probably  to  be  found  in  the  following  circumstances  : — 
When  a  liquid  moistens  a  capillary  tube,  a  very  thin  layer  of  liquid  is  formed 
against  the  sides,  and  remains  adherent  even  when  the  liquid  sinks  in  the 
tube.  The  ascent  of  the  column  of  liquid  takes  place  then,  as  it  were,  inside 
a  central  tube,  with  which  it  is  physically  and  chemically  identical.  The 
ascent  of  the  tube  is  thus  an  act  of  cohesion.  It  is  therefore  easy  to  under- 
stand why  the  nature  of  the  sides  of  the  capillary  tube  should  be  without 
influence  on  the  height  of  the  ascent,  which  only  depends  on  the  diameter. 

With  liquids,  on  the  contrary,  which  do  not  moisten  the  sides  of  the  tube, 
the  capillary  action  takes  place  between  the  sides  and  the  liquid.  The 
nature  and  structure  of  the  sides  are  never  quite  homogeneous,  and  there  is 
always,  moreover,  a  layer  of  air  on  the  inside,  which  is  not  dissolved  by  the 
liquid.  These  two  causes  exert  undoubtedly  a  disturbing  influence  on  the 
law  of  Jurin. 

134.  Ascent  and  depression  between  parallel  or  inclined  surfaces. — 
When  two  bodies  of  any  given  shape  are  dipped  in  water,  analogous  capil- 
lary phenomena  are  produced,  provided  the  bodies  are  sufficiently  near.  If, 
for  example,  two  parallel  glass  plates  are  immersed  in  water  at  a  very  small 
distance  from  each  other,  water  will  rise  between  the  two  plates  in  the 
inverse  ratio  of  the  distance  which  separates  them.  The  height  of  the 
ascent  for  any  given  distance  is  half  what  it  would  be  in  a  tube  whose  dia- 
meter is  equal  to  the  distance  between  the  plates. 

If  the  parallel  plates  are  immersed  in  mercury,  a  corresponding  depres- 
sion is  produced,  subject  to  the  same  laws. 

If  two  glass  plates  AB  and  AC  with  their  planes  vertical  and  inclined  to 
one  another  at  a  small  angle,  as  represented  in  fig.  101,  have  their  ends 
dipped  into  a  liquid  which  wets  them,  the  liquid  will  rise  between  them. 
The  elevation  will  be  greatest  at  the  line  of  contact  of  the  plates  and  from 
thence  gradually  less,  the  surface  taking  the  form  of  an  equilateral  hyper- 


io8 


On  Liquids. 


[134- 


bola,  whose  asymptotes  are  respectively  the  line  of  intersection  of  the  plates, 
and  the  line  in  which  the  plates  cut  the  horizontal  surface  of  the  liquid. 

If  a  drop  of  water  be  placed  within  a  conical  glass  tube  whose  angle  is 
small  and  axis  horizontal,  it  will    have  a  concave  meniscus  at  each  end 


Fig.  101. 


Fig.  102. 


Fig.  103. 


(fig.  102),  and  will  tend  to  move  towards  the  vertex.  But  if  the  drop  be  of 
mercury  it  will  have  a  convex  meniscus  at  each  end  (fig.  103),  and  will  tend 
to  move  from  the  vertex. 

135.  Attraction  and  repulsion  produced  by  capillarity. — The  attrac- 
tions and  repulsions  observed  between  bodies  floating  on  the  surface  of 
liquids  are  due  to  capillarity,  and  are  subject  to  the  following  laws  : — 

i.  When  two  floating  balls  both  moistened  by  the  liquid — for  example, 
cork  upon  water-— are  so  near  that  the  liquid  surface  between  them  is  not 
level,  an  attraction  takes  place. 

ii.  The  same  effect  is  produced  when  neither  of  the  balls  is  moistened,  as 
is  the  case  with  balls  of  wax  on  water. 

iii.  Lastly,  if  one  of  the  balls  is  moistened  and  the  other  not,  as  a  ball  of 
cork  and  a  ball  of  wax  in  water,  they  repel  each  other  if  the  curved  surfaces 
of  the  liquid  in  their  respective  neighbourhoods  intersect. 

As  all  these  capillary  phenomena  depend  on  the  concave  or  convex  cur- 
vature which  the  liquid  assumes  in  contact  with  the  solid,  a  short  explana- 
tion of  the  cause  which  determines  the  form  of  this  curvature  is  necessary. 

136.  Cause  of  tne  curvature  of  liquid  surfaces  in  contact  with  solids. 
— The  form  of  the  surface  of  a  liquid  in  contact  with  a  solid  depends  on  the 
relation  between  the  attraction  of  the  solid  for  the  liquid,  and  of  the  mutual 
attraction  between  the  molecules  of  the  liquid. 

Let  m  be  a  liquid  molecule  (fig.  104)  in  contact  with  a  solid.  This 
molecule  is  acted  upon  by  three  forces  :  by  gravity  which  attracts  it  in  the 
direction  of  the  vertical  mP  ;  by  the  attraction  of  the  liquid  F,  which  acts  in 
the  direction  mY ;  and  by  the  attraction  of  the  plate  n,  which  is  exerted  in 
the  direction  mn.  According  to  the  relative  intensities  of  these  forces,  their 
resultant  can  take  three  positions  : — 

i.  The  resultant  is  in  the  direction  of  the  vertical  ;#R  (fig.  104).  In  this 
case  the  surface  m  is  plane  and  horizontal  ;  for,  from  the  condition  of  the 
equilibrium  of  liquids,  the  surface  must  be  perpendicular  to  the  force  which 
acts  upon  the  molecules. 

ii.  If  the  force  n  increases  or  F  diminishes,  the  resultant  R  is  within  the 


-138]  Tension  of  the  Free  Surface  of  Liquids.  109 

angle  nniP  (fig.  105)  ;  in  this  case  the  surface  takes  a  direction  perpendicular 
to  wR,  and  becomes  concave. 

iii.  If  the  force  F  increases,  or  ;z  diminishes,  the  resultant  R  takes  the 


Fig.  104. 


Fig.  105. 


Fig.  106. 


direction  ?;zR  (fig.  106)  within  the  angle  P;«F,  and  the  surface,  becoming 
perpendicular  to  this  direction,  is  convex. 

137.  Influence    of  the    curvature    on    capillary    phenomena.— The 

elevation  or  depression  of  a  liquid  in  a  capillary  tube  depends  on  the 
concavity  or  con- 
vexity of  the 
meniscus.  In  a 
concave  menis- 
cus, abed  (fig 
107),  the  liquid 
molecules  are 
sustained  in 
equilibrium  by 
the  forces  acting  Fig.  I07.  Fig.  Io8. 

on     them,     and 

they  exercise  no  downward  pressure  on  the  inferior  layers.  On  the  contrary, 
in  virtue  of  the  molecular  attraction,  they  act  on  the  nearest  inferior  layers, 
from  which  it  follows  that  the  pressure  on  any  layer,  mn,  in  the  interior  of 
the  tube,  is  less  than  if  there  were  no  meniscus.  The  consequence  is,  that 
the  liquid  ought  to  rise  .in  the  tube  until  the  internal  pressure  on  the  layer 
mn  is  equal  to  the  pressure,  op,  which  acts  externally  on  a  point,  p,  of  the 
same  layer. 

Where  the  meniscus  is  convex  (fig.  108),  equilibrium  exists  in  virtue  of  the 
molecular  forces  acting  on  the  liquid ;  but  as  the  molecules  Avhich  would 
occupy  the  same  space  ghik,  if  there  were  no  molecular  action,  do  not  exist, 
they  exercise  no  attraction  on  the  lower  layers.  Consequently,  the  pressure 
on  any  layer  mn,  in  the  interior  of  the  tufye,  is  greater  than  if  the  space  ghik 
were  filled,  for  the  molecular  forces  are  more  powerful  than  gravity.  The 
liquid  ought  therefore  to  sink  in  the  tube  until  the  internal  pressure  on  a 
layer,  mn,  is  equal  to  the  external  pressure  on  any  point,  p,  of  this  layer. 

138.  Tension  of  the  free  surface   of  liquids. — The  free  surface  of  a 
liquid  is  that  which  is  bounded  by  a  gas  or  by  vacuum  ;  it  has  greater 
cohesion  than  any  layer  of  the  liquid  in  the  interior.    For  consider  any  particle 
at  the  surface,  it  will  be  attracted  by  the  adjacent  particles  in  all  directions 
except  in  that  above  the  surface.     The  attractions  acting  laterally  will  com- 
pensate each  other ;  and  as  there  are  no  attractions  exerted  by  the  particles 


IIO  On  Liquids.  [138- 

of  the  liquid  above  the  surface  to  counteract  those  acting  from  the  interior, 
the  latter  will  exercise  a  considerable  pull  towards  the  interior.  The  effect 
of  this  is  to  lessen  the  mobility  of  particles  on  the  surface,  while  those  in  the 
interior  are  quite  mobile  ;  the  surface,  as  it  were,  is  stretched  by  an  elastic 
skin,  the  effect  being  the  same  as  if  the  surface  layer  exerted  a  pressure  on 
the  interior.  This  surface  tension,  as  it  may  be  called,  is  greater,  the  greater 
the  cohesion  of  the  liquid. 

When  the  surface  of  a  liquid  increases,  more  particles  enter  into  the 
condition  of  the  surface  layer,  to  effect  which  a  certain  amount  of  work  is 
required.  On  the  other  hand,  when  the  surface  is  diminished,  the  molecules 
pass  into  the  state  of  the  internal  layer,  and  they  perform  work.  The  work 
done  when  a  square  mm.  of  surface  passes  into  the  interior  is  called  the 
coefficient  of  surface  tensio?i. 

The  surface  tension  depends  on  the  form  of  the  surface.  It  has  been 
determined  in  the  case  of  spheroidal  bodies.  If  the  pressure  which  is  exerted 
on  a  plane  surface  be  called  P,  the  pressure  /,  on  a  spherical  surface  of 

radius  p,  is/  =  P  +  2(r  for  convex,  and  p  =  P  -  ?x  for  concave  surfaces. 

P  P 

Hence  for  a  spheroidal  shell,  the  internal  radius  OA  of  which  isp,  and  its 

thickness  AB  —  d,  the  pressure  of  the  outer  layer  is  p  —  P  +  — — ,   and   of  the 

p  +  d 

inner  layer  fa  =  P  -  ^r  and  the  resultant  is  their  differ- 
P 

ence  =     ^    +  -?  ;  a  pressure  exerted  inwards,  since  fi±fi,. 
p  +  d     p 

This  is  well  illustrated  by  blowing  a  soap-bubble  on  a 
glass  tube.  So  long  as  the  other  end  of  the  tube  is  closed, 
F;  the  bubble  remains,  the  elastic  force  of  the  enclosed  air 

counterbalancing  the  tension  of  the  surface  ;  but  when 
the  tube  is  opened,  the  tension  of  the  surface  being  unchecked,  the  bubble 
gradually  contracts  and  finally  disappears. 

Insects  can  often  move  on  the  surface  of  water,  without  sinking.  This 
phenomenon  is  caused  by  the  fact  that,  as  their  feet  are  not  wetted  by  the 
water,  a  depression  is  produced,  and  the  elastic  reaction  of  the  surface  layer 
keeps  them  up  in  spite  of  their  weight.  Similarly  a  sewing  needle,  gently 
placed  on  water,  does  not  sink,  because  its  surface,  being  covered  with  an 
oily  layer,  does  not  become  wetted.  The  pressure  of  the  needle  brings 
about  a  concavity,  the  surface  tension  of  which  acts  in  opposition  to  the 
weight  of  the  needle.  But  if  washed  in  alcohol  or  in  potash,  it  at  once  sinks 
to  the  bottom. 

A  drop  of  mercury  on  a  table  has  a  spherical  shape,  which,  like  that  of 
the  heavenly  bodies,  is  due  to  attraction.  The  globule  of  mercury  behaves 
as  if  its  molecules  had  no  weight,  since  it  remains  spherical.  That  is,  the 
molecular  attraction  is  far  greater  than  the  weight,  which  only  alters  the 
shape  of  the  globule  if  the  quantity  of  mercury  is  much  greater  ;  it  then 
flattens,  but  always  retains  at  its  edge  the  convex  form  which  attraction  im- 
parts to  it. 

139.  Various  capillary  phenomena. — The  following  facts  are  among 
the  many  which  are  caused  by  capillarity  : — 


-140]  Endosmose  and  Exosmose.  Ill 

When  a  capillary  tube  is  immersed  in  a  liquid  which  moistens  it,  and 
is  then  carefully  removed,  the  column  of  liquid  in  the  tube  is  seen  to  be 
longer  than  while  the  tube  was  immersed  in  the  liquid.  This  arises  from 
the  fact  that  a  drop  adheres  to  the  lower  extremity  of  the  tube  and  forms  a 
concave  meniscus,  which  concurs  with  that  of  the  upper  meniscus  to  form  a 
longer  column  (132). 

For  the  same  reason  a  liquid  does  not  overflow  in  a  capillary  tube, 
although  the  latter  may  be  shorter  than  the  liquid  column  which  would 
otherwise  be  formed  in  it.  For  when  the  liquid  reaches  the  top  of  the  tube, 
its  upper  surface,  though  previously  concave,  becomes  convex,  and,  as  the 
downward  pressure  becomes  greater  than  if  the  surface  were  plane,  the 
ascending  motion  ceases. 

It  is  from  capillarity  that  oil  ascends  in  the  wicks  of  lamps,  that  water 
rises  in  woods,  sponge,  bibulous  paper,  sugar,  sand,  and  in  all  bodies  which 
possess  pores  of  a  perceptible  size.  In  the  cells  of  plants  the  sap  rises  with 
great  force,  for  here  we  have  to  do  with  vessels  whose  diameter  is  less  than 
o'oi  mm.  Efflorescence  of  salts  is  also  due  to  capillarity  ;  a  solution  rising 
against  the  side  of  a  vessel,  the  water  evaporates,  and  the  salt  forms  on  the 
side  a  means  of  furthering  still  more  the  ascent  of  a  liquid.  Capillarity  is, 
moreover,  the  cause  of  the  following  phenomenon  : — When  a  porous  sub- 
stance, such  as  gypsum,  or  chalk,  or  even  earth,  is  placed  in  a  porous  vessel 
of  unbaked  porcelain,  and  the  whole  is  dipped  in  water,  the  water  penetrates 
into  the  pores,  and  the  air  is  driven  inwards,  so  that  it  is  under  four  or  five 
times  its  usual  pressure  and  density. 

Jamin  has  proved  this  by  cementing  a  manometer  into  blocks  of  chalk, 
gypsum,  £c.,  and  he  has  made  it  probable  that  a  pressure  of  this  kind,  exerted 
upon  the  roots,  promotes  the  ascent  of  sap  in  plants. 


ENDOSMOSE,   EFFUSION,   ABSORPTION,   AND   IMBIBITION. 

140.  Endosmose  and  exosmose. — When  two  different  liquids  are  sepa- 
rated by  a  thin  porous  partition,  either  inorganic  or  organic,  a  current  sets 
in  from  each  liquid  to  the  other;  to  these  currents  the  names  endosmose 
and  exosmose  are  respectively  given.  These  terms,  which  signify  impulse 
from  'within  and  impulse  from  without,  were  originally  introduced  by 
Dutrochet,  who  first  drew  attention  to  these  phenomena.  The  general 
phenomenon  may  be  termed  diosmose.  They  may  be  well  illustrated  by 
means  of  the  endosmometer.  This  consists  of  a  long  tube,  at  the  end  of 
which  a  membranous  bag  is  firmly  bound  (fig.  1 10).  The  bag  is  then  filled 
with  a  strong  syrup,  or  some  other  solution  denser  than  water,  such  as  milk 
or  albumen,  and  is  immersed  in  water.  The  liquid  is  found  gradually  to  rise 
in  the  tube,,  to  a  height  which  may  attain  several  inches  ;  at  the  same  time, 
the  level  of  the  liquid  in  which  the  endosmometer  is  immersed  becomes 
lower.  It  follows,  therefore,  that  some  of  the  external  liquid  has  passed 
through  the  membrane  and  has  mixed  with  the  internal  liquid.  The 
external  liquid,  moreover,  is  found  to  contain  some  of  the  internal  liquid. 
Hence  two  currents  have  been  produced  in  opposite  directions.  The  flow 
cf  the  liquid  towards  that  which  increases  in  volume  is  endosmcse,  and  the 


112 


On  Liquids. 


[140- 


current  in  the  opposite  direction  is  exosmose.  If  water  is  placed  in  the  bag, 
and  immersed  in  the  syrup,  endosmose  is  produced  from  the  water  towards 

the  syrup,  and  the  liquid  in  the  interior 
diminishes  in  volume  while  the  level  of  the 
exterior  is  raised. 

The  height  of  the  ascent  in  the  endosmo- 
ineter  varies  with  different  liquids.  Of  all 
vegetable  substances,  sugar  is  that  which, 
for  the  same  density,  has  the  greatest  power 
of  endosmose,  while  albumen  has  the  highest 
power  of  all  animal  substances.  In  general 
it  may  be  said  that  endosmose  takes  place 
towards  the  denser  liquid.  Alcohol  and 
ether  form  an  exception  to  this  ;  they  be- 
have like  liquids  which  are  denser  than 
water.  With  acids,  according  as  they  are 
more  or  less  dilute,  the  endosmose  is  from 
the  water  towards  the  acid,  or  from  the  acid 
towards  the  water. 

According  to  Dutrochet,  it  is  necessary 
for  the  production  of  endosmose  :  i.  that  the 
-^   liquids  be  different  but  capable  of  mixing,  as 
I  alcohol  and  water— there  is  no  diosmose,  for 
?   instance,    with    water  and  oil  :    ii.  that  the 
liquids  be  of  different  densities  ;  and  iii.  that 
the  membrane  must  be  permeable  to  at  least 
one  of  the  substances. 

The  current  through  thin  inorganic  plates  is  feeble,  but  continuous, 
while  organic  membranes  are  rapidly  decomposed,  and  diosmose  then  ceases. 
The  well-known  fact  that  dilute  alcohol  kept  in  a  porous  vessel  becomes 
concentrated  depends  on  endosmose.  If  a  mixture  of  alcohol  and  water  be 
kept  for  some  time  in  a  bladder,  the  volume  diminishes,  but  the  alcohol  be- 
comes much  more  concentrated.  The  reason,  doubtless,  is  that  the  bladder 
permits  the  diosmose  of  water  rather  than  that  of  alcohol. 

Dutrochet's  method  is  not  adapted  for  quantitative  measurements,  for  it 
does  not  take  into  account  the  hydrostatic  pressure  produced  by  the  column. 
Jolly  has  examined  the  endosmose  of  various  liquids  by  determining  the 
weights  of  the  bodies  diffused.  He  calls  the  endosmotic  equivalent  of  a  sub- 
ritance  the  number  which  expresses  how  many  parts  by  weight  of  water  pass 
through  the  bladder  in  exchange  for  one  part  by  weight  of  the  substance. 
The  following  are  some  of  the  endosmotic  equivalents  which  he  deter- 
mined— : 
Sulphuric  acid  .  .  .0-4  Sulphate  of  copper  .  .  9-5 

Alcohol 4*2  „  magnesium      .         .     117 

Chloride  of  sodium  .  .  4*3  Caustic  potass  .  .  .  .215-0 
Sugar 7-1 

He  also  found  that  the  endosmotic  equivalent  increases  with  the  temperature, 
and  that  the  quantities  of  substances  which  pass  in  equal  times  through  the 
bladder  are  proportional  to  the  strengths  of  the  solutions. 


Fig.  IK 


-141] 


Diffusion  of  Liquids. 


141.  Diffusion  of  liquids. — If  oil  be  poured  on  water  no  tendency  to 
intermix  is  observed,  and  even  if  the  two  liquids  be  violently  agitated  to- 
gether, on  allowing  them  to  stand,  two  separate  layers  are  formed.  With 
alcohol  and  water  the  case  is  different  ;  if  alcohol,  which  is  specifically 
lighter,  be  poured  upon  water,  the  liquids  gradually  intermix,  spite  of  the 
difference  of  their  specific  gravities  :  they  diffuse  into  one  another. 

This  point  may  be  illustrated  by  the  experiment  represented  in  fig.  112. 
A  tall  jar  contains  water  coloured  by  solution  of  blue  litmus  ;  by  means  of 
a  funnel  some  dilute  sulphuric  acid  is  carefully  poured  in,  so  as  to  form  a 
layer  at  the  bottom  ;  the  colour  of  the  solution  is  changed  into  red,  progress- 
ing upwards,  and  after  forty-eight  hours  the  change  is  complete — a  result  of 


Fig.  112. 

the  action  of  the  acid,  and  a  proof,  therefore,  that  it  has  diffused  throughout 
the  entire  mass. 

The  laws  of  this  diffusion,  in  which  no  porous  diaphragm  is  used,  have 
been  completely  investigated  by  Graham.  The  method,  by  which  his  latest 
experiments  were  made,  was  the  following  : — A  small  wide-necked  bottle  A 
(fig.  in)  filled  with  the  liquid,  whose  rate  of  diffusion  was  to  be  examined, 
was  closed  by  a  thin  glass  disc  and  placed  in  a  larger  vessel  B,  in  which 
water  was  poured  to  a  height  of  about  an  inch  above  the  top  of  the  bottle. 
The  disc  was  carefully  removed,  and  then  after  a  given  time  successive 
layers  were  carefully  drawn  off  by  means  of  a  siphon  or  pipette,  and  their 
contents  examined. 

The  general  results  of  these  investigations  may  be  thus  stated  : — 

i.  When  solutions  of  the  same  substance,  but  of  different  strengths,  are 
taken,  the  quantities  diffused  in  equal  times  are  proportional  to  the  strengths 
of  the  solutions. 

ii.  In  the  case  of  solutions  containing  equal  weights  of  different  substances, 
the  quantities  diffused  vary  with  the  nature  of  the  substances.  Saline 
substances  may  be  divided  into  a  number  of  equidiffusive  groups,  the  rates 
of  diffusion  of  each  group  being  connected  with  the  others  by  a  simple 
numerical  relation. 

iii.  The  quantity  diffused  varies  with  the  temperature.  Thus,  taking  the 
rate  of  diffusion  of  hydrochloric  acid  at  15°  C.  as  unity,  at  49°  C.  it  is  2-18. 


114  On  Liquids. 

iv.  If  two  substances  which  do  not  combine  be  mixed  in  solution,  they 
may  be  partially  separated  by  diffusion,  the  more  diffusive  one  passing  out 
most  rapidly.  In  some  cases  chemical  decomposition  even  may  be  effected 
by  diffusion.  Thus,  bisulphate  of  potassium  is  decomposed  into  free  sulphuric 
acid  and  neutral  sulphate  of  potassium. 

v.  If  liquids  be  dilute  a  substance  will  diffuse  into  water,  containing 
another  substance  dissolved,  as  into  pure  water  ;  but  the  rate  is  materially 
reduced  if  a  portion  of  the  same  diffusing  substance  be  already  present. 

The  following  table  gives  the  approximate  times  of  equal  diffusion  : — 

Hydrochloric  acid       .         .         .     1*0     Sulphate  of  magnesium  .         .       7-o 

Chloride  of  sodium     .         .         .2-3     Albumen 49-0 

Sugar 7-0     Caramel 98*0 

It  will  be  seen  from  the  above  table  that  the  difference  between  the 
rates  of  diffusion  is  very  great.  Thus,  msulphate  of  agnesium,  one  of  the 
least  diffusible  saline  substances,  diffuses  7  times  as  rapidly  as  albumen  and 
14  times  as  rapidly  as  caramel  These  last  substances,  like  hydrated  silicic 
acid,  starch,  dextrine,  gum,  &c.,  constitute  a  class  of  substances  which  are 
characterised  by  their  incapacity  for  taking  the  crystalline  form  and  by  the 
mucilaginous  character  of  their  hydrates.  Considering  gelatine  as  the  type 
of  this  class,  Graham  has  proposed  to  call  them  colloids  (/co'XXr;,  glue),  in 
contradistinction  to  the  far  more  easily  diffusible  crystalloid  substances. 

This  is  possibly  owing  to  the  fact  that  the  larger  molecules  only  pass  with 
difficulty  through  minute  apertures. 

Graham  has  proposed  a  method  of  separating  bodies  based  on  their  un- 
equal diffusibility,  which  he  calls  dialysis.  His  dialyser  (fig.  113)  consists  of 


Fig.  113.  Fig.  114. 

a  ring  of  gutta  percha,  over  which  is  stretched  while  wet  a  sheet  of  parch- 
ment paper,  forming  thus  a  vessel  about  two  inches  high  and  ten  inches  in 
diameter,  the  bottom  of  which  is  of  parchment  paper.  After  pouring  in 
the  mixed  solution  to  be  dialysed,  the  whole  is  floated  on  a  vessel  containing 
a  very  large  quantity  of  water  (fig.  114).  In  the  course  of  one  or  two  days 
a  more  or  less  complete  separation  will  have  been  effected.  Thus  a  solution 
of  arsenious  acid  mixed  with  various  kinds  of  food  readily  diffuses  out.  The 
process  has  received  important  applications  to  laboratory  and  pharmaceutical, 
purposes. 

Diosmose  plays  a  most  important  part  in  organic  life  ;  the  cell-walls  are 
diaphragms,  through  which  the  liquids  in  the  cells  set  up  diosmotic  com- 
munications. 


-142] 


Endosmose  of  Gases. 


142.  Endosmose  of  gases. — The  phenomena  of  endosmose  are  seen  in  a 
high  degree  in  the  case  of  gases,  the  treatment  of  which  we  may  here  anti- 
cipate. When  two  different  gases  are  separated  by  a  porous  diaphragm,  an 
interchange  takes  place  between  them,  and  ultimately  the  composition  of 
the  gas  on  both  sides  of  the  diaphragm  is  the  same  ;  but  the  rapidity  with 
which  different  gases  diffuse  into  each  other  under  these  circumstances 
varies  considerably.  The  laws  regulating  this  phenomenon  have  been  in- 
vestigated by  Graham.  Numerous  experiments  illustrate  it,  two  of  the  most 
interesting  of  which  are  the  following  : — 

A  glass  cylinder  closed  at  one  end  is  filled  with  carbonic  acid  gas,  its 
open  end  tied  over  with  a  bladder,  and  the  whole  placed  under  a  jar  of 
hydrogen.  Diffusion  takes  place  between  them  through  the  porous  dia- 
phragm, and  after  the  lapse  of  a  certain  time  hydrogen  has  passed  through 
the  bladder  into  the  cylindrical  vessel  in  much  greater  quantity  than  the 
carbonic  acid  which  has  passed  out,  so  that  the  bladder  becomes  very  much 
distended  outwards  (fig.  115).  If  the  cylinder  be  filled  with  hydrogen  and 


Fig.  115. 


Fig.  1 1 6. 


the  bell-jar  with  carbonic  acid,  the  reverse  phenomenon  will  be  produced — 
the  bladder  will  be  distended  inwards  (fig.  116). 

A  tube  about  12  inches  long,  closed  at  one  end  by  a  plug  of  dry  plaster 
of  Paris,  is  filled  with  dry  hydrogen,  and  its  open  end  then  immersed  in  a 
mercury  bath.  Endosmose  of  the  hydrogen  towards 
the  air  takes  place  so  rapidly  that  a  partial  vacuum  is 
produced,  and  mercury  rises  in  the  tube  to  a  height  of 
several  inches  (fig.  117).  If  several  such  tubes  are 
filled  with  different  gases,  and  allowed  to  diffuse  into 
the  air  in  a  similar  manner,  in  the  same  time,  different 
quantities  of  the  various  gases  will  diffuse,  and  Graham 
found  that  the  law  regulating  these  diffusions  is  that 
the  force  of  diffusion  is  inversely  as  the  square  roots  of 
the  densities  of  gases.  Thus,  if  two  vessels  of  equal 
capacity,  containing  oxygen  and  hydrogen,  be  separated^ 
by  a  porous  plug,  diffusion  takes  place  ;  and  after  the 
lapse  of  some  time,  for  every  one  part  of  oxygen  which 
has  passed  into  the  hydrogen,  four  parts  of  hydrogen 
have  passed  into  the  oxygen.  Now  the  density  of 
hydrogen  being  i,  that  of  oxygen  is  16,  hence  the  force  of  diffusion  is 


Fig.  117. 


Il6  On  Liquids.  [142- 

inversely  as  the  square  roots  of  these  numbers.     It  is  four  times  as  great  in 
the  one  which  has  T\  the  density  of  the  other. 

Let  the  stem  of  an  ordinary  tobacco  pipe  be  cemented,  so  that  its  ends 
project,  in  an  outer  glass  tube,  which  can  be  connected  with  an  air-pump 
and  thus  exhausted.  On  allowing  then  a  slow  current  of  air  to  enter  one 
end  of  the  pipe,  its  nitrogen  diffuses  more  rapidly  on  its  way  through  the 
porous  pipe  than  the  heavier  oxygen,  so  that  the  gas  which  emerges  at  the 
other  end,  and  which  can  be  collected,  is  much  richer  in  oxygen. 

143.  Effusion  and  transpiration  of  gases. — A  gas  can  only  flow 
from  one  space  to  another  space  occupied  by  the  same  gas  when  the  pressure 
in  the  one  is  greater  than  in  the  other.  Effusion  is  the  term  applied  to  the 
phenomenon  of  the  passage  of  gases  into  vacuum,  through  a  minute  aperture 
not  much  more  or  less  than  0*013  millimetre  in  diameter,  in  a  thin  plate  of 
metal  or  of  glass  ;  for  in  a  tube  the  friction  of  gases  comes  into  play,  and  in 
a  larger  aperture  the  particles  would  strike  against  one  another  and  form 
eddies  and  whirlpools.  The  velocity  of  the  efflux  is  measured  by  the  formula 
v=  \figti~,  in  which  h  represents  the  pressure  under  which  the  gas  flows, 
expressed  in  terms  of  the  height  of  a  column  of  the  gas,  which  would  exert 
the  same  pressure  as  that  of  the  effluent  gas.  Thus  for  air  under  the  ordinary 
pressure  flowing  into  a  vacuum,  the  pressure  is  equivalent  to  a  column  of 
mercury  76  centimetres  high ;  and  as  mercury  is  approximately  10,500 
times  as  dense  as  air,  the  equivalent  column  of  air  will  be  76  centimetres 
x  10,500  =  7,980  metres.  Hence  the  velocity  of  efflux  of  air  into  vacuum  is 
=  A/2  x  9-8  x  7, 980  =  395-5  metres.  This  velocity  into  vacuum  only  holds, 
however,  for  the  first  moment,  for  the  space  contains  a  continually-increasing 
quantity  of  air,  so  that  the  velocity  becomes  continually  smaller,  and  is  null 
when  the  pressure  on  each  side  is  the  same.  If  the  height  of  the  column  of 
air  hh^  corresponding  to  the  external  pressure,  is  known,  the  velocity  may  be 
calculated  by  the  formula  v=  Vzg  (h  —  h^). 

'  For  gases  lighter  than  air  a  greater  height  must  be  inserted  in  the 
formula,  and  for  heavier  gases  a  lower  height ;  and  this  change  must  be 
inversely  as  the  change  of  density.  Hence  the  velocities  of  efflux  of  various 
gases  must  be  i?iversely  as  the  square  roots  of  their  de?isities.  A  simple 
inversion  of  this  statement  is  that  the  densities  of  two  gases  are  inversely  as 
the  squares  of  their  velocities  of  effusion.  On  this  Bunsen  has  based  an 
interesting  method  of  determining  the  densities  of  gases  and  vapours. 

If  gases  issue  through  long,  fine  capillary  tubes  into  a  vacuum,  the 
rate  of  efflux,  or  the  velocity  of  transpiration,  is  independent  of  the  rate  of 
diffusion. 

i.  For  the  same  gas,  the  rate  of  transpiration  increases,  other  things  being 
equal,  directly  as  the  pressure  ;  that  is,  equal  volumes  of  air  of  different 
densities  require  times  inversely  proportional  to  their  densities. 

ii.  With  tubes  of  equal  diameters,  the  volume  transpired  in  equal  times 
is  inversely  as  the  length  of  the  tube. 

iii.  As  the  temperature  rises  the  transpiration  becomes  slo-wer. 
iv.   The  rate  of  transpiration  is  independent  of  the  material  of  the  tube. 
144.  Absorption  of  gases. — The  surfaces  of  all  solid  bodies  exert  an 
attraction  on  the  molecules  of  gases  with  which  they  are  in  contact,  of  such 
a  nature  that  they  become  covered  with  a  more  or  less  thick  layer  of  con- 


-144] 


A  bsorption  of  Gases. 


117 


denscd  gas.  When  a  porous  body  such  as  a  piece  of  charcoal,  which  con- 
sequently presents  an  immensely  increased  surface  in  proportion  to  its  size, 
is  placed  in  a  vessel  of  ammonia  gas  over  mercury 
(fig.  1 1 8),  the  great  diminution  of  volume  which  en- 
sues indicates  that  considerable  quantities  of  gas 
are  absorbed. 

Now,  although  there  is  no  absorption  such  as 
arises  from  chemical  combinations  between  the  solid 
and  the  gas  (as  with  phosphorus  and  oxygen),  still 
the  quantity  of  gas  absorbed  is  not  entirely  dependent 
on  the  physical  conditions  of  the  solid  body;  it  is  in- 
fluenced in  some  measure  by  the  chemical  nature  both 
of  the  solid  and  the  gas.  Boxwood  charcoal  has  very 
great  absorptive  power.  The  following  table  gives 
the  volumes  of  gas,  under  standard  conditions  of  tem- 
perature and  pressure,  absorbed  by  one  volume  of 
boxwood  charcoal  and  of  meerschaum  respectively  : — 

Fig.  118. 


Ammonia 

Hydrochloric  acid    . 
Sulphurous  acid 
Sulphuretted  hydrogen 
Carbonic  acid  . 
Carbonic  oxide 
Oxygen     . 
Nitrogen  . 
Hydrogen 


Charcoal 
.      90 
.      85 
.      65 

•  55 

•  35 

•  9'4 
.    9-2 

•  7'5 
.  175 


Meerschaum. 
15 


II 

53 
I'2 

i-'S 

i -6 

0-5 


The  absorption  of  gases  is  in  general  greatest  in  the  case  of  those  which  are 
most  easily  liquefied. 

Cocoanut  charcoal  is  even  more  highly  absorbent;  it  absorbs  171  of 
ammonia,  73  of  carbonic  acid,  and  108  of  cyanogen  at  the  ordinary  pressure  ; 
the  amount  of  absorption  increases  with  the  pressure. 

The  absorptive  power  of  pine  charcoal  is  about  half  as  much  as  that  of 
boxwood.  The  charcoal  made  from  corkwood,  which  is  very  porous,  is  not 
absorbent,  neither  is  graphite.  Platinum,  in  the  finely  divided  form  known 
as  platinum  sponge,  is  said  to  absorb  250  times  its  volume  of  oxygen  gas. 
Many  other  porous  substances,  such  as  meerschaum,  gypsum,  silk,  &c.,  are 
also  highly  absorbent. 

If  a  coin  be  laid  on  a  plate  of  glass  or  of  metal,  after  some  time,  when 
the  plate  is  breathed  on,  an  image  of  the  coin  appears.  If  a  figure  is  traced 
on  a  glass  plate  with  the  finger,  nothing  appears  until  the  plate  is  breathed 
on,  when  the  figure  is  at  once  seen.  Indeed,  the  traces  of  an  engraving 
which  has  long  laid  on  a  glass  plate  may  be  produced  in  this  way. 

These  phenomena  are  known  as  Moseys  images,  for  he  first  investigated 
them,  although  he  explained  them  erroneously.  The  correct  explanation  was 
given  by  Waidele,  who  ascribed  them  to  alterations  in  the  layer  of  gas, 
vapour,  and  fine  dust  which  is  condensed  on  the  surface  of  all  solids.  If 


Ii8  On  Liquids.  [144- 

this  layer  is  removed  by  wiping,  on  afterwards  breathing  against  the  surface 
more  vapour  is  condensed  on  the  marks  in  question,  which  then  present  a 
different  appearance  to  the  rest. 

If  a  die  'or  a  stamp  is  laid  on  a  freshly  polished  metal  plate,  and  one 
therefore  which  has  been  deprived  of  its  atmosphere,  the  layer  of  vapour 
from  the  coin  will  diffuse  on  to  the  metal  plate,  which  thereby  becomes 
altered  ;  so  that  when  this  is  breathed  on  an  impression  is  seen. 

Conversely,  if  a  coin  be  polished  and  placed  on  an  ordinary  plate,  it  will 
partially  remove  the  layer  of  gas  from  the  parts  in  contact,  so  that  on 
breathing  on  the  plate  the  image  is  seen. 

145.  Occlusion. — Graham  found  that  at  a  high  temperature  platinum 
and  iron  allow  hydrogen  to  traverse  them  even  more  readily  than  does 
caoutchouc  in  the  cold.  Thus  while  a  square  metre  of  caoutchouc  0-014 
millimetres  in  thickness  allowed  129  cubic  centimetres  of  hydrogen  at  20° 
to  traverse  it  in  a  minute,  a  platinum  tube  n  millimetres  in  thickness  and 
of  the  same  surface  allowed  489  cubic  centimetres  to  traverse  it  at  a  bright 
red  heat. 

This  is  probably  connected  with  the  property  which  some  metals,  though 
destitute  of  physical  pores,  possess  of  absorbing  gases  either  on  their  surface 
or  in  their  mass,  and  to  which  Graham  has  applied  the  term  occlusion.  It 
is  best  observed  by  allowing  the  heated  metal  to  cool  in  contact  with  the 
gas.  The  gas  cannot  then  be  extracted  by  the  air-pump,  but  is  disengaged 
on  heating.  In  this  way  Graham  found  that  platinum  occluded  four  times 
its  volume  of  hydrogen  ;  iron  wire  0*44  times  its  volume  of  hydrogen,  and 
4-15  volumes  of  carbonic  oxide  ;  silver  reduced  from  the  oxide,  absorbed 
about  seven  volumes  of  oxygen,  and  nearly  one  volume  of  hydrogen  when 
heated  to  dull  redness  in  these  gases.  This  property  is  most  remarkable 
in  palladium,  which  absorbs  hydrogen,  not  only  in  cooling  after  being  heated, 
but  also  in  the  cold.  When,  for  instance,  a  palladium  electrode  is  used  in 
the  decomposition  of  water,  one  volume  of  the  metal  can  absorb  980  times 
its  volume  of  the  gas.  This  gas  is  again  driven  out  on  being  heated,  in  which 
respect  there  is  a  resemblance  to  the  solution  of  gases  in  liquids.  By  the 
occlusion  of  hydrogen  the  volume  of  palladium  is  increased  by  0-09827  of  its 
original  amount,  from  which  it  follows  that  the  hydrogen,  which  under 
ordinary  circumstances  has  a  density  0-000089546  that  of  water,  has  here  a 
density  nearly  9,868  times  as  great,  or  about  0*88  that  of  water.  Hence  the 
hydrogen  must  be  in  the  liquid  or  even  solid  state  ;  it  probably  forms  thus 
an  alloy  with  palladium,  like  a  true  metal — a  view  of  this  gas  which  is 
strongly  supported  by  independent  chemical  considerations.  The  physical 
properties,,  in  .so  far  as  they  have  been  examined,  support  this  view  of  its 
being  an  alloy. 


-147]  Expansibility  of  Gases.  1 19 


BOOK    IV. 

ON   GASES. 


CHAPTER    I. 

PROPERTIES   OF  GASES.      ATMOSPHERE.      BAROMETERS. 

146.  Physical  properties  of  gases. — Gases  are  bodies  whose  molecules 
are  in  a  constant  state  of  motion,  in  virtue  of  which  they  possess  the  most 
perfect  mobility,  and  are  continually  tending   to  occupy  a  greater  space. 
This  property  of  gases  is  known  by  the  names  expansibility,  tension,  or  elastic 

force,  from  which  they  are  often  called  elastic  fluids. 

Gases  and  liquids  have  several  properties  in  common,  and  some  in  which 
they  seem  to  differ  are  in  reality  only  different  degrees  of  the  same  property. 
Thus,  in  both,  the  particles  are  capable  of  moving  :  in  gases  quite  freely ;  in 
liquids  not  quite  freely,  owing  to  a  certain  degree  of  viscosity.  Both  are 
compressible,  though  in  very  different  degrees.  If  a  liquid  and  a  gas  both 
exist  under  the  pressure  of  one  atmosphere,  and  then  the  pressure  be 
doubled,  the  water  is  compressed  by  about  the  20800  Par^  while  the  gas  is 
compressed  by  one-half.  In  density  there  is  a  great  difference  ;  water,  which 
is  the  type  of  liquids,  is  770  times  as  heavy  as  air,  the  type  of  gaseous  bodies, 
while  under  the  pressure  of  one  atmosphere.  The  property  by  which  gases 
are  distinguished  from  liquids  is  their  tendency  to  indefinite  expansion. 

Matter  assumes  the  solid,  liquid,  or  gaseous  form  according  to  the  rela- 
tive strength  of  the  cohesive  and  repulsive  forces  exerted  between  their 
molecules.  In  liquids  these  forces  balance  ;  in  gases  repulsion  (287)  prepon- 
derates. 

By  the  aid  of  pressure  and  of  low  temperatures,  the  force  of  cohesion 
may  be  so  far  increased  in  many  gases  that  they  are  readily  converted  into 
liquids,  and  we  know  now  that  with  sufficient  pressure  and  cold  they  may  all 
be  liquefied.  On  the  other  hand,  heat,  which  increases  the  vis  viva  of  the 
molecules,  converts  liquids,  such  as.  water,  alcohol,  and  ether,  into  the  aeriform 
state  in  which  they  obey  all  the  laws  of  gases.  This  aeriform  state  of  liquids 
is  known  by  the  name  of  vapoury  while  gases  are  bodies  which,  under  ordi- 
nary temperature  and  pressure,  remain  in  the  aeriform  state. 

In  describing  the  properties  of  gases  we  shall,  for  obvious  reasons,  have 
exclusive  reference  to  atmospheric  air  as  their  type. 

147.  Expansibility  of  gases. — This  property  of  gases,  their  tendency  to 
assume  continually  a  greater  volume,  is  exhibited  by  means  of  the  following 


120 


On  Gases. 


[147- 


experiment : — A  bladder,  closed  by  a  stopcock  and  about  half-full  of  air,  is 
placed  under  the  receiver  of  the  air-pump  (fig.  119),  and  a  vacuum  is  pro- 
duced, on  which  the  bladder  immediately 
distends.  This  arises  from  the  fact  that  the 
molecules  of  air  flying  about  in  all  directions 
press  against  the  sides  of  the  bladder.  Under 
ordinary  conditions,  this  internal  pressure  is 
counterbalanced  by  the  air  in  the  receiver, 
which  exerts  an  equal  and  contrary  pressure. 
But  when  this  pressure  is  removed  by  ex- 
hausting the  receiver,  the  internal  pressure 
becomes  evident.  When  air  is  admitted  into 
the  receiver,  the  bladder  resumes  its  original 
form. 

148.  Compressibility  of  gases. — The 
compressibility  of  gases  is  readily  shown  by 
the  pneumatic  syringe  (fig.  120).  This  con- 
sists of  a  stout  glass  tube  closed  at  one  end 
and  provided  with  a  tight-fitting  solid  piston. 
When  the  rod  of  the  piston  is  pressed,  it 
moves  down  in  the  tube,  and  the  air  becomes 
compressed  into  a  smaller  volume  ;  but  as  soon  as  the  force  is  removed  the 
air  regains  its  original  volume,  and  the  piston  rises  to  its  former  position. 


Fig.  1 20. 

149.  Weight  of  gases. — From  their  extreme  fluidity  and  expansibility, 
gases  seem  to  be  uninfluenced  by  the  force  of  gravity  :  they  nevertheless 
possess  weight  like  solids  and  liquids.  To  show  this,  a  glass  globe  of  3  or  4 
quarts  capacity  is  taken  (fig.  121),  the  neck  of  which  is  provided  with  a  stop- 
cock, which  hermetically  closes  it  and  by  which  it  can  be  screwed  to  the 
plate  of  the  air-pump.  The  globe  is  then  exhausted,  and  its  weight  deter- 
mined by  means  of  a  delicate  balance.  Air  is  now  allowed  to  enter,  and  the 
globe  again  weighed.  The  weight  in  the  second  case  will  be  found  to  be 
greater  than  before,  and,  if  the  capacity  of  the  vessel  is  known,  the  increase 
will  obviously  be  the  weight  of  that  volume  of  air. 

By  a  modification  of  this  method,  and  with  the  adoption  of  certain  pre- 
cautions, the  weight  of  air  and  of  other  gases  has  been  determined.  Perhaps 
the  most  accurate  are  those  of  Regnault,  who  found  that  a  litre  of  dry  air  at 
o°  C,  and  under  a  pressure  of  760  millimetres,  weighs  1-293187  grammes. 
Since  a  litre  of  water  (or  1,000  cubic  centimetres)  at  o°  weighs  0-999877 


-151] 


The  Atmosphere.     Its  Composition. 


121 


grammes,  the  density  of  air  is  0*00129334  that  of  water  under  the  same  circum- 
stances ;  that  is,  water  is  773  times  as  heavy  as  air.     Expressed  in  English 
measures,  100  cubic  inches  of  dry  air  under  the  ordinary  at- 
mospheric pressure  of  30  in.  and  at  the  temperature  of  16°  C. 
weigh  31  grains  ;  the  same  volume  of  carbonic  acid  gas  under 
the  same   circumstances   weighs   47*25   grains ;     100  cubic 
inches  of  hydrogen,  the   lightest  of  all   gases,  weigh   2-14 
grains  ;  and  100  cubic  inches  of  hydriodic  acid  gas  weigh 
146  grains. 

1 50.  Pressures  exerted  by  gases, — Gases  exert  on  their 
own  molecules  and  on  the  sides  of  vessels  which  contain 
them,  pressures   which   may  be  regarded  from   two  points 
of  view.     First,  we   may  neglect   the  weight   of  the  gas  ; 
secondly,  we  may  take  account  of  its  weight.     If  we  neglect 
the  weight  of  any  gaseous  mass  at  rest,  and  only  consider  its 
expansive  force,  it  will  be  seen  that  the  pressures  due  to  this 
force  act  with  the  same  intensity  on  all  points,  both  of  the 
mass  itself  and  of  the  vessel  in  which  it  is  contained.     For 
it  is  a  necessary  consequence  of  the  elasticity  and  fluidity 
of  gases,  that  the  repulsive  force  between  the  molecules  is 
the  same  at  all  points,  and  acts  equally  in  all  directions. 
This  principle  of  the  equality  of  the  pressure  of  gases  in 

all  directions  may  be  shown  experimentally  by  means  of  an  apparatus 
resembling  that  by  which  the  same  principle  is  demonstrated  for  liquids 
(ng-  66}. 

If  we  consider  the  weight  of  any  gas  we  shall  see  that  it  gives  rise  to 
pressures  which  obey  the  same  laws  as  those  produced  by  the  weight  of 
jiquids.  Let  us  imagine  a  cylinder,  with  its  axis  vertical,  several  miles  high, 
closed  at  both  ends  and  full  of  air.  Let  us  consider  any  small  portion  of 
the  air  enclosed  between  two  horizontal  planes.  This  portion  must  sustain 
the  weight  of  all  the  air  above  it,  and  transmit  that  weight  to  the  air  beneath 
it,  and  likewise  to  the  curved  surface  of  the  cylinder  which  contains  it,  and 
at  each  point  in  a  direction  at  right  angles  to  the  surface.  Thus  the  pressure 
increases  from  the  top  of  the  column  to  the  base  ;  at  any  given  layer,  it 
acts  equally  on  equal  surfaces,  and  at  right  angles  to  them,  whether  they 
are  horizontal,  vertical,  or  inclined.  The  pressure  acts  on  the  sides  of 
the  vessel,  and  on  any  small  surface  it  is  equal  to  the  weight  of  a  column 
of  gas,  whose  base  is  this  surface,  and  whose  height  its  distance  from  the 
summit  of  the  column.  The  pressure  is  also  independent  of  the  shape 
and  dimensions  of  the  supposed  cylinder,  provided  the  height  remains  the 
same. 

For  a  small  quantity  of  gas  the  pressures  due  to  its  weight  are  quite  in- 
significant, and  may  be  neglected  ;  but  for  large  quantities,  like  the  atmo- 
sphere, the  pressures  are  considerable,  and  must  be  allowed  for. 

151.  The  atmosphere.     Its  composition. — The  atmosphere  is  the  layer 
of  air  which  surrounds  our  globe  in  every  part.     It  partakes  of  the  rotatory 
motion  of  the  globe,  and  would  remain  fixed  relatively  to  terrestrial  objects 
but  for  local  circumstances,  which  produce  winds,  and  are  constantly  dis- 
turbing its  equilibrium. 


122  On  Gases.  [151- 

It  is  essentially  a  mixture  of  oxygen  and  nitrogen  gases  ;  its  average  com- 
position by  volume  being  as  follows  : — 

Nitrogen 78*49 

Oxygen 20*63 

Aqueous  vapour 0-84 

Carbonic  acid  .........       0x34 

100-00 

The  carbonic  acid  arises  from  the  respiration  of  animals,  from  the  pro- 
cesses of  combustion,  and  from  the  decomposition  of  organic  substances. 
Boussingault  has  estimated  that  in   Paris  the  following  quantities  of  car- 
bonic acid  are  produced  every  24  hours  : — 

By  the  population  and  by  animals .         .     I  i,895',ooo  cubic  feet 
By  processes  of  combustion    ...         .     92,101,000        „ 

103,996,000 

Notwithstanding  this  enormous  continual  production  of  carbonic  acid 
the  composition  of  the  atmosphere  does  not  vary  ;  for  plants  in  the  process 
of  vegetation  decompose  the  carbonic  acid,  assimilating  the  carbon,  and 
restoring  to  the  atmosphere  the  oxygen,  which  is  being  continually  con- 
sumed in  the  processes  of  respiration  and  combustion. 

152.  Atmospheric  pressure. — If  we  neglect  the  perturbations  to  which 
the  atmosphere  is  subject,  as  being  inconsiderable,  we  may  consider  it 
as  a  fluid  sea  of  a  certain  depth,  surrounding  the  earth  on  all  sides,  and 
exercising  the  same  pressure  as  if  it  were  a  liquid  of  very  small  density. 
Consequently,  the  pressure  on  the  unit  of  area  is  constant  at  a  given  level, 
being  equal  to  the  weight  of  the  column  of  atmosphere  above  that  level 
whose  horizontal  section  is  the  unit  of  area.  It  will  act  at  right  angles  to 
the  surface,  whatever  be  its  position.  It  will  diminish  as  we  ascend,  and 
increase  as  we  descend  from  that  level.  Consequently,  at  the  same  height, 
the  atmospheric  pressures  on  unequal  plane  surfaces  will  be  proportional  to 
the  areas  of  those  surfaces,  provided  they  be  small  in  proportion  to  the  height 
of  the  atmosphere. 

In  virtue  of  the  expansive  force  of  the  air,  it  might  be  supposed  that  the 
molecules  would  expand  indefinitely  into  the  planetary  spaces.  But,  in  pro- 
portion as  the  air  expands,  its  expansive  force  decreases,  and  is  further 
weakened  by  the  low  temperature  of  the  upper  regions  of  the  atmosphere,  so 
that,  at  a  certain  height,  an  equilibrium  is  established  between  the  expansive 
force  which  separates  the  molecules,  and  the  action  of  gravity  which  draws 
them  towards  the  centre  of  the  earth.  It  is  therefore  concluded  that  the 
atmosphere  is  limited. 

From  the  weight  of  the  atmosphere,  and  its  increase  in  density,  and  from 
the  observation  of  certain  phenomena  of  twilight,  its  height  has  been  esti- 
mated at  from  30  to  40  miles.  Above  that  height  the  air  is  extremely  rarefied, 
and  at  a  height  of  60  miles  it  is  assumed  that  there  is  a  perfect  vacuum.  On 
the  other  hand,  meteorites  have  been  seen  at  a  height  of  200  miles,  and  as  their 
luminosity  is  undoubtedly  due  to  the  action  of  air,  there  must  be  air  at  such  a 
height.  This  higher  estimate  is  supported  by  observations  made  at  Rio 
Janeiro  on  the  twilight  arc,  by  M.  Liais,  who  estimates  the  height  of  the  atmo- 
sphere at  between  198  and  212  miles.  The  question  as  to  the  exact  height  of 
the  atmosphere  must  therefore  be  considered  as  still  awaiting  settlement. 


-154] 


Magdeburg  JlemispJieres. 


123 


As  it  has  been  previously  stated  that  100  cubic  inches  of  air  which  31 
grains,  it  will  readily  be  conceived  that  the  whole  atmosphere  exercises  a 
considerable  pressure  on  the  surface  of  the  earth.  The  existence  of  this 
pressure  is  shown  by  the  following  experiments. 

153.  Crushing  force  of  the  atmosphere. — On  one  end  of  a  stout  glass 
cylinder,  about  5  inches  high,  and  open  at  both  ends,  a  piece  of  bladder  is 
tied  quite  air-tight.    The  other  end,  the  edge  of 

which  is  ground  and  well  greased,  is  pressed  on 
the  plate  of  the  air-pump  (fig.  122).  As  soon  as 
the  air  in  the  vessel  is  rarefied,  by  working 
the  air-pump,  the  bladder  is  depressed  by  the 
weight  of  the  atmosphere  above  it,  and  finally 
bursts  with  a  loud  report  caused  by  the  sudden 
entrance  of  the  air. 

154.  Magdeburg  hemispheres. — The  pre- 
ceding experiment  only  serves  to  illustrate  the 
downward   pressure   of    the   atmosphere.      By 
means  of  the  Magdeburg  hemispheres  (figs.  123 
and  124),  the  invention  of  which  is  due  to  Otto 
von  Guericke,  burgomaster   of  Magdeburg,  it 
can   be   shown   that   the   pressure   acts   in   all 
directions.      This    apparatus    consists    of    two 
hollow  brass  hemispheres   of  4   to  4|   inches 
diameter,  the  edges  of  which  are  made  to  fit 

tightly,  and  are  well  greased.     One  of  the  hemispheres  is  provided  with  a 
stopcock,  by  which  it  can  be  screwed  on  the  air-pump,  and  on  the  other  there 


Fig.  123.  Fig.  124. 

is  a  handle.     As  long  as  the  hemispheres  contain  air  they  can  be  separated 
without  any  difficulty,  for  the  external  pressure  of  the  atmosphere  is  counter- 


G  2 


124  On  Gases.  [154- 

balanced  by  the  elastic  force  of  the  air  in  the  interior.  But  when  the  air  in 
the  interior  is  pumped  out  by  means  of  the  air-pump,  the  hemispheres 
cannot  be  separated  without  a  powerful  effort  ;  and  as  this  is  the  case  in 
whatever  position  they  are  held,  it  follows  that  the  atmospheric  pressure  is 
transmitted  in  all  directions. 


DETERMINATION   OF  THE  ATMOSPHERIC  PRESSURE.      BAROMETERS. 

155.  Torricelli's  experiment. — The  above  experiments  demonstrate  the 
existence  of  the  atmospheric  pressure,  but  they  give  no  precise  indications 

as  to  its  amount.  The  following  experi- 
ment, which  was  first  made,  in  1643,  by 
Torricelli,  a  pupil  of  Galileo,  gives  an 
exact  measure  of  the  weight  of  the  atmo- 
sphere. 

A  glass  tube  is  taken,  about  a  yard 
long  and  a  quarter  of  an  inch  internal 
diameter  (fig.  125).  It  is  sealed  at  one 
end,  and  is  quite  filled  with  mercury. 
The  aperture  C  being  closed  by  the 
thumb,  the  tube  is  inverted,  the  open  end 
placed  in  a  small  mercury  trough,  and 
the  thumb  removed.  The  tube  being  in 
a  vertical  position,  the  column  of  mercury 
sinks,  and,  after  oscillating  some  time,  it 
finally  comes  to  rest  at  a  height  A,  which 
at  the  level  of  the  sea  is  about  30  inches 
above  the  mercury  in  the  trough.  The 
mercury  is  raised  in  the  tube  by  the 
pressure  of  the  atmosphere  on  the  mer- 
cury in  the  trough.  There  is  no  contrary 
pressure  on  the  mercury  in  the  tube, 
because  it  is  closed.  But  if  the  end  of 
the  tube  be  opened,  the  atmosphere  will 
press  equally  inside  and  outside  the  tube, 
and  the  mercury  will  sink  to  the  level  of 
that  in  the  trough.  It  has  been  shown  in 
hydrostatics  (108)  that  the  heights  of  two 
columns  of  liquid  in  communication  with  each  other  are  inversely  as  their 
densities,  and  hence  it  follows  that  the  pressure  of  the  atmosphere  is  equal 
to  that  of  a  column  of  mercury,  the  height  of  which  is  30  inches.  If.  however, 
the  weight  of  the  atmosphere  diminishes,  the  height  of  the  column  which  it 
can  sustain  must  also  diminish. 

156.  Pascal's  experiments. — Pascal,  who  wished  to  ascertain  whether 
the  force  which  sustained  the  mercury  in  the  tube  was  really  the  pressure  of 
the  atmosphere,  made  the  following  experiments,     i.  If  it  were  the  case,  the 
column   of  mercury  ought  to  descend  in   proportion  as  we  ascend  in  the 
atmosphere.      He   accordingly   requested   one    of  his    relations   to    repeat 
Torricelli's  experiment  on  the  summit  of  the  Puy  de  Dome  in  Auvergne. 


Fig.  125. 


-158  ]  Different  Kinds  of  Barometers.  1 2  5 

This  was  done,  and  it  was  found  that  the  mercurial  column  was  about  3 
inches  lower,  thus  proving  that  it  is  really  the  weight  of  the  atmosphere 
which  supports  the  mercury,  since,  when  this  weight  diminishes,  the  height 
of  the  column  also  diminishes,  ii.  Pascal  repeated  Torricelli's  experiment 
at  Rouen,  in  1646,  with  other  liquids.  He  took  a  tube  closed  at  one  end, 
nearly  50  feet  long,  and,  having  filled  it  with  water,  placed  it  vertically  in  a 
vessel  of  water,  and  found  that  the  water  stood  in  the  tube  at  a  height  of 
34  feet ;  that  is,  13-6  times  as  high  as  mercury.  But  since  mercury  is  13-6 
times  as  heavy  as  water,  the  weight  of  the  column  of  water  was  exactly 
equal  to  that  of  the  column  of  mercury  in  Torricelli's  experiment,  and  it  was 
consequently  the  same  force,  the  pressure  of  the  atmosphere,  which  succes- 
sively supported  the  two  liquids.  Pascal's  other  experiments  with  oil  and 
with  wine  gave  similar  results. 

1 57.  Amount  of  the  atmospheric  pressure. — Let  us  assume  that  the 
tube  in  the  above  experiment  is  a  cylinder,  the  section  of  which  is  equal  to  a 
square  inch,  then,  since  the  height  of  the  mercurial  column  in  round  numbers 
is  30  inches,  the  column  will  contain  30  cubic  inches,  and  as  a  cubic  inch  ot 
mercury  weighs  3433*5  grains  =  0-49  of  a  pound,  the  pressure  of  such   a 
column   on  a  square   inch  of  surface  is  equal  to  147   pounds.     In  round 
numbers  the  pressure  of  the  atmosphere  is  taken  at  1 5  pounds  on  the  square 
inch.     A  surface  of  a  foot  square  contains  144  square  inches,  and  therefore 
the  pressure  upon  it  is  equal  to  2,160  pounds,  or  nearly  a  ton.     Expressed  in 
the  metrical  system,  the  standard  atmospheric  pressure  at  o°  and  the  sea 
level  is  760  millimetres,  which  is  equal  1029-9217  inches;  and  a  calcula- 
tion similar  to  the  above  shows  that  the  pressure  on  a  square  centimetre  is 
=  1*03296  kilogramme. 

A  gas  or  liquid  which  acts  in  such  a  manner  that  a  square  inch  of  surface 
is  exposed  to  a  pressure  of  1 5  pounds,  is  called  a  pressure  of  one  atmosphere. 
If,  for  instance,  the  elastic  force  of  the  steam  of  a  boiler  is  so  great  that 
each  square  inch  of  the  internal  surface  is  exposed  to  a  pressure  of  90  pounds 
( =  6  x  15),  we  say  it  is  under  a  pressure  of  six  atmospheres. 

The  surface  of  the  body  of  a  man  of  middle  size  is  about  16  square  feet ; 
the  pressure,  therefore,  which  a  man  supports  on  the  surface  of  his  body  is 
35,560  pounds,  or  nearly  16  tons.  Such  an  enormous  pressure  might  seem 
impossible  to  be  borne  ;  but  it  must  be  remembered  that,  in  all  directions, 
there  are  equal  and  contrary  pressures  which  counterbalance  one  another. 
It  might  also  be  supposed  that  the  effect  of  this  force,  acting  in  all  directions, 
would  be  to  press  the  body  together  and  crush  it.  But  the  solid  parts  of  the 
skeleton  could  resist  a  far  greater  pressure  ;  and  as  to  the  air  and  liquids 
contained  in  the  organs  and  vessels,  the  air  has  the  same  density  as  the 
external  air,  and  cannot  be  further  compressed  by  the  atmospheric  pressure  ; 
and  from  what  has  been  said  about  liquids  (98),  it  is  clear  that  they  are 
virtually  incompressible.  When  the  external  pressure  is  removed  from  any 
part  of  the  body,  either  by  means  of  a  cupping  vessel  or  by  the  air-pump, 
the  pressure  from  within  is  seen  by  the  distension  of  the  surface. 

158.  Different    kinds    of    barometers. — The    instruments    used    for 
measuring  the  atmospheric  pressure  are   called   barometers.     In  ordinary 
barometers,  the  pressure  is  measured  by  the  height  of  a  column  of  mercury, 
as  in  Torricelli's  experiment :  the  barometers  which  we  are  about  to  describe 


126 


On  Gases. 


[158 


arc  of  this  kind.     But  there  are  barometers  without  any  liquid,  one  of  which, 
the  aneriod)  181),  is  remarkable  for  its  simplicity  and  portability. 

1 59.  Cistern  barometer. — The  cistern  barometer  consists  of  a  straight 
glass  tube  closed  at  one  end,  about  33  inches  long,  filled  with  mercury,  and 
dipping  into  a  cistern  containing  the  same  metal.  In  order  to  render  the 
barometer  more  portable,  and  the  variations  of  the  level  in  the  cistern  less 
perceptible  when  the  mercury  rises  or  falls  in  the  tube,  several  different 


A. 

IB 


Fig.  126. 


Fig.  127. 


Fig.  128. 


forms  have  been  constructed.  Fig.  126  represents  one  form  of  the  cistern 
barometer.  The  apparatus  is  fixed  to  a  mahogany  stand,  on  the  upper  part 
of  which  there  is  a  scale  graduated  in  millimetres  or  inches  from  the  level  of 
the  mercury  in  the  cistern  :  a  movable  index,  /,  shows  on  the  scale  the 
level  of  the  mercury.  A  thermometer  on  one  side  of  the  tube  indicates  the 
temperature. 

There  is  one  fault  to  which  this  barometer  is  liable,  in  common  with  all 
others  of  the  same  kind.     The  zero  of  the  scale  does  not  always  correspond 


-160]  Barometers.  127 

to  the  level  of  the  mercury  in  the  cistern.  For,  as  the  atmospheric  pressure 
is  not  always  the  same,  the  height  of  the  mercurial  column  varies  ;  some- 
times mercury  is  forced  from  the  cistern  into  the  tube,  and  sometimes  from 
the  tube  into  the  cistern,  so  that,  in  the  majority  of  cases,  the  graduation  of 
the  barometer  does  not  indicate  the  true  height.  If  the  diameter  of  the 
cistern  is  large,  relatively  to  that  of  the  tube,  the  error  from  this  source  is 
lessened.  The  height  of  the  barometer  is  the  distance  between  the  levels  of 
the  mercury  in  the  tube  and  in  the  cistern.  Hence  the  barometer  should 
always  be  perfectly  vertical,  for,  if  not,  the  tube  being  inclined,  the  column 
of  mercury  is  elongated  (fig.  127),  and  the  number  read  off  on  the  scale  is 
too  great.  As  the  pressure  which  the  mercury  exerts  by  its  weight  at  the 
base  of  the  tube  is  independent  of  the  form  of  the  tube  and  of  its  diameter 
(102),  provided  it  is  not  capillary,  the  height  of  the  barometer  is  independent 
of  the  diameter  of  the  tube  and  of  its  shape,  but  is  inversely  as  the  density 
of  the  liquid.  With  mercury  the  mean  height  at  the  level  of  the  sea  is  29-92, 
or  in  round  numbers  30,  inches  ;  in  a  water  barometer  it  would  be  about  34 
feet,  or  10-33  metres. 

The  '  Philosophical  Magazine,'  vol.  xxx.  Fourth  Series,  page  349,  contains 
a  detailed  account  of  a  method  of  constructing  a  water  barometer. 

1 60.  Fortin's  barometer. — Fortiris  barometer  differs  from  that  just 
described,  in  the  shape  of  the  cistern.  The  base  of  the  cistern  is  made  of 
leather,  and  can  be  raised  or  lowered  by  means  of  a  screw ;  this  has  the 
advantage,  that  a  constant  level  can  be  obtained,  and  also  that  the  instru- 
ment is  made  more  portable.  For,  in  travelling,  it  is  only  necessary  to 
raise  the  leather  until  the  mercury,  which  rises  with  it,  quite  fills  the  cistern  , 
the  barometer  may  then  be  inclined,  and  even  inverted,  without  any  fear 
that  a  bubble  of  air  may  enter,  or  that  the  shock  of  the  mercury  may  crack 
the  tube. 

Fig.  128  represents  the  arrangement  of  the  barometer,  the  tube  of  which 
is  placed  in  a  brass  case.  At  the  top  of  this  case  there  are  two  longitudinal 
apertures,  on  opposite  sides,  so  that  the  level  of  the  mercury,  B,  is  seen. 
The  scale  on  the  case  is  graduated  in  millimetres.  An  index  A,  moved  by 
the  hand,  gives,  by  means  of  a  vernier,  the  height  of  the  mercury  to  ^th  of  a 
millimetre.  At  the  bottom  of  the  case  there  is  a  cistern  <£,  containing 
mercury,  O. 

Fig.  129  shows  the  details  of  the  cistern  on  a  larger  scale.  It  consists  of 
a  glass  cylinder  £,  through  which  the  mercury  can  be  seen  ;  this  is  closed  at 
the  top  by  a  box-wood  disc  fitted  on  the  under  surface  of  the  brass  cover  M. 
Through  this  passes  the  barometer  tube  E,  which  is  drawn  out  at  the  end, 
and  dips  in  the  mercury  ;  the  cistern  and  the  tube  are  connected  by  a  piece 
of  buckskin  ce,  which  is  firmly  tied  at  c  to  a  contraction  in  the  tube,  and  at  e 
to  a  brass  tubulure  in  the  cover  of  the  cistern.  This  mode  of  closing 
prevents  the  mercury  from  escaping  when  the  barometer  is  inverted,  while 
the  pores  of  the  leather  transmit  the  atmospheric  pressure.  The  bottom  of 
the  cylinder  b  is  cemented  on  a  box-wood  cylinder  zz,  on  a  contraction  in 
which,  z'/,  is  firmly  tied  the  buckskin  mn,  which  forms  the  base  of  the  cistern. 
On  this  skin  is  fastened  a  wooden  button  ;r,  which  rests  against  the  end  of 
a  screw  C.  According  as  this  is  turned  in  one  direction  or  the  other,  the 
skin  mn  is  raised  or  lowered,  and  with  it  the  mercury.  In  using  this  baro- 


128  On  Gases.  [160- 

meter  the  mercury  is  first  made  exactly  level  with  the  point  <2,  which  is 
effected  by  turning  the  screw  C  either  in  one  direction  or  the  other.  The 
graduation  of  the  scale  is  counted  from  this  point  #,  and  thus  the  distance 
of  the  top  B  of  the  column  of  mercury  from  a  gives  the  height  of  the 
barometer.  The  bottom  of  the  cistern  is  surrounded  by  a  brass  case,  which 
is  fastened  to  the  cover  M  by  screws,  k,  k,  k.  We  have  already  seen  (159) 
the  importance  of  having  the  barometer  quite  vertical,  which  is  effected  by 
the  following  plan,  known  as  Cardan's  suspension. 

The  metal  case  containing  the  barometer  is  filled  in  a  copper  sheath  X 
by  two  screws  a  and  b  (fig.  1 30).     This  is  provided  with  two  axles  (only  one 


Fig.  129. 


Fig.  130. 


of  which,  0,  is  seen  in  the  figure),  which  turn  freely  in  two  holes  in  a  ring  Y. 
In  a  direction  at  right  angles  to  that  of  the  axles,  00,  the  ring  has  also  two 
similar  axles,  m  and  /z,  resting  on  a  support  Z.  By  means  of  this  double 
suspension,  the  barometer  can  oscillate  freely  about  the  axes,  mn  and  00,  in 
two  directions  at  right  angles  to  each  other.  But  as  care  is  taken  that  the 
point  at  which  these  axes  cross  corresponds  to  the  tube  itself,  the  centre  of 
gravity  of  the  system,  which  must  always  be  lower  than  the  axis  of  suspen- 
sion, is  below  the  point  of  intersection,  and  the  barometer  is  then  perfectly 
vertical. 


-161] 


Barometers. 


129 


161,  Gay-Xittssac's  syphon  barometer. — The  syphon  barometer  is  a 
bent  glass  tube,  one  of  the  branches  of  which  is  much  longer  than  the  other. 
The  longer  branch,  which  is  closed  at  the  top,  is  filled  with  mercury  as  in 
the  cistern  barometer,  while  the  shorter  branch,  which  is  open,  serves  as  a 
cistern.  The  difference  between  the  two  levels  is  the  height  of  the  barometer. 

Fig.  131  represents  the  syphon  barometer  as  modified  by  Gay-Lussac. 
In  order  to  render  it  more  available  for  travelling  by  preventing  the  entrance 
of  air,  he  joined  the  two  branches  by  a  capillary  tube  (fig.  132) ;  when  the 


Fig.  131. 


Fig.  132. 


Fig.  133. 


Fig.  134- 


instrument  is  inverted  (fig.  133)  the  tube  always  remains  full  in  virtue  of  its 
capillarity,  and  air  cannot  penetrate  into  the  longer  branch.  A  sudden  shock, 
however,  might  separate  the  mercury  and  admit  some  air.  To  avoid  this, 
M.  Bunten  has  introduced  an  ingenious  modification  into  the  apparatus. 
The  longer  branch  is  drawn  out  to  a  fine  point,  and  is  joined  to  a  tube  B  of 

03 


130  On  Gases.  [161- 

the  form  represented  in  fig.  134.  By  this  arrangement,  if  air  passes  through 
the  capillary  tube  it  cannot  penetrate  the  drawn-out  extremity  of  the  longer 
branch,  but  lodges  in  the  upper  part  of  the  enlargement  B.  In  this  position 
it  does  not  affect  the  observations,  since  the  vacuum  is  always  at  the  upper 
part  of  the  tube  ;  it  is,  moreover,  easily  removed. 

In  Gay-Lussac's  barometer  the  shorter  branch  is  closed,  but  there  is  a 
capillary  aperture  in  the  side  z,  through  which  the  atmospheric  pressure  is 
transmitted. 

The  barometric  height  is  determined  by  means  of  two  scales,  which  have 
a  common  zero  at  O,  towards  the  middle  of  the  longer  branch,  and  are 
graduated  in  contrary  directions,  the  one  from  O  to  E,  and  the  other  from  O 
to  B,  either  on  the  tube  itself,  or  on  brass  rules  fixed  parallel  to  the  tube. 
Two  sliding  verniers,  m  and  ;/,  indicate  tenths  of  a  millimetre.  The  total 
height  of  the  barometer,  AB,  is  the  sum  of  the  distances  from  O  to  A  and 
from  O  to  B. 

162.  Precautions  in  reference  to  barometers. — In  constructing  baro- 
meters, mercury  is  chosen  in  preference  to  any  other  liquid.  For  being  the 
densest  of  all  liquids,  it  stands  at  the  least  height.  When  the  mercurial 
barometer  stands  at  30  inches,  the  water  barometer  would  stand  at  about 
34  feet  (159).  It  also  deserves  preference  because  it  does  not  moisten  the 
glass.  It  is  necessary  that  the  mercury  be  pure  and  free  from  oxide,  other- 
wise it  adheres  to  the  glass  and  tarnishes  it.  Moreover,  if  it  is  impure  its 
density  is  changed,  and  the  height  of  the  barometer  is  too  great  or  too  small. 
Mercury  is  purified,  before  being  used  for  barometers,  by  treatment  with 
dilute  nitric  acid,  and  by  distillation. 

The  space  at  the  top  of  the  tube  (figs.  126  and  131),  which  is  called  the 
Torricellian  vacuum,  must  be  quite  free  from  air  and  from  aqueous  vapour, 
for  otherwise  either  would  depress  the  mercurial  column  by  its  elastic  force. 
To  obtain  this  result,  a  small  quantity  of  pure  mercury  is  placed  in  the  tube 
and  boiled  for  some  time.  It  is  then  allowed  to  cool,  and  a  further  quantity, 
previously  warmed,  added,  which  is  boiled,  and  so  on,  until  the  tube  is  quite 
full ;  in  this  manner  the  moisture  and  the  air  which  adhere  to  the  sides  of  the 
tube"  (144)  pass  off  with  the  mercurial  vapour.  A  barometer  tube  should  not 
be  too  narrow,  for  otherwise  the  mercury  is  moved  with  difficulty  ;  and  before 
reading  off,  the  barometer  should  be  tapped  so  as  to  get  rid  of  the  adhesion 
to  the  glass. 

A  barometer  is  free  from  air  and  moisture  if,  when  it  is  inclined,  the 
mercury  strikes  with  a  sharp  metallic  sound  against  the  top 
of  the  tube.  If  there  is  air  or  moisture  in  it,  the  sound  is 
deadened. 

163.  Correction  for  capillarity. — In  cistern  barometers 
\6  there  is  always  a  certain  depression  of  the  mercurial  column 
due  to  capillarity,  unless  the  internal  diameter  of  the  tube 
exceeds  O'8  inch.  To  make  the  correction  due  to  this 
depression,  it  is  not  enough  to  know  the  diameter  of  the 
tube  ;  we  must  also  know  the  height  of  the  meniscus  od  (fig. 
135))  which  varies  according  as  the  meniscus  has  been 
formed  during  an  ascending  or  descending  motion  of  the  mercury  in  the 
tube.  Consequently  the  height  of  the  meniscus  must  be  determined  by 


-165]  Barometers.  131 

bringing  the  pointer  to  the  level  ab,  and  then  to  the  level  d,  when  the  differ- 
ence of  the  readings  will  give  the  height  od  required.  These  two  terms — 
namely,  the  internal  diameter  of  the  tube  and  the  height  of  the  meniscus — 
being  known,  the  resulting  correction  can  be  taken  out  of  the  following  table  : 


Internal 

Height  of  Sagitta  of  Meniscus  in  inches 

inches 

O'OIO 

o'ois 

O'O2O 

0*025 

0*030 

0-035 

0*040 

0-157 

0-0293 

0-043I 

0-0555 

0-0677 

0-0780 

0-0870 

0-0948 

0-236 

O-OIIQ 

0-OI76 

0-023I 

0-0294 

0-0342 

0-0398 

0-0432 

0-315 

0-0000 

0-0088 

O'OIlS 

0-0144 

0-0175 

0-0196 

0-0221 

Q'394 

0-0039 

0*0048 

0-0063 

0-0078 

0-0095 

O'OIIO 

0-OI25 

0-472 

0-0020 

0-0029 

0-0036 

0-0045 

0-0053 

0-0063 

0-0073 

0-550 

o-oo  10 

0-0017 

0-0024 

0-0029 

0-0034 

0-0039 

0-0044 

In  Gay-Lussac's  barometer  the  two  tubes  are  made  of  the  same  diameter, 
so  that  the  error  caused  by  the  depression  in  the  one  tube  very  nearly  cor- 
rects that  caused  by  the  depression  in  the  other.  As,  however,  the  meniscus 
in  the  one  tube  is  formed  by  a  column  of  mercury  with  an  ascending  motion, 
while  that  in  the  other  is  formed  by  a  column  with  a  descending  motion,  their 
heights  will  not  be  the  same,  and  the  reciprocal  correction  will  not  be  quite 
exact. 

164.  Correction  for  temperature. — In  all  observations  with  barometers, 
whatever  be  their  construction,  a  correction  must  be  made  for  temperature. 
Mercury   contracts   and   expands   with    different    temperatures ;    hence   its 
density  changes,  and  consequently  the  barometric  height,  for  this  height  is 
inversely  as  the  density  of  the  mercury,  so  that  for  different  atmospheric 
pressures  the  mercurial  column  might  have  the  same  height.     Accordingly, 
in  each  observation,  the  height  observed  must  be  reduced  to  a  determinate 
temperature.     The  choice  of  this  is  quite  arbitrary,  but  that  of  melting  ice  is 
in  practice  always  adopted.     It  will  be  seen,  in  the  Book  on  Heat,  how  this 
correction  is  made. 

165.  Variations  in  the  height  of  the  barometer. — When  the  barometer 
is  observed  for  several  days,  its  height  is  found  to  vary  in  the  same  place, 
not  only  from  one  day  to  another,  but  also  during  the  same  day. 

The  extent  of  these  variations — that  is,  the  difference  between  the  greatest 
and  the  least  height — is  different  in  different  places.  It  increases  from  the 
equator  towards  the  poles.  Except  under  extraordinary  circumstances,  the 
greatest  variations  do  not  exceed  six  millimetres  under  the  equator,  30  under 
the  tropic  of  Cancer,  40  in  France,  and  60  at  25  degrees  from  the  pole.  The 
greatest  variations  are  observed  in  winter. 

The  mean  daily  height  is  the  height  obtained  by  dividing  the  sum  of  24 
successive  hourly  observations  by  24.  In  our  latitudes  the  barometric  height 
at  noon  corresponds  to  the  mean  daily  height. 

The  mean  monthly  height  is  obtained  by  adding  together  the  mean  daily 
heights  for  a  month,  and  dividing  by  30.  The  mean  yearly  height  is  simi- 
larly obtained. 


132  On  Gases,  [165- 

Under  the  equator,  the  mean  annual  height  at  the  level  of  the  sea  is 
om758,  or  29-84  inches.  It  increases  from  the  equator,  and  between  the 
latitudes  30°  and  40°  it  attains  a  maximum  of  om763,  or  30*04  inches.  In 
lower  latitudes  it  decreases,  and  in  Paris  it  does  not  exceed  om7568. 

The  general  mean  at  the  level  of  the  sea  is  om76i,  or  29-96  inches. 

The  mean  monthly  height  is  greater  in  winter  than  in  summer,  in  conse- 
quence of  the  cooler  atmosphere. 

Two  kinds  of  variations  are  observed  in  the  barometer  : — 1st,  the  acci- 
dental variations,  which  present  no  regularity  ;  they  depend  on  the  seasons, 
the  direction  of  the  winds,  and  the  geographical  position,  and  are  common 
in  our  climates  ;  2nd,  the  daily  variations,  which  are  produced  periodically 
at  certain  hours  of  the  day. 

At  the  equator,  and  between  the  tropics,  no  accidental  variations  are 
observed ;  but  the  daily  variations  take  place  with  such  regularity  that  a 
barometer  may  serve  to  a  certain  extent  as  a  clock.  The  barometer  sinks 
from  midday  till  towards  four  o'clock  ;  it  then  rises,  and  reaches  its  maximum 
at  about  ten  o'clock  in  the  evening.  It  then  again  sinks,  and  reaches  a 
second  minimum  towards  four  o'clock  in  the  morning,  and  a  second  maxi- 
mum at  ten  o'clock. 

In  the  temperate  zones  there  are  also  daily  variations,  but  they  are 
detected  with  difficulty,  since  they  occur  in  conjunction  with  accidental 
variations. 

The  hours  of  the  maxima  and  minima  appear  to  be  the  same  in  all 
climates,  whatever  be  the  latitude  ;  they  merely  vary  a  little  with  the  seasons. 

166.  Causes  of  barometric  variations. — It  is  observed  that  the  course 
of  the  barometer  is  generally  in  the  opposite  direction  to  that  of  the  thermo- 
meter ;  that  is,  that  when  the  temperature  rises  the  barometer  falls,  and  vice 
versa  ;  which  indicates  that  the  barometric  variations  at  any  given  place  are 
produced  by  the  expansion  or  contraction  of  the  air,  and  therefore  by  its 
change  in  density.     If  the  temperature  were  the  same  throughout  the  whole 
extent  of  the  atmosphere,  no  currents  would  be  produced,  and,  at  the  same 
height,  atmospheric  pressure  would  be  everywhere  the  same.    But  when  any 
portion  of  the  atmosphere  becomes  warmer  than  the  neighbouring  parts,  its 
specific  gravity  is  diminished,  and  it  rises  and  passes   away  through  the 
upper  regions  of  the  atmosphere,  whence  it  follows  that  the  pressure  is 
diminished,   and  the  barometer  falls.     If  any  portion    of  the  atmosphere 
retains  its  temperature,  while  the  neighbouring  parts  become  cooler,  the  same 
effect  is  produced  ;  for  in  this  case,  too,  the  density  of  the  first-mentioned 
portion  is  less  than  that  of  the  others.     Hence,  also,  it  usually  happens  that 
an  extraordinary  fall  of  the  barometer  at  one  place  is  counterbalanced  by  an 
extraordinary  rise  at  another  place.     The  daily  variations  appear  to  result 
from  the  expansions  and  contractions  which  are  periodically  produced  in 
the  atmosphere  by  the  heat  of  the  sun  during  the  rotation  of  the  earth. 

167.  Relation  of  barometric  variations  to  tbe  state  of  the  weather. — 
It  has  been  observed  that,  in  our  climate,  the  barometer  in  fine  weather  is 
generally  above  30  inches,  and  is  below  this  point  when  there  is  rain,  snow, 
wind,  or  storm,  and  also,  that  for  any  given  number  of  days  at  which  the 
barometer  stands  at  30  inches,  there  are  as  many  fine  as  rainy  days.     From 
this  coincidence  between  the  height  of  the  barometer  and  the  state  of  the 


-168]  Barometers.  133 

weather,  the  following  indications  have  been  marked  on  the  barometer, 
counting  by  thirds  of  an  inch  above  and  below  30  inches  : — 

Height  State  of  the  weather 

31  inches  ....  Very  dry. 

3o|  „     .  .  .  .  .  Settled  weather. 

3o|  „  .  .  .  .  Fine  weather. 

30  „.  .  .  .  .  Variable. 

29!  „  .  .  .  .  Rain  or  wind. 

29^  „     .  .  .  .  .  Much  rain. 

29  „.  .  .  .  .  Tempest. 

In  using  the  barometer  as  an  indicator  of  the  state  of  the  weather,  we 
must  not  forget  that  it  really  only  serves  to  measure  the  weight  of  the  atmo- 
sphere, and  that  it  only  rises  or  falls  as  the  weight  increases  or  diminishes  ; 
and  although  a  change  of  weather  frequently  coincides  with  a  change  in  the 
pressure,  they  are  not  necessarily  connected.  This  coincidence  arises  from 
meteorological  conditions  peculiar  to  our  climate,  and  does  not  always  occur. 
That  a  fall  in  the  barometer  usually  precedes  rain  in  our  latitudes,  is  caused 
by  the  position  of  Europe.  The  south-west  winds,  which  are  hot  and  conse- 
quently light,  make  the  barometer  sink  ;  but  at  the  same  time,  as  they  become 
charged  with  aqueous  vapour  in  crossing  the  ocean,  they  bring  us  rain.  The 
winds  of  the  north  and  north-east,  on  the  contrary,  being  colder  and  denser, 
make  the  barometer  rise ;  and  as  they  only  reach  us  after  having  passed 
over  vast  continents,  they  are  generally  dry. 

When  the  barometer  rises  or  sinks  slowly,  that  is,  for  two  or  three  days, 
towards  fine  weather  or  towards  rain,  it  has  been  found  from  a  great  number 
of  observations  that  the  indications  are  then  extremely  probable.  Sudden 
variations  in  either  direction  indicate  bad  weather  or  wind. 

1 68.  Wheel  barometer. — The  wheel  barometer,  which  was  invented  by 
Hooke,  is  a  syphon  barometer,  and  is  especially  intended  to  indicate  good 
and  bad  weather  (fig.  136).  In  the  shorter  leg  of  the  syphon  there  is  a  float 
which  rises  and  falls  with  the  mercury  (fig.  137).  A  string  attached  to  this 
float  passes  round  a  pulley,  O,  and  at  the  other  end  there  is  a  weight,  P, 
somewhat  lighter  than  the  float.  A  needle  fixed  to  the  pulley  moves  round 
a  graduated  circle,  on  which  is  marked  variable,  rain,  fine  weather,  &c. 
When  the  pressure  varies  the  float  sinks  or  rises,  and  moves  the  needle 
round  to  the  corresponding  points  on  the  scale. 

The  barometers  ordinarily  met  with  in  houses,  and  which  are  called 
weather  glasses,  are  of  this  kind.  They  are,  however,  of  little  use,  for  two 
reasons.  The  first  is,,  that  they  are  neither  very  delicate  nor  very  accurate 
in  their  indications.  The  second,  which  applies  equally  to  all  barometers, 
is  that  those  commonly  in  use  in  this  country  are  made  in  London,  and  the 
indications,  if  they  are  of  any  value,  are  only  so  for  a  place  of  the  same  level 
and  of  the  same  climatic  conditions  as  London.  Thus  a  barometer  standing 
at  a  certain  height  in  London  would  indicate  a  certain  state  of  weather,  but 
if  removed  to  Shooter's  Hill  it  would  stand  half  an  inch  lower,  and  would 
indicate  a  different  state  of  weather.  As  the  pressure  differs  with  the  level 
and  with  geographical  conditions,  it  is  necessary  to  take  these  into  account 
if  exact  data  are  wanted. 


134 


On  Gases. 


[169 


169.  Fixed  barometer. — For  accurate  observations  Regnault  uses  a 
barometer  the  height  of  which  he  measures  by  means  of  a  cathetometer  (89). 
The  cistern  (fig.  138)  is  of  cast  iron  ;  against  the  frame  on  which  it  is  sup- 
ported a  screw  is  fitted,  which  is  pointed  at  both  ends,  and  the  length  of 
which  has  been  determined,  once  for  all,  by  the  cathetometer.  To  measure 
the  barometric  height,  the  screw  is  turned  until  its  point  grazes  the  surface 


Fig.  136 


Fig.  137- 


Fig.  138. 


of  the  mercury  in  the  bath,  which  is  the  case  when  the  point  and  its  image 
are  in  contact.  The  distance  then  from  the  top  of  the  point  to  the  level  of 
the  mercury  in  the  tube  b  is  measured  by  the  cathetometer,  and  this,  together 
with  the  length  of  the  screw,  gives  the  barometric  height  with  great  accuracy. 
This  barometer  has  moreover  the  advantage  that,  as  a  tube  an  inch  in  dia- 
meter may  be  used,  the  influence  of  capillarity  becomes  inappreciable.  Its 
construction,  moreover,  is  very  simple,  and  the  position  of  the  scale  leads  to 
no  kind  of  error,  since  this  is  transferred  to  the  cathetometer.  Unfortunately 
the  latter  instrument  requires  great  accuracy  in  its  construction,  and  is  very 
expensive. 


-171] 


HuygJiens  Barometer. 


135 


170.  Glycerine  barometer.  —  Jordan   has  recently  constructed  a  baro- 
meter in  which  the  liquid  used  is  pure  glycerine.     This  has  the  specific 
gravity  1*26,  and  therefore  the  length  of  the  column  of  liquid  is  rather  more 
than  ten  times  that  of  mercury  ;  hence  small  alterations  in  the  atmospheric 
.pressure  produce  considerable  oscillations  in  the  height  of  the  liquid.     The 
tube   consists   of  ordinary   composition   gas  tubing  about  §  of  an  inch  in 
diameter  and  28  feet  or  so  in  length  ;  the  lower  end  is  open  and  dips  in  the 
cistern,  which  may  be  placed  in  a  cellar  ;  the  top  is  sealed  to  a  closed  glass 
tube  an  inch  in  diameter,  in  which  the  fluctuations  of  the  column  are  ob- 
served.    This  may  be  arranged  in  an  upper  storey,  and  the  tubing,  being 
easily  bent,  lends  itself  to  any  adjustment  which  the  locality  requires. 

The  vapour  of  glycerine  has  very  low  tension  at  ordinary  temperatures, 
and  is  therefore  not  so  exposed  to  such  back  pressures,  varying  with  the 
temperature,  as  is  water.  On  the  other  hand,  it  readily  attracts  moisture 
from  the  air,  whereby  the  density  and  therewith  the  height  of  the  liquid 
column  vary.  This  is  prevented  by  covering  the  liquid  in  the  cistern  with 
a  layer  of  paraffine  oil. 

171.  Huygrhens'  barometer.  —  The  desire  to  amplify  the  small  variations 
which  take  place  in  the  barometer  has  led  to  a  number  of  contrivances,  one  of  the 
best  known  of  which  was  invented  by  Huyghens  (fig.  139.) 

The  barometer  tube  a  is  wider  at  the  closed  end  b, 
and  also  at  c,  where  a  liquid  of  smaller  specific  gravity 
than  mercury,  such  as  coloured  water,  is  poured  on  the 
mercury  ;  it  fills  the  rest  of  the  tube  c  and  a  portion  of  d. 

Suppose  b  and  c  to  have  the  same  diameter,  which  is  n 
times  that  of  d.  When  the  column  of  mercury  in  b  sinks 
through  x  millimetres,  the  level  of  the  mercury  in  c  rises 
just  as  much,  while  the  coloured  liquid  rises  nx  milli- 
metres, and  therefore  its  level  is  (»-i)  x  millimetres 
higher.  A  column  of  this  liquid  (n  —  i)  x  in  height,  has 

the  same  pressure  as  a  column  of  mercury-  —  —  —  *  in 

height  where  s  is  the  number  expressing  the  ratio  of 
the  specific  gravities  of  mercury  and  the  liquid. 

When  therefore  the  mercury  in  b  sinks  x  millimetres, 


is  the  height  of  the  column  of  mercury  which  corresponds  to 
the  decrease  of  atmospheric  pressure.     From  this  we  have 


2  s  +  n  — 


Thus,  if  the  section  of  the  tubes  b  and  c  is  20  times  that 
of  d,  and  if  the  coloured  liquid  be  water,  we  have 


Fig-  139- 


=  0- 


27'2  +  20-I      46-2 

When,  therefore,  an  ordinary  barometer  sinks  through  y  millimetres,  the 


136  On  Gases.  [171- 

mercury  in  b  sinks  0*294^  millimetres,  while  the  coloured  liquid  rises 
20  x  o'294_y  =  5-88y.  Whenever,  that  is,  an  ordinary  barometer  sinks  or  rises 
i  millimetre,  the  coloured  liquid  rises  or  sinks  5-98  millimetres,  or  nearly 
six  times  as  much. 

Such  barometers  are  useful  in  cases  where  the  variations  in  the  height 
of  the  barometer,  rather  than  its  actual  height,  are  to  be  observed.  The 
scale  should  be  placed  behind  the  tube  d  and  two  points  fixed,  near  the  top 
and  bottom,  by  comparison  with  standard  barometers  ;  the  interval  between 
the  two  is  then  suitably  divided. 

172.  Determination  of  heights  by  the  barometer.- Since  the  atmo- 
spheric pressure  decreases  as  we  ascend,  it  is  obvious  that  the  barometer 
will  keep  on  falling  as  it  is  taken  to  a  greater  and  greater  height.  On  this 
depends  a  method  of  determining  the  difference  between  the  heights  of  two 
stations,  such  as  the  base  and  summit  of  a  mountain.  The  method  may  be 
explained  as  follows. 

It  will  be  seen  in  the  next  chapter  that,  according  to  Boyle's  law,  if  the 
temperature  of  an  enclosed  portion  of  air  continues  constant,  its  volume  will 
vary  inversely  as  the  pressure  ;  that  is  to  say,  if  we  double  the  pressure  we 
shall  halve  the  volume.     But  if  we  halve  the  volume  we  manifestly 
T7*    double  the  quantity  of  air  in  each  cubic  inch— that  is  to  say,  we  double 
the  density  of  the  air  ;  and  so  on  in  any  proportion.     Consequently 
the  law  is  equivalent  to  this  : — That  for  a  constant  temperature  the 
density  of  air  is  proportional  to  the  pressure  which  it  sustains. 

Now  suppose  A  and  B  (fig.  140)  to  represent  two  stations,  and  that 
it  is  required  to  determine  the  vertical  height  of  B  above  A,  it  being 
borne  in  mind  that  A  and  B  are  not  necessarily  in  the  same  vertical 
line.  Take  P,  any  point  in  AB,  and  Q,  a  point  at  a  small  distance 
above  P.  Suppose  the  pressure  on  a  square  inch  of  the  atmosphere 
at  P  to  be  denoted  by^,  and  at  Q  let  it  be  diminished  by  a  quantity 
denoted  by  dp.  It  is  clear  that  this  diminution  equals  the  weight  of 
the  column  of  air  between  P  and  Q,  whose  section  is  one  square  inch. 
^1  But,  since  the  density  of  the  air  is  directly  proportional  to  p,  the 
Fig.  i4o.weU>kt  °f  a  cubic  inch  of  air  will  equal  kgp,  where  k  denotes  a 
certain  quantity  to  be  determined  presently,  and  g  the  accelerating 
force  of  gravity  (80).  Hence,  if  we  denote  PQ  in  inches  by  dx,  the  pressure 
will  be  diminished  by  kpg .  dx,  and  we  may  represent  this  algebraically  by' 
the  equation 

kpg  .  dx  =  dp. 

By  a  certain  algebraical  process  this  leads  to  the  conclusion  that 


ri 

where  X  denotes  the  height  of  AB,  and  P  and  P.,  the  atmospheric  pressures 
at  A  and  B  respectively,  the  logarithms  being  what  are  called  '  Napierian 
logarithms.'  Now,  if  H  and  Hj  are  the  heights  of  the  barometer  at  A  and 
B  respectively,  the  temperature  of  the  mercury  being  the  same  at  both  sta- 
tions, their  ratio  equals  that  of  P  to  P1}  and  therefore 


-172]  Determination  of  Heights  by  the  Barometer.  137 

It  remains  to  determine  k  and  g. 

(i)  Since  the  force  of  gravity  is  different  for  places  in  different  latitudes, 
g  will  depend  upon  the  latitude  (83).  It  is  found  that  if  g  is  the  accelerating 
force  of  gravity  in  latitude  $,  and/  that  force  in  latitude  45°,  then 


I  +0-00256  COS  2  0 

where/has  a  definite  numerical  value. 

(2)  From  what  has  been  stated  above  it  will  be  seen,  that  if  p  is  the 
density  of  air  at  a  temperature  of  /°  C.,  under  Q,  the  pressure  exerted  by 
29-92  inches  of  mercury,  we  shall  have 


But  it  will  be  afterwards  shown  that  if  p0  is  the  density  of  air  under  the  same 
pressure  O  at  o°  C.,  we  shall  have 


i+at 

where  a  represents  the  coefficient  of  expansion  of  gases.     Therefore 

^Q_    Pn 
i  +  at 

Now  if  a-  is  the  density  of  mercury,  and  if  the  latitude  is  45°,  we  shall 
have 

0  =  29-92.  a/; 
and  therefore 

£f-Pj)       I 

a-  '  29-92  (I  +  af) 

But  p0^-(r  is  the  ratio  which  the  density  of  dry  air  at  a  temperature  o°  C, 
in  latitude  45°,  under  a  pressure  of  29-92  inches  of  mercury,  bears  to  the 
density  of  mercury  at  o°  C.,  and  therefore  p0-*-<r  is  a  determinate  number. 
Substituting,  wre  have 

TT 

P  =  29-92  in.  .  — (i  +0-00256  cos  2$).  (i  +af)  log-—  . 
Po  Hi 

The  value  of  a  is  0-003665,  which  is  nearly  equal  to  3^5.  If  we  substitute 
the  proper  values  for  <r-*-p0,  and  change  the  logarithms  into  common  loga- 
rithms, and  instead  of  /  use  the  mean  of  T  and  T1?  the  temperatures  at  the 
upper  and  lower  stations,  it  will  be  found  that 

X  (in  feet)  =60346  (i  +  0*00256  cos  2<f>)     (i  +  Q — - — lA  log  — 

which  is  La  Place's  barometric  formula.  In  using  it,  we  must  remember 
that  T  and  Tx  are  temperatures  on  the  Centigrade  thermometer,  and  that  H 
and  Hj  are  the  heights  of  the  barometer  reduced  to  o°  C.  Thus  if  h  is  the 
measured  height  of  the  barometer  at  the  lower  station  we  have 


H  - > 

6500 

If  the  height  to  be  measured  is  not  great,  one  observer  is  enough.     For 
ater  heights  the  ascent  takes  some  time,  and  in  the  interval  the  pressure 


138  On  Gases.  [172- 

may  vary.  Consequently  in  this  case  there  must  be  two  observers,  one  at 
each  station,  who  make  simultaneous  observations. 

Let  us  take  the  following  example  of  the  above  formula  : — Suppose  that 
in  latitude  65°  N.  at  the  lower  of  the  two  stations  the  height  of  the  barometer 
were  30*025  inches,  and  the  temperature  of  air  and  mercury  I7°'32  C.,  while 
at  the  upper  the  height  of  the  barometer  was  23-230  inches,  and  the  tempera- 
ture of  air  and  mercury  was  io°'55  C.  Determine  the  height  of  the  upper 
station  above  the  lower. 

(i)  Find  H  and  H1  :  viz. 


30-025  (  l~-z-^ -  J  =29'945 
28-230  (r-^fU  28-184. 


TT 

Hence  log  -  -  «.  1-4763243  —  1-4500026  =  0-0263217. 

(2)  Find  i+2CI     -Tl)  viz.  1-05574. 

(3)  Find  i +0-00256  cos  20. 

Since  0*00256  cos  130°=  —0*00256  cos  50°=  —0*001645 

therefore  i  +0*00256  cos  20  =  —  o-998355. 

Hence  the  required  height  in  feet  equals 

60346  x  0-998355  x  1-05574  x  0-00632 17=  1674 
It  may  be  easily  proved  that  if  H  and  Hl  do  not  greatly  differ,  the 

TT  TT   TT 

Napierian  logarithm  of  -—  equals  2    -      -A     If  for  instance  H  equals  30 
H  j  rl  +  rl  j 

inches,  and  Hx  equals  29  inches,  the  resulting  error  would  not  exceed  the 
50*00  Par*  °f  ^e  whole.  Accordingly  for  heights  not  exceeding  2000  ft.  we 
may  without  much  error  use  the  formula, 


173.  Ruhlmann's  observations. — The  results  obtained  for  the  differen 
in  height  of  places  by  using  the  above  formula  often  differ  from  the  true 
heights  as  measured  trigonometrically,  to  an  extent  which  cannot  be  as- 
cribed to  errors  in  observation.  The  numbers  thus  found  for  the  heights 
of  places  are  influenced  by  the  time  of  day,  and  also  by  the  season  of  year, 
at  which  they  are  made.  Ruhlmann  has  investigated  the  cause  of  this  dis- 
crepancy by  a  series  of  direct  barometric  and  thermometric  observations 
made  at  two  different  stations  in  Saxony,  and  also  by  a  comparison  of  the 
continuous  series  of  observations  made  at  Geneva  and  on  the  St.  Bernard. 

Ruhlmann  has  ascertained  thus  that  the  cause  of  the  discrepancy  is  to  be 
found  in  the  fact  that  the  mean  of  the  temperatures  indicated  by  the  ther- 
mometer at  the  two  stations  is  not  an  accurate  measure  of  the  actual  mean 
temperature  of  the  column  of  air  between  the  two  stations,  a  condition 
which  is  assumed  in  the  above  formula.  The  variations  in  the  temperature 


. 

in- 


-173]  RitJilinanns  Observations.  139 

of  the  column  of  air  are  not  of  the  same  extent  as  those  indicated  by  the 
thermometer,  nor  do  they  follow  them  so  rapidly  ;  they  drag  after  them  as  it 
were.  If  the  mean  monthly  temperatures  at  the  two  fixed  stations  are 
introduced  into  the  formula,  they  give  in  winter  heights  which  are  somewhat 
too  low,  and  in  summer  such  as  are  too  high.  The  results  obtained  by 
introducing  the  mean  yearly  temperature  of  the  two  stations  are  very  near 
the  true  ones. 

This  influence  of  temperature  is  most  perceptible  in  individual  obser- 
vations of  low  heights.  Thus,  using  the  observed  temperatures  in  the 
barometric  formula,  the  error  in  height  of  the  Uetliberg  above  Zurich  (about 
1,700  feet)  was  found  to  be  5\-  of  the  total,  while  the  height  of  the  St.  Bernard 
above  Geneva  was  found  within  T|g  of  the  true  height. 

The  reason  the  thermometers  do  not  indicate  the  true  temperature  of  the 
air  is  undoubtedly  that  they  are  too  much  influenced  by  radiation  from  the 
earth  and  surrounding  bodies.  The  earth  is  highly  absorbent,  and  becomes 
rapidly  heated  under  the  influence  of  the  sun's  rays,  and  becomes  as  rapidly 
cooled  at  night  ;  the  air,  as  a  very  diathermanous  body,  is  but  little  heated 
by  the  sun's  rays,  and  on  the  contrary  is  little  cooled  by  radiation  during  the 
night. 


140  On  Cases.  [174- 


CHAPTER   II. 

MEASUREMENT   OF  THE   ELASTIC   FORCE   OF   GASES. 

174.  Boyle's  law. — The  law  of  the  compressibility  of  gases  was  dis- 
covered by  Boyle  in  1662,  and  afterwards  independently  by  Mariottein  1679. 
It  is  in  England  commonly  called  '  Boyle's  law,'  and,  on  the  Continent, 
'  Mariotte's  law'.'  It  is  as  follows  : — 

The  temperature  remaining  the  same,  the  volume  of  a  given  qtiantity  of 
gas  is  inversely  as  the  pressure  which  it  bears. 

This  law  may  be  verified  by  means  of  an  apparatus  devised  by  Boyle 
(fig.  141).  It  consists  of  a  long  glass  tube  fixed  to  a  vertical  support  ;  it  is 
open  at  the  upper  part,  and  the  other  end,  which  is  bent  into  a  short  vertical 
leg,  is  closed.  On  the  shorter  leg  there  is  a  scale,  which  indicates  equal 
capacities  ;  the  scale  against  the  long  leg  gives  the  heights.  The  zero  of 
both  scales  is  in  the  same  horizontal  line. 

A  small  quantity  of  mercury  is  poured  into  the  tube,  so  that  its  level  in  : 
both  branches  is  at  zero,  which  is  effected  without  much  difficulty  after  a  few 
trials  (fig.  141).  The  air  in  the  short  leg  is  thus  under  the  ordinary  atmo- 
spheric pressure  which  is  exerted  through  the  open  tube.  Mercury  is  then 
poured  into  the  longer  tube  until  the  volume  of  the  air  in  the  smaller  tube  is 
reduced  to  one-half;  that  is,  until  it  is  reduced  from  10  to  5,  as  shown  in 
fig.  142.  If  the  height  of  the  mercurial  column,  CA,  be  measured,  it  will  be 
found  exactly  equal  to  the  height  of  the  barometer  at  the  time  of  the  experi- 
ment. The  pressure  of  the  column  CA  is  therefore  equal  to  an  atmosphere 
which,  with  the  atmospheric  pressure  acting  on  the  surface  of  the  column  at 
C,  makes  two  atmospheres.  Accordingly,  by  doubling  the  pressure,  the 
volume  of  the  gas  has  been  diminished  to  one-half. 

If  mercury  be  poured  into  the  longer  branch  until  the  volume  of  the 
air  is  reduced  to  one-third  its  original  volume,  it  will  be  found  that  the 
distance  between  the  level  of  the  two  tubes  is  equal  to  two  barometric 
columns.  The  pressure  is  now  three  atmospheres,  while  the  volume  is 
reduced  to  one-third.  Dulong  and  Petit  have  verified  the  law  for  air  up  to 
27  atmospheres,  by  means  of  an  apparatus  analogous  to  that  which  has  been 
described. 

The  law  also  holds  good  in  the  case  of  pressures  of  less  than  one  at- 
mosphere. To  establish  this,  mercury  is  poured  into  a  graduated  tube  until 
it  is  about  two-thirds  full,  the  rest  being  air.  It  is  then  inverted  in  a  deep 
trough  M  containing  mercury  (fig.  143),  and  lowered  until  the  levels  of  the 
mercury  inside  and  outside  the  tube  are  the  same,  and  the  volume  AB  noted. 
The  tube  is  then  raised,  as  represented  in  the  figure,  until  the  volume  of  air, 
AC,  is  double  that  of  AB  (fig.  144).  The  height  of  the  mercury  in  the  tube 


-174] 


Boyle's  Law. 


141 


above  the  mercury  in  the  trough,  CD,  is  then  found  to  be  exactly  half  the 
height  of  the  barometric  column.  The  air,  whose  volume  is  now  doubled,  is 
now  only  under  the  pressure  of  half  an  atmosphere ;  for  it  is  the  elastic 
force  of  this  air  which,  added  to  the  weight  of  the  column  CD,  is  equivalent 
to  the  atmospheric  pressure.  Hence  the  volume  is  inversely  as  the  pressure. 
In  the  experiment  with  Mariotte's  tube,  as  the  quantity  of  air  remains  the 
same,  its  density  must  obviously  increase  as  its  volume  diminishes,  and  vice 


Fig.  141. 


Fig.  142. 


Fig.  143.         Fig.  144. 


versa.  The  law  may  thus  be  enunciated  :  '  For  the  same  temperature  the 
density  of  a  gas  is  proportional  to  its  pressure?  Hence  as  water  is  773 
times  as  heavy  as  air,  under  a  pressure  of  773  atmospheres,  air  would  be  as 
dense  as  water. 

Boyle's  law  must  not  be  understood  to  mean  that  gases  of  equal  density 
have  equal  elastic  force  ;  different  gases  of  various  densities  have  the  same 
tension  when  they  are  under  the  same  pressure.  A  given  volume  of  hydrogen 
under  the  ordinary  atmospheric  pressure  has  the  same  elastic  force  as  the 
same  volume  of  air,  although  the  latter  is  14  times  as  heavy  as  the  former. 
Since,  for  the  same  volume,  there  are  the  same  number  of  atoms  in  all  gases, 


142 


On  Gases. 


[174- 


the  lighter  atoms  must  possess  a  greater  velocity  in  order  to  exert  the  same 
pressure  as  the  same  number  of  atoms  of  greater  mass. 

175.  Boyle's*  law  is  only  approximately  true. — Until  within  the  last 
few  years  Boyle's  law  was  supposed  to  be  absolutely  true  for  all  gases  at  all 

pressures,  but  Despretz 
obtained  results  incom 
patible  with  the  law.  He 
took  two  graduated  glass 
tubes  of  the  same  length, 
and  filled  one  with  air 
and  the  other  with  the 
gas  to  be  examined. 
These  tubes  were  placed 
in  the  same  mercury 
trough,  and  the  whole 
apparatus  immersed  in  a 
strong  glass  cylinder  filled 
with  water.  By  means 
of  a  piston  moved  by  a 
screw  which  worked  in  a 
cap  at  the  top  of  a  cylin- 
der, the  liquid  could  be 
subjected  to  an  increasing 
pressure,  and  it  could  be 
seen  whether  the  com- 
pression of  the  two  gases 
was  the  same  or  not.  The 
apparatus  resembled  that 
used  for  examining  the 
compressibility  of  liquids 
(fig.  63).  In  this  manner 
Despretz  found  that  car- 
bonic acid,  sulphuretted 
hydrogen,  ammonia,  and 
cyanogen  are  more  com- 
pressible than  air  :  hydro- 
gen, which  has  the  same 
compressibility  as  air  up  to  15  atmospheres,  is  then  less  compressible. 
From  these  experiments  it  was  concluded  that  the  law  of  Boyle  was  not 
general. 

In  some  experiments  on  the  elastic  force  of  vapours,  Dulong  and  Arago 
had  occasion  to  test  the  accuracy  of  Boyle's  law.  The  method  adopted  was 
exactly  that  of  Mariotte,  but  the  apparatus  had  gigantic  dimensions. 

The  gas  to  be  compressed  was  contained  in  a  strong  glass  tube,  GF  (fig. 
145),  about  six  feet  long  and  closed  at  the  top,  G.  The  pressure  was  pro- 
duced by  a  column  of  mercury,  which  could  be  increased  to  a  height  of  65 
feet,  contained  in  a  long  vertical  tube,  KL,  formed  of  a  number  of  tubes 
firmly  joined  by  good  screws,  so  as  to  be  perfectly  tight. 

The  tubes  KL  and  GF  were  hermetically  fixed  in  a  horizontal  iron  pipe 


: 


Fig-  145- 


-175]  Boyle's  Law.  143 

DE,  which  formed  part  of  a  mercurial  reservoir,  A.  On  the  top  of  this 
reservoir  there  was  a  force  pump,  BC,  by  which  mercury  could  be  forced 
into  the  apparatus. 

At  the  commencement  of  the  experiment,  the  volume  of  the  air  in  the 
manometer  (177)  was  observed,  and  the  initial  pressure  determined,  by 
adding  to  the  pressure  of  the  atmosphere  the  height  of  the  mercury  in  K 
above  its  level  in  H.  If  the  level  of  the  mercury  in  the  manometer  had 
been  above  the  level  in  KL,  it  would  have  been  necessary  to  subtract  tne 
difference. 

By  means  of  the  pump,  water  was  injected  into  A.  The  mercury  being 
then  pressed  by  the  water,  rose  in  the  tube  GF,  where  it  compressed  the 
air,  and  in  the  tube  KL,  where  it  rose  freely.  It  was  only  then  necessary 
to  measure  the  volume  of  the  air  in  GF  ;  the  height  of  the  mercury  in  KL 
above  the  level  in  GF,  together  with  the  pressure  of  the  atmosphere,  was 
the  total  pressure  to  which  the  gas  was  exposed.  These  were  all  the  elements 
necessary  for  comparing  different  volumes  and  the  corresponding  tempera- 
tures. The  tube  GF  was  kept  cold  during  the  experiment  by  a  stream  of 
cold  water. 

The  long  tube  was  attached  to  a  long  mast  by  means  of  staples.  The 
individual  tubes  were  supported  at  the  junction  by  cords,  which  passed 
round  pulleys  R  and  R',  and  were  kept  stretched  by  small  buckets,  P,  con- 
taining shot.  In  this  manner,  each  of  the  thirteen  tubes  having  been  sepa- 
rately counterpoised,  the  whole  column  was  perfectly  free  notwithstanding  its 
weight. 

Dulong  and  Arago  experimented  with  pressures  up  to  27  atmospheres, 
and  observed  that  the  volume  of  air  always  diminished  a  little  more  than  is 
required  by  Boyle's  law.  But  as  these  differences  were  very  small,  they  at- 
tributed them  to  errors  of  observation,  and  concluded  that  the  law  was  per- 
fectly exact,  at  any  rate  up  to  27  atmospheres. 

Regnault  investigated  the  same  subject  with  an  apparatus  resembling 
that  of  Dulong  and  Arago,  but  in  which  all  the  sources  of  error  were  taken 
into  account,  and  the  observations  made  with  remarkable  precision.  He  found 
that  air  does  not  exactly  follow  Boyle's  law,  but  experiences  a  greater  com- 
pressibility, which  increases  with  the  pressure  ;  so  that  the  difference  between 
the  calculated  and  the  observed  diminution  of  volume  is  greater  in  proportion 
as  the  pressure  increases. 

Regnault  found  that  nitrogen  was  like  air,  but  is  less  compressible. 
Carbonic  acid  exhibits  considerable  deviation  from  Boyle's  law  even  under 
small  pressures.  Hydrogen  also  deviates  from  the  law,  but  its  compressi- 
bility diminishes  with  increased  pressure. 

Cailletet  examined  the  compressibility  of  gases  by  a  special  method  in 
which  the  pressure  could  be  carried  as  high  as  600  atmospheres.  His  results 
confirm  those  of  Regnault  as  regards  hydrogen  ;  nitrogen  was  found  to 
present  the  curious  feature  that  towards  80  atmospheres  it  has  a  maximum 
relative  compressibility ;  beyond  this  point  it  gradually  becomes  less  com- 
pressible, its  compressibility  diminishing  more  rapidly  than  that  of  hydrogen. 
Carbonic  acid  deviates  less  from  the  law  in  proportion  as  the  temperature  is 
higher.  This  is  also  the  case  with  other  gases.  And  experiment  shows 
thai  the  deviation  from  the  law  is  greater  in  proportion  as  the  gas  is  nearer 


144  On  Gases.  [175- 

its  liquefying  point  ;  and,  on  the  contrary,  the  farther  a  gas  is  from  this 
point,  the  more  closely  does  it  follow  the  law.  For  gases  which  are  the 
most  difficult  to  liquefy,  the  deviations  from  the  law  are  inconsiderable,  and 
may  be  quite  neglected  in  ordinary  physical  and  chemical  experiments, 
where  the  pressures  are  not  great. 

176.  Applications  of  Boyle's  law,—  Observations  on  the  volumes  of 
gases  are  only  comparable  when  made  at  the  same  pressure.  Usually, 
therefore,  in  gas  analyses,  all  measurements  are  reduced  to  the  standard 
pressure  of  760  millimetres,  or  29*92  inches.  This  is  easily  done  by  Boyle's 
law,  for,  since  the  volumes  are  inversely  as  the  pressures,  V  :  V  =  P'  :  P. 
Knowing  the  volume  V  at  the  pressure  P,  we  can  easily  calculate  its  volume 
V  at  the  given  pressure  P',  for 

V'P'  =  VP;  thatis,  V'  =  Y-?. 

Suppose  a  volume  of  gas  to  measure  340  cubic  inches  under  a  pressure 
of  535  mm.,  what  will  be  its  volume  at  the  standard  pressure,  760  mm.  ? 

We  have  V  =  34--X  5^>  =  238  cubic  inches. 

760 

In  like  manner  let  it  be  asked,  if  D'  is  the  density  of  a  gas  when  the 
barometer  stands  at  H'  mm.,  what  will  be  its  density  D  at  the  same  tem- 
perature when  the  barometer  stands  at  H  mm.  ? 

Let  M  be  the  mass  of  the  gas,  V7  its  volume  in  the  first  case,  V  its  volume 
in  the  second.  Therefore, 

DV-M-D'V' 


_==  -  =  - 

D7     V~     P'     H'' 
Thus,  if  H'  denote  760  mm.,  we  have 

IT 

Density  at  H'  =  (Density  at  standard  pressure)  -     . 

760 

177.  Manometers.  —  Manometers    are    instruments    for  measuring  the 
tension  of  gases  or  vapours.     In  all  such  instruments  the  unit  chosen  is  the 
pressure  of  one  atmosphere  or  30  inches  of  mercury  at  the  standard  tem- 
perature, which,  as  we  have  seen,  is  nearly  15  Ibs.  to  the  square  inch. 

178.  Open-air    manometer.—  The    open-air  manometer  consists    of  a 
bent  glass  tube  BD  (fig.  146),  fastened  to  the  bottom  of  a  reservoir  AC, 
of  the   same  material,  containing  mercury,  which   is  connected  with  the 
closed  recipient  containing  the  gas  or  vapour  the  pressure  of  which  is  to 
be   measured.     The   whole   is   fixed   on   a  long   plank  kept  in  a  vertical 
position. 

In  graduating  this  manometer  C  is  left  open,  and  the  number  I  marked 
at  the  level  of  the  mercury,  for  this  represents  one  atmosphere.  From  this 
point  the  numbers  2,  3,  4,  5,  6  are  marked  at  each  30  inches,  indicating  so 
many  atmospheres,  since  a  column  of  mercury  30  inches  represents  a  pres- 
sure of  one  atmosphere.  The  intervals  from  I  to  2,  and  from  2  to  3,  &c.,  are 
divided  into  tenths.  C  being  then  placed  in  connection  with  a  boiler,  for 
example,  the  mercury  rises  in  the  tube  BD  to  a  height  which  measures  the 


-179] 


Manometer  with  Compressed  A  ir. 


tension  of  the  vapour.  In  the  figure  the  manometer  marks  2  atmospheres, 
which  represents  a  height -of  30  inches,  plus  the  atmospheric  pressure  exerted 
at  the  top  of  the  column  through  the  aperture  D. 

This  manometer  is  only  used  when  the  pressures  do  not  exceed  5  to  6 
atmospheres.  Beyond  this,  the  length  of  tube  necessary  makes  it  very  in- 
convenient, and  the  following  apparatus  is  commonly  used. 

179.  Manometer  with  compressed  air. — The  manometer  with  com- 
pressed air  is  founded  on  Boyle's  law  :  it  consists  of  a  glass  tube  closed  at 
the  top,  and  filled  with  dry  air.  It  is  firmly  cemented  in 
a  small  iron  box  containing  mercury.  By  a  tubulure,  A, 
in  the  side  (fig.  146),  this  box  is  connected  with  the  closed 
vessel  containing  the  gas  or  vapour  whose  tension  is  to 
be  measured. 

In  the  graduation  of  this  manometer,  the  quantity  of 
air  contained  in  the  tube  is  such  that  when  the  aperture 
A  communicates  freely  with  the  atmosphere,  the  level 
of  the  mercury  is  the  same  in  the  tube  and  in  the  tubu- 
lure. Consequently,  at  this  level,  the  number  i  is  marked 
on  the  scale  to  which  the  tube  is  affixed.  As  the  pres- 
sure acting  through  the  tubulure  A  increases,  the  mercury 


. 

••"• 


Fig.  146. 


Fig.  147. 


Fig.  148. 


rises  in  the  tube,  until  its  weight,  added  to  the  tension  of  the  compressed 
air,  is  equal  to  the  external  pressure.  It  would  consequently  be  incorrect 
to  mark  two  atmospheres  in  the  middle  of  the  tube  ;  for  since  the  volume 
of  the  air  is  reduced  to  one-half,  its  tension  is  equal  to  two  atmospheres, 
and,  together  with  the  weight  of  the  mercury  raised  in  the  tube,  is  there- 

H 


146 


On  Gases. 


[179 


fore  more  than  two  atmospheres.  The  position  of  the  number  is  a  little 
below  the  middle,  at  such  a  height  that  the  elastic  force  of  the  com- 
pressed air,  together  with  the  weight  of  the  mercury  in  the  tube,  is  equal  to 
two  atmospheres.  The  exact  position  of  the  numbers,  2,  3,  4,  &c.,  on  the 
manometer  scale  can  only  be  determined  by  calculation.  Sometimes  this 
manometer  is  made  of  one  glass  tube  (as  represented  in  fig.  148).  The 
principle  is  obviously  the  same. 

1 80.  Volumometer. — An  interesting  application  of  Boyle's  law  is  met 
with  in  the  volumometer.     This  consists  of  a  glass  tube  with  a  cylinder  G  at 

the  top  (fig.  149),  the  edges  of  which  are  carefully  ground, 
and  which  can  be  closed  hermetically  by  means  of  a  ground- 
glass  plate  D.  The  top  being  open,  the  tube  is  immersed 
until  the  level  of  the  mercury  inside  and  outside  is  the  same ; 
this  is  represented  by  the  mark  Z.  The  apparatus  is  then 
closed  air-tight  by  the  plate,  and  is  raised  until  the  mercury 
stands  at  a  height  //,  above  the  level  Q  in  the  bath.  The 
original  volume  of  the  enclosed  air  V,  which  was  under  the 
pressure  of  the  atmosphere,  is  now  increased  to  V  +  z/,  since 
the  pressure  has  diminished  by  the  height  of  the  column  of 
mercury  h.  Calling  the  pressure  of  the  atmosphere  at  the 
time  of  observation  £,  we  shall  have  V  :  V  +  v  =  b  —  h  :  b. 

Placing  now  in  the  cylinder  a  body  K  whose  volume  oc  is 
unknown,  the  same  operations  are  repeated,  the  tube  is  raised 
until  the  mercury  again  stands  at  the  same  mark  as  before, 
but  its  height  above  the  bath  is  now  different ;  a  second  reading, 
/Zj,  is  obtained,  and  we  have  (V  —  x]  :  (V  —  x)  +  v  =  b  —  /i1  :  b. 

Combining  and  reducing  we  get  x=(V  +  v)  (i  — /-).       The 

Fig.  149.         volume  V  +  v  is  constant,   and  is  determined  numerically, 
once  for  all,  by  making  the  experiment  with  a  substance  of 
known  volume,  such  as  a  glass  bulb. 

181.  Regnault  s    barometric    manometer. — For   measuring   pressures 
of  less  than  one  atmosphere,  Regnault  devised  the  following  arrangement, 
which   is  a  modification  of  his  fixed  barometer  (fig.   138).      In  the  same 
cistern  dips  a  second  tube  <?,  of  the  same  diameter,  open  at  both  ends,  and 
provided  at  the  top  with  a  three-way  cock,  one  of  which  is  connected  with 
an  air-pump  and  the  other  with  the  space  to  be  exhausted.     The  further  the 
exhaustion    is    carried    the  higher  the  mercury   rises  in   the  tube  a.     The 
differences  of  level  in  the  tubes  b   and  a  give  the  pressures.     Hence,  by 
measuring  the  height  ab,  by  means  of  the  cathetometer,  the  pressure  in  the 
space  that  is  being  exhausted  is  accurately  given.     This  apparatus  is  also 
called  the  differential  barovicter. 

182.  Aneroid  barometer. — This  instrument  derives  its  name  from  the 
circumstance  that  no  liquid  is  used  in  its  construction   (a,  without,  vypos, 
moist).     Fig.   150  represents  one  of  the  forms  of  these  instruments,    con- 
structed by  Casella  ;  it  consists  of  a  cylindrical  metal  box,  exhausted  of  air, 
the  top  of  which  is  made  of  thin  corrugated  metal,  so  elastic  that  it  readily 
yields  to  alterations  in  the  pressure  of  the  atmosphere. 

When  the  pressure  increases,  the  top  is  pressed  inwards  ;  when  on  the 


-183] 


Laws  of  the  Mixture  of  Gases. 


contrary  it  decreases,  the  elasticity  of  the  lid,  aided  by  a  spring,  tends  to 
move  it  in  the  opposite  direction.  These  motions  are  transmitted  by  delicate 
multiplying  levers  to  an  index 
which  moves  on  a  scale.  The 
instrument  is  graduated  empiri- 
cally by  comparing  its  indica- 
tions, under  different  pressures, 
with  those  of  an  ordinary  mer- 
curial barometer. 

The  aneroid  has  the  advan- 
tage of  being  portable,  and  can 
be  constructed  of  such  delicacy 
as  to  indicate  the  difference  in 
pressure  between  the  height  of 
an  ordinary'  table  and  the 
ground.  It  is  hence  much  used 
in  determining  heights  jn  moun- 
tain ascents.  But  it  is  some- 
what liable  to  get  out  of  order, 
especially  when  it  has  been  sub- 
jected to  great  variations  of 
pressure  ;  and  its  indications 
must  from  time  to  time  be  compared  with  those  of  a  standard  barometer. 

The  errors  arising  from  the  use  of  the  aneroid  are  mainly  due  to  the 
transmission  of  the  motion  of  the  lid  by  the  multiplying  arrangement. 
Goldsmid  of  Zurich  devised  a  form  in  which  the  motion  of  the  lid  is  directly 
obsen  ed. 

Like  that  of  other  aneroids,  the  lid  of  the  box  a  (fig.  151),  in  which  the 
alterations  of  pressure  are  determined,  is  of  fine  corrugated  sheet  metal.  To 
this  is  fixed  a  horizontal  metal  strip  b,  on  the  front  end 
of  which  is  a  small  square  <?,  acting  as  index.  This 
rises  and  falls  with  the  movement  of  the  lid,  and 
indicates  on  a  scale//',  on  the  sides  of  the  slit  dd ', 
alterations  in  pressure  of  centimetres.  To  this  strip 
a  second  and  more  delicate  one,  ^,  is  fixed,  on 
the  front  end  of  which  is  also  fixed  an  index  e'. 
Before  making  an  observation,  the  horizontal  line 
of  this  index  is  made  to  coincide  with  that  of  e  ; 
this  is  effected  by  means  of  a  micrometer  screw  in, 
which  is  raised  or  lowered  by  the  movable  ring  //  ; 
on  the  corresponding  scale  millimetres  and  tenths 
of  a  millimetre  are  read  off.  To  do  this  the  in- 
strument is  provided  with  a  lens  not  represented  in 
the  figure.  There  is  also  a  small  thermometer  / ; 
from  its  indications  a  correction  is  made  for  tem- 
peratures according  to  an  empirical  scale  specially 
constructed  for  each  instrument. 


Fig.  151. 


183.  Laws  of  the  mixture  of  erases. — If  a  communication  is  opened 
between   two  closed  vessels  containing  gases,  they  at  once  begin  to  mix, 

H  2 


148 


On  Gases. 


[183- 


whatever  be  their  density,  and  in  a  longer  or  shorter  time  the  mixture  is  ' 
complete,  and  will  continue  so,  unless  chemical  action  or  some  other  ex- 
traneous cause  intervene.     The  laws  which  govern  the  mixture  of  gases  may 
be  thus  stated  :  — 

I.  The  mixture  takes  place  rapidly  and  is  homogeneous  ;  that  is,  each 
portion  of  the  mixture  contains  the  two  gases  in  the  same  proportion. 

II.  If  the  gases  severally  and  the  mixture  have  the  same  temperature,  and 
if  the  gases   severally  and  the  mixture  occupy  the  same  volume,  then  the 
pressure  on  the  unit  of  area  exerted  by  the  mixture  will  equal  the  sum  of 
pressures  on  the  unit  of  area  exerted  by  the  gases  severally. 

From  the  second  law  a  very  convenient  formula  can  be  easily  deduced. 

Let  vlt  v.2,  vs  ....  be  the  volumes  of  several  gases  under  pressure  of 
P\i  Pv  Pz  •  '  -  •  resPectively.  Suppose  these  gases  when  mixed  to  have  a 
volume  V,  under  a  pressure  P,  the  temperatures  being  the  same.  By  Boyle's 
law  we  know  that  VL  will  occupy  a  volume  V  under  a  pressure  p{  provided 
that 

VA'-ViA 

Similarly  V/./  •-=  v.zp* 

and  so  on.     But  we  learn  from  the  above  law  that 


therefore  VP  =  v^p^  +  v^p*  +  v3p3  +   .  .  . 

It  obviously  follows  that  if  the  pressures  are  all  the  same,  the  volume  of  the 

mixture  equals  the  sum  of  the  separate  volumes. 

The  first  law  was  shown  experimentally  by  Berthollet,  by  means  of  an 

apparatus  represented  in  fig.  152.  It  consists  of  two  glass  globes  provided 
with  stopcocks,  which  can  be  screwed  one  on 
the  other.  The  upper  globe  was  filled  with 
hydrogen,  and  the  lower  one  with  carbonic  acid, 
which  has  22  times  the  density  of  hydrogen. 
The  globes  having  been  fixed  together  were 
placed  in  the  cellars  of  the  Paris  Observatory 
and  the  stopcocks  then  opened,  the  globe  con- 
taining hydrogen  being  uppermost.  Berthollet 
found  after  some  time  that  the  pressure  had  not 
changed,  and  that,  in  spite  of  the  difference  in 
density,  the  two  gases  had  become  uniformly 
mixed  in  the  two  globes.  Experiments  made 
in  the  same  manner  with  other  gases  gave  the 
same  results,  and  it  was  found  that  the  diffusion 
was  more  rapid  in  proportion  as  the  difference 
between  the  densities  was  greater. 

The  second  law  may  be  demonstrated  by 
passing  into  a  graduated  tube,  over  mercury, 
known  volumes  of  gas  at  known  pressures. 
The  pressure  and  volume  of  the  whole  mixture 

are  then  measured,  and  found  to  be  in  accordance  with  the  law. 

Gaseous   mixtures  follow   Boyle's  law,  like   simple  gases,  as   has  been 

proved  for  air  (174),  which  is  a  mixture  of  nitrogen  and  oxygen. 


—184]    Mixture  of  Gases  and  Liquids,     Absorption  of  Gases.    149 

184.  Mixture  of  erases  and  liquids.  Absorption  of  gases. — Water 
and  many  liquids  possess  the  property  of  absorbing  gases.  Under  the  same 
conditions  of  pressure  and  temperature  a  liquid  does  not  absorb  equal  quan- 
tities of  different  gases.  At  the  temperature  crC.  and  pressure  760  mm.  one 
volume  of  \vaterdissolves  the  following  volumes  of  gas  : — 

Nitrogen         ....     0*020     Sulphuretted  hydrogen .         .         4-37 

( ) \ygen 0*041     Sulphurous  Acid    .         .         .       7979 

Carbonic  Acid        .         .         .     179       Ammonia       ....   1046.63 

From  the  very  great  condensation,  to  which  the  latter  correspond,  it  may  be 
inferred  that  the  gases  are  in  the  liquid  state. 

Guses  are  more  soluble  in  alcohol ;  thus  at  O'C.  alcohol  dissolves  4-33 
volumes  of  carbonic  acid  gas. 

The  whole  subject  of  gas  absorption  has  been  investigated  by  Bunsen. 
The  general  laws  are  the  following  : — 

I.  For  the  same  gas,  the  sains  liquid,  and  the  same  temperature,  the 
Jit  of  gas  absorbed  is  proportional  to  the  pressure.     This  may  also  be 

expressed  by  saying  that  at  all  pressures  the  volume  dissolved  is  the  same  ; 
or  that  the  density  of  the  gas  absorbed  is  in  a  constant  relation  with  that  of 
the  external  gas  which  is  not  absorbed. 

Accordingly,  when  the  pressure  diminishes,  the  quantity  of  dissolved  gas 
decreases.  If  a  solution  of  gas  be  placed  under  the  air-pump  and  a  vacuum 
created,  the  gas  obeys  its  expansive  force  and  escapes  with  effervescence. 

II.  Tfi3  quantify  of  gas  absorbed  decreases  -with  the  temperature  ;  that  is 
to  say,  when  the  elastic  force  of  the  gas  is  greater.     Thus  at  15°  water  only 
absorbs  i  -oo  of  carbonic  acid. 

III.  The  quantity  of  gas  which  a  liquid  can  dissolve  is  independent  of 
the  nature  and  of  the  quantity  of  other  gases  which  it  may  already  hold  in 
solution. 

In  every  gaseous  mixture  each  gas  exercises  the  same  pressure  as  it 
would  if  its  volume  occupied  the  whole  space  ;  and  the  total  pressure  is 
equal  to  the  sum  of  the  individual  pressures.  When  a  liquid  is  in  contact 
with  a  gaseous  mixture,  it  absorbs  a  certain  part  of  each  gas,  but  less  than 
it  would  if  the  whole  space  were  occupied  by  each  gas.  The  quantity  of 
each  gas  dissolved  is  proportional  to  the  pressure  which  the  unabsorbed 
gas  exercises  alone.  For  instance,  oxygen  forms  only  about  |  the  quantity 
of  air  ;  and  water,  under  ordinary  conditions,  absorbs  exactly  the  same 
quantity  of  oxygen  as  it  would  if  the  atmosphere  were  entirely  formed  of  this 
gas  under  a  pressure  equal  to  §  that  of  the  atmosphere. 


On  Gases. 


[185- 


CHAPTER    III. 

PRESSURE    ON   BODIES   IN   AIR.      BALLOONS. 

185.  Archimedes'  principle  applied  to  gases. — The  pressure  exerted 
by  gases,  on  bodies  immersed  in  them,  is  transmitted  equally  in  all  directions, 

as  has  been  shown  by  the  experiment 
with  the  Magdeburg  hemispheres.  It 
therefore  follows  that  all  which  has 
been  said  about  the  equilibrium  of 
bodies  in  liquids  applies  to  bodies  in 
air ;  they  lose  a  part  of  their  weight 
equal  to  that  of  the  air  which  they  dis- 
place. 

The  loss  of  weight  in  air  is  demon- 
strated by  means  of  the  baroscope, 
which  consists  of  a  scalebeam,  at  one 
of  whose  extremities  a  small  leaden 
weight  is  supported,  and  at  the  other 
there  is  a  hollow  copper  sphere  (fig. 
153).  In  the  air  they  exactly  balance 
one  another ;  but  when  they  are  placed 
under  the  receiver  of  the  air-pump, 
and  a  vacuum  is  produced,  the  sphere 
sinks,  thereby  showing  that  in  reality 
it  is  heavier  than  the  small  leaden 
weight.  Before  the  air  is  exhausted  each  body  is  buoyed  up  by  the  weight 
of  the  air  which  it  displaces.  But  as  the  sphere  is  much  the  larger  of  the 
two,  its  weight  undergoes  most  apparent  diminution,  and  thus,  though  in 
reality  the  heavier  body,  it  is  balanced  by  the  small  leaden  weight.  It 
may  be  proved  by  means  of  the  same  apparatus  that  this  loss  is  equal  to 
the  weight  of  the  displaced  air.  Suppose  the  volume  of  the  sphere  is  10 
cubic  inches.  The  weight  of  this  volume  of  air  is  3-1  grains.  If  now  this 
weight  be  added  to  the  leaden  weight,  it  will  overbalance  the  sphere  in  air, 
but  will  exactly  balance  it  in  vacuo. 

The  principle  of  Archimedes  is  true  for  bodies  in  air  ;  all  that  has  been 
said  about  bodies  immersed  in  liquids  applies  to  them  ;  that  is,  that  when  a 
body  is  heavier  than  air,  it  will  sink,. owing  to  the  excess  of  its  weight  over 
the  buoyancy.  If  it  is  as  heavy  as  air,  its  weight  will  exactly  counterbalance 
the  buoyancy,  and  the  body  will  float  in  the  atmosphere.  If  the  body  is 
lighter  than  air,  the  buoyancy  of  the  air  will  prevail,  and  the  body  will  rise 
in  the  atmosphere  until  it  reaches  a  layer  of  the  same  density  as  its  own. 
The  force  of  the  ascent  is  equal  to  the  excess  of  the  buoyancy  over  the 


Fig-  153- 


-187]  Construction  and  Management  of  Balloons.  151 

weight  or  the  body.     This  is  the  reason  why  smoke,  vapours,  clouds,  and 
air  balloons  rise  in  the  air. 


AIR    BALLOONS. 

1 86.  Air  balloons. — Air  balloons  are  hollow  spheres  made  of  some  light 
impermeable  material,  which,  when  filled  with  heated  air,  with  hydrogen  gas, 
or  with  coal  gas,  rise  in  the  air  by  virtue  of  their  relative  lightness. 

They  were  invented  by  the  brothers  Mongolfier  of  Annonay,  and  the 
first  experiment  was  made  at  that  place  in  June  1783.  Their  balloon  was  a 
sphere  of  forty  yards  in  circumference,  and  weighed  500  pounds.  At  the 
lower  part  there  was  an  aperture,  and  a  sort  of  boat  wras  suspended,  in  which 
fire  was  lighted  to  heat  the  internal  air.  The  balloon  rose  to  a  height  of 
2,200  yards,  and  then  descended  without  any  accident. 

Charles,  a  professor  of  physics  in  Paris,  substituted  hydrogen  for  hot  air. 
He  himself  ascended  in  a  balloon  of  this  kind  in  December  1783.  The  use 
of  hot-air  balloons  \vas  entirely  given  up  in  consequence  of  the  serious 
accidents  to  which  they  were  liable. 

Since  then  the  art  of  ballooning  has  been  greatly  extended,  and  many 
ascents  have  been  made.  That  which  Gay-Lussac  made  in  1804  was  the 
most  remarkable  for  the  facts  with  which  it  has  enriched  science,  and  for  the 
height  which  he  attained — 23,000  feet  above  the  sea  level.  At  this  height 
the  barometer  descended  to  12 -6  inches,  and  the  thermometer  which  was 
31°  C.  on  the  ground  was  9  degrees  below  zero. 

In  these  high  regions,  the  dryness  was  such  on  the  day  of  Gay-Lussads 
ascent,  that  hygrometric  substances,  such  as  paper,  parchment,  &c.,  became 
dried  and  crumpled  as  if  they  had  been  placed  near  the  fire.  The  respira- 
tion and  circulation  of  the  blood  were  accelerated  in  consequence  of  the 
great  rarefaction  of  the  air.  Gay-Lussac's  pulse  made  120  pulsations  in  a 
minute  instead  of  66,  the  normal  number.  At  this  great  height  the  sky  had 
a  very  dark  blue  tint,  and  an  absolute  silence  prevailed. 

One  of  the  most  remarkable  of  recent  ascents  was  made  by  Mr.  Glaisher 
and  Mr.  Coxwell,  in  a  large  balloon  belonging  to  the  latter.  This  was  filled 
with  90,000  cubic  feet  of  coal  gas  (sp.  gr.  0*37  to  0*33)  ;  the  weight  of  the 
load  was  600  pounds.  The  ascent  took  place  at  I  P.M.  on  September  5, 
1 86 1  ;  at  1.28  they  had  reached  a  height  of  15,750  feet,  and  in  eleven 
minutes  after  a  height  of  21,000  feet,  the  temperature  being  —  10*4°;  at  1.50 
they  were  at  26,200  feet,  with  the  thermometer  at  —15-2°.  At  1.52  the 
height  attained  was  29,000  feet,  and  the  temperature  -  16°  C.  At  this  height 
the  rarefaction  of  the  air  was  so  great,  and  the  cold  so  intense,  that  Mr. 
Glaisher  fainted,  and  could  no  longer  observe.  According  to  an  approxi- 
mate estimation  the  lowest  barometric  height  they  attained  was  7  inches, 
which  would  correspond  to  an  elevation  of  36,000  to  37,000  feet. 

187.  Construction  and  management  of  balloons. — A  balloon  is  made 
of  long  bands  of  silk  sewed  together  and  covered  with  caoutchouc  varnish, 
which  renders  it  air-tight.     At  the  top  there  is  a  safety  valve  closed  by  a 
spring,  which  the  aeronaut  can  open  at  pleasure  by  means  of  a  cord.    A  light 
wickerwork  boat  is  suspended  by  means   of  cords   to  a  network,  which 
entirely  covers  the  balloon. 


152  On  Gases.  [187- 

A  balloon  of  the  ordinary  dimensions,  which  can  carry  three  persons,  is 
about  1 6  yards  high,  12  yards  in  diameter,  and  its  volume,  when  it  is  quite 

full,  is  about  680  cubic  yards.  •  The  bal- 
loon itself  weighs  200  pounds  ;  the  ac- 
cessories, such  as  the  rope  and  boat,  100 
pounds. 

The  balloon  is  filled  either  with  hy- 
drogen or  with  coal  gas.  Although  the 
latter  is  heavier  than  the  former,  it  is 
generally  preferred,  because  it  is  cheaper 
and  more  easily  obtained.  It  is  passed 
into  the  balloon  from  the  gas  reservoir 
by  means  of  a  flexible  tube.  It  is  im- 
portant not  to  fill  the  balloon  quite 
full,  for  the  atmospheric  pressure  dimin- 
ishes as  it  rises  (fig.  154),  and  the  gas 
inside,  expanding  in  consequence  of  its 
elastic  force,  tends  to  burst  it.  It  is 
sufficient  for  the  ascent  if  the  weight  of 
the  displaced  air  exceeds  that  of  the 
balloon  by  8  or  10  pounds.  And  this 
force  remains  constant  so  long  as  the 
balloon  is  not  quite  distended  by  the 
dilatation  of  the  air  in  the  interior.  If 
the  atmospheric  pressure,  for  example, 
has  diminished  to  one-half,  the  gas  in  the 
balloon,  according  to  Boyle's  law,  has 
doubled  its  volume.  The  volume  of  the 
air  displaced  is  therefore  twice  as  great  ; 
but  since  its  density  has  become  only 
one-half,  the  weight  and  consequently 
the  upward  buoyancy  are  the  same. 
When  once  the  balloon  is  completely 
dilated,  if  it  continues  to  rise,  the  force  of 
the  ascent  decreases,  for  the  volume  of 
the  displaced  air  remains  the  same,  but 
its  density  diminishes,  and  a  time  arrives 
at  which  the  buoyancy  is  equal  to  the 
weight  of  the  balloon.  The  balloon  can  now  only  take  a  horizontal  direction, 
carried  by  the  currents  of  air  which  prevail  in  the  atmosphere.  The  aero- 
naut knows  by  the  barometer  whether  he  is  ascending  or  descending,  and 
by  the  same  means  he  determines  the  height  which  he  has  reached.  A  long 
flag  fixed  to  the  boat  would  indicate,  by  the  position  it  takes  either  above  or 
below,  whether  the  balloon  is  descending  or  ascending. 

When  the  aeronaut  wishes  to  descend,  he  opens  the  valve  at  the  top  of 
the  balloon  by  means  of  the  cord,  which  allows  gas  to  escape,  and  the 
balloon  sinks.  If  he  wants  to  descend  more  slowly,  or  to  rise  again,  he 
empties  out  bags  of  sand,  of  which  there  is  an  ample  supply  in  the  car.  The 
descent  is  facilitated  by  means  of  a  grappling  iron  fixed  to  the  boat.  When 


Fig-  154- 


-189]     Calculation  of  the  WeigJit  which  a  Balloon  can  raise.     153 

once  this  is  fixed  to  any  obstacle,  the  balloon  is  lowered  by  pulling  the 
cord. 

The  only  practical  applications  which  air  balloons  have  hitherto  had 
have  been  in  military  reconnoitring.  At  the  battle  of  Fleurus,  in  1794,  a 
captive  balloon — that  is,  one  held  by  a  rope — was  used,  in  which  there  was 
an  observer  who  reported  the  movements  of  the  enemy  by  means  of  signals. 
At  the  battle  of  Solferino  the  movements  and  dispositions  of  the  Austrian 
troops  were  watched  by  a  captive  balloon  ;  and  in  the  war  in  America, 
balloons  were  frequently  used,  while  their  importance  during  the  siege  of 
Paris  is  fresh  in  all  memories.  The  whole  subject  of  military  ballooning 
was  treated  in  two  papers  by  Captain  Grover  and  by  Captain  Beaumont,  in  a 
volume  of  the  Professional  Papers  of  the  Royal  Engineers  ;  and  experiments 
are  now  in  progress,  at  Woolwich  and  at  Aldershot,  with  a  view  of  ascertain- 
ing the  most  practicable  means  of  inflating  balloons  and  the  best  form  and 
equipment  for  service  in  the  field.  It  has  been  proposed  to  use  captive 
balloons  for  observations  on  the  changes  of  temperature  in  the  air,  £c.  Air 
balloons  can  only  be  truly  useful  when  they  can  be  guided,  and  as  yet  all 
attempts  made  with  this  view  have  completely  failed.  There  is  no  other 
course  at  present  than  to  rise  in  the  air  until  there  is  a  current  which  has 
more  or  less  the  desired  direction.  Unfortunately  the  currents  in  the  higher 
regions  of  the  atmosphere  are  variable  and  irregular. 

1 88.  Parachute. — The  object  of 
the  parachute  is  to  allow  the  aero- 
naut to  leave  the  balloon,  by  giving 
him  the  means  of  lessening  the 
rapidity  of  his  descent.  It  consists 
of  a  large  circular  piece  of  cloth  (fig. 
155),  about  16  feet  in  diameter,  and 
which  by  the  resistance  of  the  air 
spreads  out  like  a  gigantic  um- 
brella. In  the  centre  there  is  an 
aperture,  through  which  the  air 
compressed  by  the  rapidity  of  the 
descent  makes  its  escape ;  for 
otherwise  oscillations  might  be 
produced,  which,  when  communi- 
cated to  the  boat,  would  be  dan- 
gerous. 

In  fig.  154  there  is  a  parachute 
attached    to    the   network   of  the  f* 
balloon  by  means  of  a  cord  which  ^ 
passes  round  a  pulley,  and  is  fixed 
at  the  other  end  to  the  boat.    When 
the  cord  is  cut  the  parachute  sinks, 
at    first    very    rapidly,    but    more 
slowly  as  it  becomes  distended,  as 
represented  in  the  figure. 

189.   Calculation   of    tbe    weight    which   a    balloon    can    raise. — To 
calculate  the  weight  which    can   be  raised  by  a  balloon    of  given   dimen- 

H  3 


154  On  Gases.  [189- 

sions,  let  us  suppose  it  perfectly  spherical,  and  premise  that  the  formulas  which 


express  the  volume  and  the  superficies  in  terms  of  the  radius  are  V 


S  =  47rR~  ;  TT  being  the  ratio  of  the  circumference  to  the  diameter.  The 
radius  R  being  measured  in  feet,  let  p  be,  in  pounds,  the  weight  of  a 
square  foot  of  the  material  of  which  the  balloon  is  constructed  ;  let  P 
be  the  weight  of  the  car  and  the  accessories,  a  the  weight  in  pounds  of 
a  cubic  foot  of  air  at  zero,  and  under  the  pressure  O'76m,  and  a'  the  weight 
of  the  same  volume,  under  the  same  conditions,  of  the  gas  with  which 
the  balloon  is  inflated  (149).  Then  the  total  weight  of  the  envelope  in 

pounds  will  be  47rR2^  ;  that  of  the  gas  will  be   —  -  ,  and   that  of  the  dis- 

placed air  4^  —  a.  If  X  be  the  weight  which  the  balloon  can  support,  we 
have 


Whence 


X  =  ^ 


_  p. 


But  as  we  have  before  seen  (186),  in  order  that  the  balloon  may  rise,  the 
weights  must  be  less  by  8  or  10  pounds  than  that  given  by  this  equation. 


-190] 


Air- Pump. 


155 


CHAPTER    IV. 

APPARATUS   WHICH    DEPEND  ON   THE  PROPERTIES   OF   AIR. 

iyo.  Air-pump. — The  air-pump  is  an  instrument  by  which  a  vacuum  can 
be  produced  in  a  given  space,  or  rather  by  which  air  can  be  greatly  rarefied, 
for  an  absolute  vacuum  cannot  be  produced  by  its  means.  It  was  invented 
by  Otto  von  Guericke  in  1650,  a  few  years  after  the  invention  of  the  baro- 
meter. 

The  air-pump,  as  now  usually  constructed,  may  be  described  as  follows. 
In  fig.  156,  which  shows  the  general  arrangement,  E  is  the  receiver,  in  which 
the  vacuum  is  to  be 
produced.  It  is  a 
bell  glass  resting  on 
a  plate  D,  of  thick 
glass  ground  per- 
fectly smooth.  In 
the  centre  of  D,  at 
C.  there  is  an  open- 
ing by  which  a  com- 
munication is  made 
between  the  interior 
of  the  receiver  and 
of  the  cylinders  P, 
P.  This  communi- 
cation is  effected  by 
a  tube  or  pipe  pass- 
ing through  the 
body  of  the  plate  A, 
and  then  branching 
off  at  right  angles,  as 
shown  by  Kco  Kcs, 
in  fig.  157,  which 
represents  a  hori- 
zontal section  of  the 
machine.  In  the 

cylinders — which  are  commonly  of  glass  and  which  are  firmly  cemented  to 
the  plate  A — are  two  pistons,  P  and  Q,  moving  air-tight.  Each  piston  is 
moved  by  a  rack,  working  with  a  pinion,  H,  turning  by  a  handle,  M.  This 
is  shown  more  plainly  in  fig.  158,  which  represents  a  vertical  section  of  the 
machine  through  the  cylinders  ;  here  H  is  the  piniop,  and  MN  the  handle. 
When  M  is  forced  down  one  piston  is  raised,  and  the  other  depressed. 


156 


On  Gases. 


[190- 


When  M's  action  is  reversed,  the  former  piston  is  depressed,  and  the  latter 
raised. 

The  action  of  the  machine  is  this.  Each  cylinder  is  fitted  with  a  valve 
so  contrived  that,  when  its  piston  is  raised,  communication  is  opened  between 
the  cylinder  and  the  receiver  :  when  it  is  depressed  the  communication  is 
closed.  Now  if  P  were  simply  raised,  a  vacuum  would  be  formed  below  P  ; 
but  as  a  communication  is  opened  with  the  receiver  E,  the  air  in  E  expands 
so  as  to  fill  both  the  receiver  and  the  cylinder.  As  soon  as  the  piston 
begins  to  descend,  the  communication  is  closed,  and  none  of  the  air  in  the 
cylinder  returns  to  the  receiver,  but,  by  means  of  properly  constructed 


Fi?.    1 60 


Fig.  157- 


Fig.  158. 


Fig.  159- 


valves,  escapes  into  the  atmosphere.  Consequently  the  rarefaction  which 
the  air  in  the  receiver  has  undergone  is  permanent.  By  the  next  stroke  a 
further  rarefaction  is  produced  :  and  so  on,  at  each  succeeding  stroke. 

It  is  clear  that  when  the  rarefaction  has  proceeded  to  a  considerable 
extent,  the  atmospheric  pressure  on  the  top  of  P  will  be  very  great,  but  it  will 
be  very  nearly  balanced  by  the  atmospheric  pressure  on  the  top  of  the  other 
piston.  Consequently  the  experimenter  will  have  to  overcome  only  the 
difference  of  the  two  pressures.  This  is  the  reason  why  two  cylinders  are 
employed. 

To  explain  the  action  of  the  valves  we  must  go  into  particulars.  The 
general  arrangement  of  the  interior  of  the  cylinders  is  shown  in  fig.  1 58. 
Fig  161  shows  the  section  of  a  piston  in  detail.  The  piston  is  formed  of 
two  brass  discs  (X  and  V),  screwed  to  one  another,  and  compressing  between 
them  a  series  of  leather  discs  Z,  whose  diameters  are  slightly  greater  than 
those  of  the  brass  discs.  The  leather  is  thoroughly  saturated  with  oil,  so  as 
to  slide  air-tight,  though  with  but  little  friction,  within  the  cylinder.  To  the 
centre  of  the  upper  disc  is  screwed  a  piece,  B,  to  which  the  rack  H  is  riveted. 
The  piece  B  is  pierced,  so  as  to  put  the  interior  of  the  cylinder  into  commu- 
nication with  the  external  air.  This  communication  is  closed  by  a  valve  /, 
held  down  by  a  delicate  spring  r.  When  the  piston  is  moved  downward 


-191] 


Air- Pump  Gauge. 


'57 


Fig.  161. 


the  air  below  the  piston  is  compressed  until  it  forces  up  t  and  escapes. 
The  instant  the  action  is  reversed,  the  valve  /  falls,  and  is  held  down  by  the 
spring,  and  by  the  pressure  of  the  external  air} 
which  is  thereby  kept  from  coming  in.  The  com- 
munication between  the  cylinder  below  the  piston 
and  the  receiver  is  opened  and  closed  by  the  valve 
marked  o  in  fig.  158,  and  sg  in  fig.  161.  The  rod 
sg  passing  through  the  piston  is  held  by  friction, 
and  is  raised  with  it  ;  but  is  kept  from  being  lifted 
through  more  than  a  very  small  distance  by  the 
top  of  the  cylinder,  while  the  piston,  in  continuing 
its  upward  motion,  slides  over  sg.  When  the 
piston  descends  it  brings  the  valve  with  it,  which 
at  once  cuts  off  the  communication  between  the 
cylinder  and  the  receiver. 

191.  Air-pump  gauge. — When  the  pump  has 
been  worked  some  time,  the  pressure  in  the  re- 
ceiver is  indicated  by  the  difference  of  level  of  the 
mercury-  in  the  two  legs  of  a  glass  tube  bent  like  a 
syphon,  one  of  which  is  opened,  and  the  other 
closed  like  the  barometer.  This  little  apparatus, 
which  is  called  the  gauge,  is  fixed  to  an  upright 
scale,  and  placed  under  a  small  bell  jar,  which 
communicates  with  the  receiver  E  by  a  stopcock,  A,  inserted  in  the  tube 
leading  from  the  orifice  C  to  the  cylinders,  fig.  1 56. 

Before  commencing  to  exhaust  the  air  in  the  receiver,  its  elastic  force 
exceeds  the  weight  of  the  column  of  mercury,  which  is  in  the  closed  branch 
and  which  consequently  remains  full.  But  as  the  pump  is  worked,  the 
elastic  force  soon  diminishes,  and  is  unable  to  support  the  weight  of  the 
mercury,  which  sinks  and  tends  to  stand  at  the  same  level  in  both  legs.  If 
an  absolute  vacuum  could  be  produced,  they  would  be  exactly  on  the  same 
level,  for  there  would  be  no  pressure  either  on  the  one  side  or  the  other.  But 
with  the  very  best  machines  the  level  is  always  about  a  thirtieth  of  an  inch 
higher  in  the  closed  branch,  which  indicates  that  the  vacuum  is  not  absolute, 
for  the  elastic  force  of  the  residue  is  equal  to  the  pressure  of  a  column  of 
mercury  of  that  height. 

Theoretically  an  absolute  vacuum  is  impossible  ;  for,  since  the  volume 
of  each  cylinder  is,  say,  i  that  of  the  receiver,  only  ^f  of  the  air  in  the 
receiver  is  extracted  at  each  stroke  of  the  piston,  and  consequently  it  is  im- 
possible to  exhaust  all  the  air  which  it  contains.  The  theoretical  degree  of 
exhaustion  after  a  given  number  of  strokes  is  easily  calculated  as  follows  : — 
Let  A  denote  the  volume  of  the  receiver,  including  in  that  term  the  pipe  ; 
B  the  volume  of  the  cylinder  between  the  highest  and  lowest  positions  of 
the  piston  ;  and  assume  for  the  sake  of  distinctness  that  there  is  only  one 
cylinder ;  then  the  air  which  occupied  A  before  the  piston  is  lifted  occupies 
A  +  B  after  it  is  lifted,  and  consequently  if  D,  is  the  density  at  the  end  of  the 
first  stroke  and  D  the  orginal  density,  we  must  have 


158  On  Gases.  [191- 

If  D2  is  the  density  at  the  end  of  the  second  stroke,  we  have  for  just  the 
same  reason 


Now  this  reasoning  will  apply  to  n  strokes  ; 

/    A    \m 
consequently  Dn  =  Df-  —  -j 

If  there  are  two  equal  cylinders,  the  same  formula  holds  ;  but  in  this  case, 
in  counting  ;/,  upstrokes  and  downstrokes  equally  reckon  as  one. 

It  is  obvious  that  the  exhaustion  is  never  complete,  since  D  can  be  zero 
only  when  n  is  infinite.  However,  no  very  great  number  of  strokes  is  re- 
quired to  render  the  exhaustion  virtually  complete,  even  if  A  is  several  times 
greater  than  B.  Thus  if  A=  10  B,  a  hundred  strokes  will  reduce  the  density 
from  D  to  O'OOO4  D  ;  that  is,  if  the  initial  pressure  is  30  in.,  the  pressure  at 
the  end  of  100  strokes  is  0-012  of  an  inch. 

Pcactically,  however,  a  limit  is  placed  on  the  rarefaction  that  can  be  pro- 
duced by  any  given  air-pump  ;  for,  as  we  have  seen,  the  air  becomes  ulti- 
mately so  rarefied  that,  when  the  pistons  are  at  the  bottom  of  the  cylinder, 
its  elastic  force  cannot  overcome  the  pressure  on  the  valves  in  the  inside  of 
the  piston  ;  they  therefore  do  not  open,  and  there  is  no  further  action  of  the 
pump. 

192.  Doubly-exhausting-  stopcock.  —  Babinet  invented  an  improved 
stopcock,  by  which  the  exhaustion  of  the  air  can  be  carried  to  a  very  high 
degree.  This  stopcock  is  placed  in  the  fork  of  the  pipe  leading  from  the 
receiver  to  the  two  cylinders  ;  it  is  perforated  by  several  channels,  which 
are  successively  used  by  turning  it  into  two  different  positions.  Fig.  157  re- 
presents a  horizontal  section  of  the  stopcock  R,  in  such  a  position  that,  by 
its  central  opening  and  two  lateral  openings,  it  forms  a  communication 
between  the  orifice  K  of  the  plate,  and  the  two  valves  #  -and  s.  The  machine 
then  works  as  has  been  described.  In  fig.  160  the  stopcock  has  been 
turned  a  quarter,  and  the  transversal  channel  ab,  which  was  horizontal  in 
fig.  157,  is  now  vertical,  and  its  extremities  are  closed  by  the  side  of  the  hole 
in  which  the  stopcock  works.  But  a  second  channel,  which  was  closed 
before,  and  which  has  taken  the  place  of  the  first,  now  places  the  right 
cylinder  alone  in  communication  with  the  receiver  by  the  channel  cbs  (fig. 
1  60),  and  it  further  connects  the  right  with  the  left  cylinder  by  a  channel 
aeo  (fig.  1  60),  or  aico  (fig.  158).  This  channel  passes  from  a  central  opening 
«,  placed  at  the  base  of  the  right  cylinder,  across  the  stopcock  to  the  valve, 
0,  of  the  other  cylinder,  as  represented  in  figs.  159  and  160;  but  this  channel 
is  closed  by  the  stopcock  when  it  is  in  its  first  position,  as  is  seen  in  figs. 
157  and  158. 

The  right  piston  in  rising  exhausts  the  air  of  the  receiver,  but  when  it 
descends  the  exhausted  air  is  driven  into  the  left  cylinder  through  the 
orifice  a,  the  channel  io,  and  the  valve  o  (fig.  159),  which  is  open.  When 
the  same  piston  rises,  that  of  the  left  sinks  ;  but  the  air  which  is  above 
it  does  not  return  into  the  right  cylinder,  because  the  valve  o  is  now 
closed.  As  the  right  cylinder  continues  to  exhaust  the  air  in  the  receiver, 


493]  Bianchts  Air- Pump.  1 59 

md  to  force  it  into  the  left  cylinder,  the  air  accumulates  here,  and  ulti- 
mately acquires  sufficient  tension  to  raise  the  valve  of  the  piston  Q,  which 
,vas  impossible  before  the  stopcock  was  turned,  for  it  is  only  when  the 
,-alves  in  the  piston  no  longer  open,  that  a  quarter  of  a  turn  is  given  to  the 
stopcock. 

193.  Bianchi's   air-pump.— Bianchi   invented   an  air-pump  which  has 
several  advantages.     It  is  made  entirely  of  iron,  and  it  has  only  one  cylinder, 


Fig.  162. 

which  oscillates  on  a  horizontal  axis  fixed  at  its  base  as  seen  in  -fig.  162 
A  horizontal  shaft,  with  heavy  fly-wheel,  V,  works  in  a  frame,  and  is  turned 
by  a  handle,  M.     A  crank,  ;;/,  which  is  joined  to  the  top  of  the  pistoi   rod,  is 
fixed  to  the  same  shaft,  and  consequently  at  every  revolution  of  the  wheel 
the  cylinder  makes  two  oscillations. 


160  On  Gases.  [193- 

In  some  cases,  as  in  that  shown  in  the  figure,  the  crank  and  the  fly-wheel 
are  on  parallel  axes  connected  by  a  pair  of  cog-wheels.  The  modification  in 

the  action  produced  by  this  ar- 
rangement is  as  follows  : — If  the 
cog-wheel  on  the  former  axis  has 
twice  as  many  teeth  as  that  on  the 
latter  axis,  the  pressure  which  raises 
the  piston  is  doubled ;  an  advantage 
which  is  counterbalanced  by  the 
inconvenience  that  now  the  piston 
will  make  one  oscillation  for  one 
revolution  of  the  fly-wheel. 

The  machine  is  double  acting  ; 
that  is,  the  piston  PP  (fig.  163)  pro- 
duces a  vacuum,  both  in  ascending 
and  descending.  This  is  effected 
by  the  following  arrangements  : — 
In  the  piston  there  is  a  valve,  /;, 
opening  upwards  as  in  the  ordinary- 
machine.  The  piston  rod  AA  is 
hollow,  and  in  the  inside  there  is  a 
copper  tube,  X,  by  which  the  air 
makes  its  escape  through  the  valve 
b.  At  the  top  of  the  cylinder  there 
is  a  second  valve,  #,  opening  up- 
wards. An  iron  rod,  D,  works  with 
gentle  friction  in  the  piston,  and 
terminates  at  its  ends  in  two  conical 
valves,  s  and  s',  which  fit  into  the 
openings  of  the  tube  BB  leading  to 
the  receiver. 

Let  us  suppose  the  piston  de- 
scends. The  valve  s'  is  then  closed, 
and,  the  valve  ^  being  open,  the  air 

of  the  receiver  passes  in  the  space  above  the  piston,  while  the  air  in  the 
space  below  the  piston  undergoes  compression,  and,  raising  the  valve, 
escapes  by  the  tube  X,  which  communicates  with  the  atmosphere.  When 
the  piston  ascends,  the  exhaustion  takes  place  through  j',  and  the  valve  s 
being  closed,  the  compressed  air  escapes  by  the  valve  a. 

The  machine  has  a  stopcock  for  double  exhaustion,  similar  to  that 
already  described  (192).  It  is  also  oiled  in  an  ingenious  manner.  A  cup,  E, 
round  the  rod  is  filled  with  oil,  which  passes  into  the  annular  space  between 
the  rod  AA  and  the  tube  X  ;  it  passes  then  into  a  tube  00,  in  the  piston,  and, 
forced  by  the  atmospheri'c  pressure,  is  uniformly  distributed  on  the  surface 
of  the  piston. 

The  apparatus,  being  of  iron,  may  be  made  of  much  greater  dimensions 
than  the  ordinary  air-pump.  A  vacuum  can  also  be  produced  with  it  in  far 
less  time  and  in  apparatus  of  greater  size  than  usual. 

194.  Deieuil  s  air-pump. — In  this  air-pump  the  main  peculiarity  is  its 


-195] 


Sprengel's  Air-Pump. 


161 


piston,  which  is  of  considerable  length  and  consists  of  a  series  of  accurately 
constructed  metal  discs  bolted  together.  This  works  easily  and  smoothly  in 
the  barrel,  and  no  packing  or  lubricator  is  used  ;  or  rather  the  lubricator  is 
the  air  in  the  space  between  the  piston  and  the  barrel.  The  internal 
friction  of  the  air  in  this  narrow  space  is  so  great  that  the  rate  at  which  it 
leaks  into  the  barrel  is  far  inferior  to  the  rate  at  which  the  pump  is  exhausting 
air  from  the  receiver.  And  Clerk  Maxwell  has  shown  that  the  internal 
friction  is  not  diminished  even  when  its  density  is  greatly  reduced.  Hence 
the  pump  works  very  satisfactorily  up 
to  a  considerable  degree  of  exhaustion 
— to  a  millimetre  of  mercury,  for  in- 
stance. 

195.  Sprengels  air-pump.— 
Sprengel  has  devised  a  form  of  air- 
pump  which  depends  on  the  principle 
of  converting  the  space  to  be  exhausted 
into  a  Torricellian  vacuum. 

If  an  aperture  be  made  in  the  top 
of  a  barometer  tube,  the  mercury  sinks 
and  draws  in  ai'r  ;  if  the  experiment 
be  so  arranged  as  to  allow  air  to  enter 
along  with  mercury,  and  if  the  supply 
of  air  be  limited  while  that  of  mercury 
is  unlimited,  the  air  will  be  carried 
away  and  a  vacuum  produced.  The 
following  is  the  simplest  form  of  the  ap- 
paratus in  which  this  action  is  realised. 
In  fig.  164  cd  is  a  glass  tube  longer 
than  a  barometer,  open  at  both  ends, 
and  connected,  by  means  of  india- 
rubber  tubing,  with  a  funnel,  A,  filled 
with  mercury  and  supported  by  a  stand. 
Mercury  is  allowed  to  fall  in  this  tube 
at  a  rate  regulated  by  a  clamp  at  c ; 
the  lower  end  of  the  tube  cd  fits  in  the 
flask  B,  which  has  a  spout  at  the  side 
a  little  higher  than  the  lower  end  of 
cd ;  the  upper  part  has  a  branch  at  x 
to  which  a  receiver  R  can  be  tightly 
fixed.  When  the  clamp  at  c  is  opened, 
the  first  portions  of  mercury  which  run 
out  close  the  tube  and  prevent  air 

from  entering  below.  As  the  mercury  is  allowed  to  run  down,  the  ex- 
haustion begins,  and  the  whole  length  of  the  tube  from  x  to  d  is  filled 
with  cylinders  of  air  and  mercury  having  a  downward  motion.  Air  and 
mercury  escape  through  the  spout  of  the  bulb  B  which  is  above  the  basin  A, 
where  the  mercury  is  collected.  It  is  poured  back  from  time  to  time  into 
the  funnel  A,  to  be  repassed  through  the  tube  until  the  exhaustion  is  com- 
plete. As  this  point  is  approached,  the  enclosed  air  between  the  mercury 


Fig.  164. 


1 62 


On  Gases. 


[195- 


cylinders  is  seen  to  diminish,  until  the  lower  part  of  cd  forms  a  continuous 
column  of  mercury  about  30  inches  high.  Towards  this  stage  of  the  process 
a  noise  is  heard  like  that  of  a  water-hammer  when  shaken  ;  the  operation  is 
completed  when  the  column  of  mercury  encloses  no  air,  and  a  drop  of  mercury 
falls  on  the  top  of  the  column  without  enclosing  the  slightest  air-bubble. 
The  height  of  the  column  then  represents  the  height  of  the  column  of 
mercury  in  the  barometer  ;  in  other  words  it  is  a  barometer  whose  Torricellian 
vacuum  is  the  receiver  R.  This  apparatus  has  been  used  with  great  success 
in  experiments  in  which  a  very  complete  exhaustion  is  required,  as  in  the 
preparation  of  Geissler's  tubes.  (See  Book  X.  Chapter  VI.)  It  may  be 
advantageously  combined  with  an  exhausting  syringe,  which  first  removes 
the  greater  part  of  the  air,  the  exhaustion  being  then  completed  as  above. 

The  most  perfect  vacua  are  obtained  by  absorbing  the  residual  gas,  after 
the  exhaustion  has  been  pushed  as  far  as  possible,  either  mechanically,  or 
by  some  substance  with  which  it  combines  chemically.  Thus  Dewar  has 
produced  a  vacuum  which  he  estimates  at  -^  of  a  millimetre  by  heating 
charcoal  to  redness,  in  a  vessel  from  which  air  had  been  exhausted  by  the 
Sprengel  pump,  and  then  allowing  it  to  cool.  Finkener  filled  a  vessel  with 

oxygen,  then  exhausted  as  far 
as  possible,  and  finally  heated 
to  redness  some  copper  con- 
tained in  the  vessel.  This  ab- 
sorbed the  minute  quantity  of 
gas  left,  with  the  formation  of 
cupric  oxide.  In  some  of  his 
experiments  Crookes  obtained 
by  chemical  means  a  vacuum  of 
is^oo  °f  a  millimetre.  In  these 
highly  rarefied  gases  the  pres- 
sure is  so  low  that  it  is  very 
difficult  to  measure  minute  dif- 
ferences. For  such  cases 
McLeod  has  devised  a  very 
valuable  method,  the  principle 
of  which  is  to  condense  a  mea- 
sured volume  of  the  highly 
rarefied  gas  to  a  much  smaller 
volume,  and  then  to  measure 
its  pressure  under  the  new  con- 
ditions. 

196.  Bunsen's  filter  pump. 
—This  is  a  very  convenient 
arrangement  for  producing  a 
vacuum  in  cases  where  a  good 
supply  of  water  is  available,  as 
in  laboratories.  Its  principle  is 
the  same  as  that  of  Sprengel's  pump.  A  composition  tube  a  (fig.  165), 
connected  with  the  service-pipe  of  a  water-supply,  is  joined  by  means  of  a 
caoutchouc  tube  to  a  glass  tube  cdf,  to  which  is  attached  at  /"a  leaden  tube 


Fig.  165. 


_198]  Morrerfs  Mercury  Pump.  163 

about  10  to  12  yards 'long.  The  tube  sr  is  connected  with  the  space  to  be 
exhausted.  The  water  enters  by  a,  and  in  falling  down  the  tube  carries 
with  it  air  from  the  space  to  be  exhausted.  The  supply  of  water,  and 
therewith  the  rate  of  exhaustion,  can  be  regulated  by  the  stopcock  b  ;  the 
bent  tube,  pq,  which  contains  mercury,  measures  the  degree  of  exhaustion, 
which  may  be  reduced  to  a  pressure  of  10  to  15  millimetres. 

197.  Aspirating:  action  of  currents  of  air. — When  a  jet  of  liquid  or  of 
a  gas  passes  through  air  it  carries  the  surrounding  air  along  with  it ;    fresh 
air  rushes  in  to  supply  its  place,  comes  also  in  contact  with  the  jet,  and  is  in 
like  manner  carried  away.     Thus,  then,  there  is  a   continual  rarefaction 
of  the  air  around  the  jet,  in  consequence  of  which  it  exerts  an  aspiratory 
action. 

This  phenomenon  may  be  well  illustrated  by  means  of  an  apparatus  re- 
presented in  fig.  1 66,  the  analogy  of  which  to  the  experiment  described  (213) 
will  be  at  once  evident.    It  consists  of  a  wide 
glass  tube  in  the  two  ends  of  which  are  fitted 
two   small  tubes  nd  and  B  ;  in  the  bottom 
is  a  manometer  tube  containing  a  coloured 
liquid.    On  blowing  through  the  narrow  tube 
the  liquid  at  o  is  seen  to  rise.    If,  on  the  con- 
trary, the  wide  tube  be  blown  into,  a  depres- 
sion is  produced  at  o. 

To  this  class  of  phenomena  belongs  the 
following  experiment,  which  is  a  simple  mo- 
dification by  Faraday  of  one  originally  de-  Fig.  166. 
scribed  by  Clement  and  Desormes.    Holding 

one  hand  horizontal,  the  palm  downwards  and  the  fingers  closed,  you  blow 
through  the  space  between  the  index  and  middle  finger.  If  a  piece  of  light 
paper,  of  2  or  3  square  inches,  is  held  against  the  aperture,  it  does  not  fall  as 
long  as  the  blowing  continues. 

The  old  water-bellows  still  used  in  mountainous  places  where  there  is  a 
continuous  fall  is  a  further  application  of  the  principle.  Water  falling  from 
a  reservoir  down  a  narrow  tube  divides  and  carries  air  along  with  it ;  and  if 
there  are  apertures  in  the  side  through  which  air  can  enter,  this  also  is 
carried  along,  and  becomes  accumulated  in  a  reservoir  placed  below,  from 
which  by  means  of  a  lateral  tube  it  can  be  directed  into  the  hearth  of  a 
forge. 

By  the  locomotive  steampipe  a  jet  of  steam  entering  the  chimney  of  the 
locomotive  carries  the  air  away,  so  that  fresh  air  must  arrive  through  the 
fire  and  thus  the  draught  be  kept  up.  In  Gijfard^s  injector  water  is  pumped 
by  means  of  a  jet  of  steam  into  the  boiler  of  a  steam-engine. 

198.  Morren's  mercury  pump. — Figs.  167  and  168  represent  a  mercu- 
rial air-pump,  which  is  an  improvement  by  Alvergniat  of  a  form  devised  by 
Morren. 

It  consists  of  two  reservoirs,  A  and  B,  figs.  167  and  168,  connected  by  a 
barometer  tube  T  and  a  long  caoutchouc  tube  C.  The  reservoir  B  and  the 
tube  T  are  fixed  to  a  vertical  support  A,  which  is  movable  and  open,  and 
can  be  alternately  raised  and  lowered  through  a  distance  of  nearly  four  feet. 
This  is  effected  by  means  of  a  long  wire  rope,  which  is  fixed  at  one  end  to 


164 


On  Gases. 


[198- 


the  reservoir  A,  and  passes  over  two  pulleys,  a  and  £,  the  latter  of  which  is 
turned  by  a  handle.  Above  the  reservoir  B  is  a  three-way  cock  n  ;  to  this  is 
attached  a  tube  d,  for  exhaustion,  and  on  the  left  is  an  ordinary  stopcock  m, 
which  communicates  with  a  reservoir  of  mercury  v,  and  with  the  air.  The 
exhausting  tube  d  is  not  in  direct  communication  with  the  receiver  to  be  ex- 
hausted ;  it  is  first  connected  with  a  reservoir  0,  partially  filled  with  sulphuric 
acid,  and  designed  to  dry  the  gases  which  enter  the  apparatus.  A  caout- 


Fig.  167. 


Fig.  168. 


chouc  tube,  c,  makes  communication  with  the  receiver  which  is  to  be  ex- 
hausted.    On  the  reservoir  o  is  a  small  mercury  manometer^. 

These  details  being  understood,  suppose  the  reservoir  A  at  the  top  of  il 
course  (fig.  167),  the  stopcock  m  open,  and  the  stopcock  n  turned  as  seen  ii 
Z  ;  the  caoutchouc  tube  C,  the  tube  T,  the  reservoir  B,  and  the  tube  above 
are  filled  with  mercury  as  far  as  v  ;  closing  then  the  stopcock  ;;/,  and  lower- 
ing the  reservoir  A  (fig.  168),  the  mercury  sinks  in  the  reservoir  B,  and  in  the 


-200] 


Uses  of  the  Air- Pump. 


165 


tube  T,  until  the  difference  of  levels  in  the  two  tubes  is  equal  to  the  baro- 
metric height,  and  there  is  a  vacuum  in  the  reservoir  B.  Turning  now  the 
stopcock  ;/,  as  shown  in  figure  X,  the  gas  from  the  space  to  be  exhausted 
passes  into  the  barometric  chamber  B,  by  the  tubes  c  and  d,  and  the  level 
again  sinks  in  the  tube  T.  The  stopcocks  are  now  replaced  in  the  first  posi- 
tion (fig.  Z),  and  the  reservoir  A  is  again  lifted,  the  excess  of  pressure  of 
mercury  in  the  caoutchouc  tube  expels  through  the  stopcocks  n  and  m  the 
gas  which  had  passed  into  the  chamber  B,  and  if  a  few  droplets  of  mercury 
are  carried  along  with  them  they  are  collected  in  the  vessel  v.  The  pro- 
cess is  repeated  until  the  mercury  is  virtually  at  the  same  level  in  both 

°  Like  Sprengel's  pump,  this  is  very  slow  in  its  working,  and,  like  it,  is  best 
employed  in  completing  the  exhaustion  of  a  space  which  has  already  been 
partially  rarefied  ;  for  a  vacuum  of  i  of  a  millimetre  may  be  obtained 
by  its  means. 

199.  condensing  pump.— The  condensing  pump  is  an  apparatus  for 
compressing  air,  or  any  other  gas.  The  form  usually  adopted  is  the  follow- 
ing :_in  a  cylinder,  A,  of  small  diameter 
(fig.  170),  there  is  a  solid  piston,  the  rod 
of  which  is  moved  by  the  hand.  The 
[  cylinder  is  provided  with  a  screw  which 
;  fits  into  the  receiver  K.  Fig.  169  shows 
the  arrangement  of  the  valves,  which  are 
so  constructed  that  the  lateral  valve  o 
opens  from  the  outside,  and  the  lower 
valve  s  from  the  inside. 

When  the  piston  descends,  the  valve 
10  closes,  and  the  elastic  force  of  the  com- 
pressed air  opens  the  valve  j,  which  thus 
allows   the   compressed  air  to  pass  into 
the  receiver.     When  the  piston  ascends, 
\s  closes   and  o  opens,  and   permits   the 
entrance  of  fresh  air,  which  in  turn  be- 
comes compressed  by  the  descent  of  the 
piston,  and  so  on. 

This  apparatus  is  chiefly  used  for 
charging  liquids  with  gases.  For  this 
purpose  the  stopcock  B  is  connected  with 
a  reservoir  of  the  gas,  by  means  of  the 
tube  D.  The  pump  exhausts  this  gas, 
and  forces  it  into  the  vessel  K,  in  which 
the  liquid  is  contained.  The  artificial 
gaseous  waters  are  made  by  means  of 
analogous  apparatus. 

The  principle  of  the  condensing  pump  has  many  applications,  such  as  in 
the  small  pump  used  by  plumbers  for  testing  and  for  clearing  gas  pipes,  in 
ventilating  mines,,  in  supplying  air  to  blast  furnaces,  and  so  forth. 

200.  Uses  of  the  air-pump. — A  great  many  experiments  with  the  air- 
pump  have  been  already  described.  Such  are  the  mercurial  rain  (13),  the 


Fig.  170. 


1 66 


On  Gases. 


[200 


fall  of  bodies  in  vacuo  (77),  the  bladder  (147),  the  bursting  of  a  bladder  (153), 
the  Magdeburg  hemispheres  (154),  and  the  baroscope  (184). 

The  fountain  in  vacuo  (fig.  171)  is  an  experiment  made  with  the  air-pump, 
and  shows  the  elastic  force  of  the  air.  It  consists  of  a  glass  vessel.  A, 

provided  at  the 
bottom  with  a 
stopcock,  and  a 
tubulure  which 
projects  into  the 
interior.  Having 
screwed  this  ap- 
paratus to  the 
air-pump  it  is  ex- 
hausted, and,  the 
stopcock  being 
closed,  it  is 
placed  in  a  vessel 
of  water,  R. 
Opening  then  the 
stopcock,  the  at- 
mospheric pres- 
sure upon  the 
water  in  the  ves- 
sel makes  it  jet 
HiiiiiiiiiiiinniiiiniiinimjB|i|iin[|ir  through  the  tu- 
bulure into  the 
interior  of  the 
vessel,  as  shown 
in  the  drawing. 

Fig.  172  represents  an  experiment  illustrating  the  effect  of  atmospheric 
pressure  on  the  human  body.  A  glass  vessel,  open  at  both  ends,  being  placed 
on  the  plate  of  the  machine,  the  upper  end  of  the  cylinder  is  closed  by  the 
hand,  and  a  vacuum  is  made.  The  hand  then  becomes  pressed  by  the 
weight  of  the  atmosphere,  and  can  only  be  taken  away  by  a  great  effort. 
And  as  the  elasticity  of  the  fluids  contained  in  the  organs  is  not  counter- 
balanced by  the  weight  of  the  atmosphere,  the  palm  of  the  hand  swells,  and 
blood  tends  to  escape  from  the  pores. 

By  means  of  the  air-pump  it  may  be  shown  that  air,  by  reason  of  the 
oxygen  it  contains,  is  necessary  for  the  support  of  combustion  and  of  life. 
For  if  we  place  a  lighted  taper  under  the  receiver,  and  begin  to  exhaust  the 
air,  the  flame  becomes  weaker  as  rarefaction  proceeds,  and  is  finally  extin- 
guished. Similarly  an  animal  faints  and  dies  if  a  vacuum  is  formed  in  a 
receiver  under  which  it  is  placed.  Mammalia  and  birds  soon  die  in  vacuo. 
Fish  and  reptiles  support  the  loss  of  air  for  a  much  longer  time.  Insects 
can  live  several  days  in  vacuo. 

Substances  liable  to  ferment  may  be  kept  in  vacuo  for  a  long  time  with- 
out alteration,  as  they  are  not  in  contact  with  oxygen,  which  is  necessary  for 
fermentation.  Food  kept  in  hermetically-closed  cases,  from  which  the  air 
had  been  exhausted,  has  been  found  as  fresh  after  several  years  as  on  the 
first  day. 


Fig.  172. 


_201]  Herds  Fountain.  167 

201.  Hero's  fountain.— Hero's  fountain,  which  derives  its  name  from  its 
inventor,  Hero,  who  lived  at  Alexandria,  120  B.C.,  depends  on  the  elasticity 
of  the  air.  It  consists  of 
a  brass  dish,  D  (fig.  173), 
and  of  two  glass  globes, 
M  and  X.  The  dish  com- 
municates with  the  lower 
part  of  the  globe  N  by  a 
long  tube,  B;  and  another 
tube,  A,  connects  the  two 
globes.  A  third  tube 
passes  through  the  dish 
D  to  the  lower  part  of 
the  globe  M.  This  tube 
having  been  taken  out, 
the  globe  M  is  partially 
filled  with  water,  the  tube 
is  then  replaced,  and 
water  is  poured  into  the 
dish.  The  water  flows 
through  the  tube  B  into 
the  lower  globe,  and  ex- 
pels the  air,  which  is 
forced  into  the  upper 
globe  ;  the  air,  thus  com- 
pressed, acts  upon  the 
water,  and  makes  it  jet 
out  as  represented  in  the 
figure.  If  it  were  not  for 
the  resistance  of  the  at- 
mosphere and  friction, 


Fig-  173- 


Fig.  174. 


the  liquid  would  rise  to  a  height  above  the  water  in  the  dish  equal  to  the 
difference  of  the  level  in  the  two  globes. 

202.  Intermittent  fountain. — The  intermittent  fountain  depends  partly 
on  the  elastic  force  of  the  air  and  partly  on  the  atmospheric  pressure.  It 
consists  of  a  stoppered  glass  globe  (C,  fig.  174),  provided  with  two  or  three 
capillary  tubulures,  D.  A  glass  tube  open  at  both  ends  reaches  at  one  end 
to  the  upper  part  of  the  globe  C  ;  the  other  end  terminates  just  above  a  little 
aperture  in  the  dish  B,  which  supports  the  whole  apparatus. 

The  water  with  which  the  globe  C  is  nearly  two-thirds  filled,  runs  out  by 
the  tubes  D,  as  shown  in  the  figure  ;  the  internal  pressure  at  D  being  equal 
to  the  atmospheric  pressure,  together  with  the  weight  of  the  column  of  water 
CD,  while  the  external  pressure  at  that  point  is  only  that  of  the  atmosphere. 
These  conditions  prevail  so  long  as  the  lower  end  of  the  glass  tube  is  open  ; 
that  is,  so  long  as  air  can  enter  C  and  keep  the  air  in  C  at  the  same  density 
as  the  external  air ;  but  the  apparatus  is  arranged  so  that  the  orifice  in  the 
dish  B  does  not  allow  so  much  water  to  flow  out  as  it  receives  from  the  tubes 
D,  in  consequence  of  which  the  level  gradually  rises  in  the  dish,  and  closes 
the  lower  end  of  the  glass  tube.  As  the  external  air  cannot  now  enter  the 


1 68  On  Gases.  [202- 

globe  C,  the  air  becomes  rarefied  in  proportion  as  the  flow  continues,  until 
the  pressure  of  the  column  of  water  CD,  together  with  the  tension  of  the  air 
contained  in  the  globe,  is  equal  to  this  external  pressure  at  D  ;  the  flow  con- 
sequently stops.  But  as  water  continues  to  flow  out  of  the  dish  B,  the  tube 
D  becomes  open  again,  air  enters,  and  the  flow  recommences,  and  so  on,  as 
long  as  there  is  water  in  the  globe  C. 

203.  Tine  syphon. — The  syphon  is  a  bent  tube  open  at  both  ends,  and 
with  unequal  legs  (fig.  175).     It  is  used  in  transferring  liquids  in  the  following 

manner  : — The  syphon  is  filled  with  some 
liquid,  and,  the  two  ends  being  closed, 
the  shorter  leg  is  dipped  in  the  liquid,  as 
represented,  in  fig.  175  ;  or  the  shorter  leg 
having  been  dipped  in  the  liquid,  the  air 
is  exhausted  by  applying  the  mouth  at  B. 
A  vacuum  is  thus  produced,  the  liquid  in 
C  rises  and  fills  the  tube  in  consequence 
of  the  atmospheric  pressure.  It  will  then 
run  out  through  the  syphon  as  long  as  the 
shorter  end  dips  in  the  liquid. 

To  explain  this  flow  of  water  from  the 
syphon,  let  us  suppose  it  filled  and  the 
short  leg  immersed  in  the  liquid.  The 
pressure  then  acting  on  C,  and  tending  to 
raise  the  liquid  in  the  tube,  is  the  atmo- 
spheric pressure  minus  the  height  of  the 
column  of  liquid  DC.  In  like  manner, 

the  pressure  on  the  end  of  the  tube,  B,  is  the  weight  of  the  atmosphere  less 
the  pressure  of  the  column  of  liquid  AB.  But  as  this  latter  column  is  longer 
than  CD,  the  force  acting  at  B  is  less  than  the  force  acting  at  C,  and  con- 
sequently a  flow  takes  place  proportional  to  the  difference  between  these 
two  forces.  The  flow  will  therefore  be  more  rapid  in  proportion  as  the 
difference  of  level  between  the  aperture  B  and  the  surface  of  the  liquid  in  C 
is  greater. 

It  follows  from  the  theory  of  the  syphon  that  it  would  not  work  in  vacuo, 
nor  if  the  height  CD  were  greater  than  that  of  a 
column  of  liquid  which  counterbalances  the  atmo- 
spheric pressure. 

204.  The  intermittent  syphon. — In  the  inter- 
mittent syphon  the  flow  is  not  continuous.  It  is 
arranged  in  a  vessel,  so  that  the  shorter  leg  is  near 
the  bottom  of  the  vessel,  while  the  longer  leg  passes 
through  it  (fig.  176).  Being  fed  by  a  constant  sup- 
ply of  water,  the  level  gradually  rises  both  in  the 
vessel  and  in  the  tube  to  the  top  of  the  syphon, 
which  it  fills,  and  water  begins  to  flow  out.  But  the 
apparatus  is  arranged  so  that  the  flow  of  the  syphon 
is  more  rapid  than  that  of  the  tube  which  supplies 

the  vessel,  and  consequently  the  level  sinks  in  the  vessel  until  the  shorter 
branch  no  longer  dips  in  the  liquid  ;  the  syphon  is  then  empty,  and  the  flow 


Fig.  176. 


-206]  Different  Kinds  of  Pumps.  1 69 

ceases.  But  as  the  vessel  is  continually  fed  from  the  same  source,  the  level 
again  rises,  and  the  same  series  of  phenomena  is  reproduced. 

The  theory  of  the  intermittent  syphon  explains  the  natural  intermittent 
springs  which  are  found  in  many  countries,  and  of  which  there  is  an  excel- 
lent example  near  Giggleswick  in  Yorkshire.  Many  of  these  springs  furnish 
water  for  several  days  or  months,  and  then,  after  stopping  for  a  certain  in- 
terval, again  recommence.  In  others  the  flow  stops  and  recommences 
several  times  in  an  hour. 

These  phenomena  are  explained  by  assuming  that  there  are  subterranean 
fountains,  which  are  more  or  less  slowly  filled  by  springs,  and  which  are  then 
emptied  by  fissures  so  occurring  in  the  ground  as  to  form  an  intermittent 
syphon. 

205.  Different  kinds  of  pumps. — Pumps  are  machines  which  serve  to 
raise  water  either  by  suction,  by  pressure,  or  by  both  efforts  combined ;  they 
are  consequently  divided  into  suction  or  lift  pumps,  force  pumps,  and  suction 
and  forcing  pumps. 

The  various  parts  entering  into  the  construction  of  a  pump  are  the  barrel, 
the  piston,  the  valves,  and  the  pipes.  The  barrel  is  a  cylinder  of  metal  or 


Fig.  177.  Fig.  178. 

of  wood,  in  which  is  the  piston.  The  latter  is  a  metal  or  wooden  cylinder 
wrapped  with  tow,  and  working  with  gentle  friction  the  whole  length  of  the 
barrel. 

The  valves  are  discs  of  metal  or  leather,  which  alternately  close  the 
apertures  which  connect  the  barrel  with  the  pipes.  The  most  usual  valves 
are  the  clack  valve  (fig.  177)  and  the  conical  valve  (fig.  178).  The  first  is  a 
metal  disc  fixed  to  a  hinge  on  the  edge  of  the  orifice  to  be  closed.  In  order 
more  effectually  to  close  it,  the  lower  part  of  the  disc  is  covered  with  thick 
leather.  Sometimes  the  valve  consists  merely  of  a  leather  disc,  of  larger 
diameter  than  the  orifice,  nailed  on  the  edge  of  the  orifice.  Its  flexibility 
enables  it  to  act  as  a  hinge. 

The  conical  valve  consists  of  a  metal  cone  fitting  in  an  aperture  of  the 
same  shape.  Below  this  is  an  iron  loop,  through  which  passes  a  bolt-head 
fixed  to  the  valve.  The  object  of  this  is  to  limit  the  play  of  the  valve  when 
it  is  raised  by  the  water,  and. to  prevent  its  removal. 

206.  Suction  pump. — Fig.  179  represents  a  model  of  a  suction  pump  sucji 
as  is  used  in  lectures,  but  which  has  the  same  arrangement  as  the  pumps  in 
.common  use.  It  consists,  ist,  of  zglass  cylinder,  B,  at  the  bottom  of  which 
there  is  a  valve,  S,  opening  upwards  ;  .  2nd,  of  a  suction  tube,  A,  which 
dips  into  the  reservoir  from  which  water  is  to  be  raised  ;  3rd,  of  a  piston, 
which  is  moved  up  and  down  by  a  rod  worked  by  a  handle,  P.  The  piston 
is  perforated  by  a  hole  ;  the  upper  aperture  is  closed  by  a  valve,  O,  open- 
ing upwards. 

I 


I/O 


On  Gases. 


[206- 


When  the  piston  rises  from  the  bottom  of  the  cylinder  B,  a  vacuum  is 
produced  below,  and  the  valve  O  is  kept  closed  by  the  atmospheric  pres- 
sure, while  the  air  in  the  pipe  A,  in 
consequence  of  its  elasticity,  raises  the 
valve  S,  and  partially  passes  into  the 
cylinder.  The  air  being  thus  rarefied, 
water  rises  in  the  pipe  until  the  pres- 
sure of  the  liquid  column,  together 
with  the  tension  of  the  rarefied  air 
which  remains  in  the  tube,  counter- 
balances the  pressure  of  the  atmo- 
sphere on  the  water  of  the  reservoir. 

When  the  piston  descends,  the 
valve  S  closes  by  its  own  weight,  and 
prevents  the  return  of  the  air  from  the 
cylinder  into  the  tube  A.  The  air 
compressed  by  the  piston  opens  the 
valve  O,  and  escapes  into  the  atmo- 
sphere by  the  pipe  C.  With  a  second 
stroke  of  the  piston  the  same  series  ot 
phenomena  is  produced,  and  after  a 
few  strokes  the  water  reaches  the 
cylinder.  The  effect  is  now  somewhat 
modified  ;  during  the  descent  of  the 
piston,  the  valve  S  closes,  and  the 
water  raises  the  valve  O,  and  passes 
above  the  piston  by  which  it  is  lifted 
into  the  upper  reservoir  D.  There  is 
now  no  more  air  in  the  pump,  and  the 
water  forced  by  the  atmospheric  pres- 
sure rises  with  the  piston,  provided 
that  when  it  is  at  the  summit  of  its  course  it  is  not  more  than  34  feet 
above  the  level  of  the  water  in  which  the  tube  A  dips,  for  we  have  seen 
(156)  that  a  column  of  water  of  this  height  is  equal  to  the  pressure  of  the 
atmosphere. 

In  practice  the  height  of  the  tube  A  does  not  exceed  26  to  28  feet, 
for,  although  the  atmospheric  pressure  can  support  a  higher  column,  the 
vacuum  produced  in  the  barrel  is  not  perfect,  owing  to  the  fact  that  the  piston 
does  not  fit  exactly  on  the  bottom  of  the  barrel.  But  when  the  water 
has  passed  the  piston,  it  is  the  ascending  force  of  the  latter  which  raises  it, 
and  the  height  to  which  it  can  be  brought  depends  on  the  force  which  moves 
the  piston. 

207.  Suction  and  force  pump. — The  action  of  this  pump,  a  model  of 
which  is  represented  in  fig.  180,  depends  both  on  exhaustion  and  on  pressure. 
At  the  base  of  the  barrel,  where  it  is  connected  with  the  tube  A,  there  is  a 
valve,  S,  which  opens  upwards.  Another  valve,  O,  opening  in  the  same 
direction,  closes  the  aperture  of  a  conduit,  which  passes  from  a  hole,  o,  near 
the  valve  S  into  a  vessel  M,  which  is  called  the  air  chamber.  From  this 
chamber  there  is  another  tube,  D,  up  which  the  water  is  forced. 


Fig.  179. 


-208] 


Pumps. 


At  each  ascent  of  the  piston  B,  which  is  solid,  the  water  rises  through 
the  tube  A  into  the  barrel.  When  the  piston  sinks,  the  valve  S  closes,  and 
the  water  is  forced  through  the  valve  O  into  the  reservoir  M,  and  from  thence 
into  the  tube  D.  The  height  to  which  it  can  be  raised  in  this  tube  depends 
solely  on  the  motive  force  which  works  the  pump. 

If  the  tube  D  were  a  prolongation  of  the  tube  ]ao,  the  flow  would  be  in- 
termittent ;  it  would  take  place  when  the  piston  descended,  and  would  cease 
as  soon  as  it  ascended.  But  between  these  tubes  there  is  an  interval,  which, 
by  means  of  the  air  in  the  reservoir  M,  ensures  a  continuous  flow.  The 
water  forced  into  the  reservoir  M  divides  into  two  parts,  one  of  which,  rising 
in  D,  presses  on  the  water  in  the  reservoir  by  its  weight  ;  while  the  other,  in 
virtue  of  this  pressure,  rises  in  the  reservoir  above  the  lower  orifice  of  the 


Fig.  180. 


tube  D,  compressing  the  air  above.  Consequently,  when  the  piston  ascends, 
and  no  longer  forces  the  water  into  M,  the  air  of  the  reservoir,  by  the  pressure 
it  has  received,  reacts  on  the  liquid,  and  raises  it  in  the  tube  D,  until  the 
piston  again  descends,  so  that  the  jet  is  continuous. 

208.  load  which  the  piston  supports. — In  the  suction  pump,  when 
once  the  water  fills  the  pipe,  and  the  barrel,  as  far  as  the  spout,  the  effort 
necessary  to  raise  the  piston  is  equal  to  the  'weight  of  a  column  of  water,  the 
base  of  which  is  this  piston^  and  the  height  the  vertical  distance  of  the  spout 

1  2 


172 


On  Gases. 


[208- 


from  the  level  of  the  water  in  the  reservoir;  that  zV,  the  height  to  which  the 
water  is  raised.  For  if  H  is  the  atmospheric  pressure,  h  the  height  of  the 
water  above  the  piston,  and  h'  the  height  of  the  column  which  fills  the  suction 
tube  A  (fig.  1 80),  and  the  lower  part  of  the  barrel,  the  pressure  above  the 
piston  is  obviously  H  +  //,  and  that  below  is  H-/J',  since  the  weight  of  the 
column  h'  tends  to  counterbalance  the  atmospheric  pressure.  But  as  the 
pressure  H— //  tends  to  raise  the  piston,  the  effective  resistance  is  equal  to 
the  excess  of  H  +/i  over  H  -h',  that  is  to  say,  to  h  +  h'. 

In  the  suction  and  force  pump  it  is  readily  seen  that  the  pressure  which 
the  piston  supports  is  also  equal  to  the  weight  of  a  column  of  water,  the  base 
of  which  is  the  section  of  the  piston,  and  the  height  that  to  which  the  water 
is  raised.  .  .  .  .. 

209.  Fire  engine. — The  fire  engine  is  a  force  pump  in  which  a  steady  jet 
is  obtained  by  the  aid  of  an  air  chamber,  and  also  by  two  pumps  working 
alternately  (fig.  181).  The  two  pumps  m  and  ;/,  worked  by  the  same  lever 


Fig.  1 8 1. 

PQ,  are  immersed  in  a  tank,  which  is  kept  filled  with  water  as  long  as  the 
pump  works.  From  the  arrangement  of  the  valves  it  will  be  seen,  that  when 
one  pump  n  draws  water  from  the  tank,  the  other  m  forces  it  into  the  air 
chamber  R  ;  whence,  by  an  orifice  Z,  it  passes  into  the  delivery  tube,  by 
which  it  can  be  sent  in  any  direction. 

Without  the  air  chamber  the  jet  would  be  intermittent.  But  as  the  velo- 
city of  the  water  on  entering  the  reservoir  is  less  than  on  emerging,  the  level 
of  the  water  rises  above  the  orifice  Z,  compressing  the  air  which  fills  the 
reservoir.  Hence,  whenever  the  piston  stops,  the  air  thus  compressed,  re- 
acting on  the  liquid,  forces  it  out  during  its  momentary  stoppage,  and  thus 
keeps  up  a  constant  flow. 


-211] 


Velocity  of  Efflux. 


173 


210.  Velocity  of  efflux.  Torricelli's  theorem. —  Let  us  imagine  an 
aperture  made  in  the  bottom  of  any  vessel,  and  consider  the  case  of  a  par- 
ticle of  liquid  on  the  surface,  without  reference  to  those  which  are  beneath. 
If  this  particle  fell  freely,  it  would  have  a  velocity  on  reaching  the  orifice  equal 
to  that  of  any  other  body  falling  through  the  distance  between  the  level  of  the 
liquid  and  the  orifice.  This,  from  the  laws  of  falling  bodies,  is  -Jzgh,  in  which 
g  is  the  accelerating  force  of  gravity,  and  h  the  height.  If  the  liquid  be  main- 
tained at  the  same  level,  for  instance,  by  a  stream  of  water  running  into  the 
vessel  sufficient  to  replace  what  has  escaped,  the  particles  will  follow  one 
another  with  the  same  velocity,  and  will  issue  in  the  form  of  a  stream.  Since 
pressure  is  transmitted  equally  in  all  directions,  a  liquid  would  issue  from 
an  orifice  in  the  side  with  the  same  velocity  provided  the  depth  were  the 
same. 

The  law  of  the  velocity  of  efflux  was  discovered  by  Torricelli.  It  may  be 
enunciated  as  follows  : — The  velocity  of  efflux  is  the  velocity  which  a  freely 
falling  body  would  have  on  reaching  the  orijice  after  having  started  from  a 
state  of  rest  at  the  surface.  It  is  algebraically  expressed  by  the  formula 


It  follows  directly  from  this  law  that  the  velocity  of  efflux  depends  on  the 
depth  of  the  orifice  below  the  surface,  and  not  on  the  nature  of  the  liquid. 
Through  orifices  of  equal  size  and  of  the  same  depth,  water  and  mercury 
would  issue  with  the  same  velocity,  for  although  the  density  of  the  latter 
liquid  is  greater,  the  weight  of  the  column,  and  consequently  the  pressure,  is 
greater  too.  It  follows  further  that  the  velocities  of  efflux  are  directly  pro- 
portional to  the  square  roots  of  the  depth  of  the  orifices.  Water  would  issue 
from  an  orifice  100  inches  below  the  surface  with  ten  times  the  velocity  with 
which  it  would  issue  from  one  an  inch  below  the  surface. 

The  quantities  of  water  which  issue  from  orifices  of  different  areas  are 
very  nearly  proportional  to  the  size  of  the  orifice,  provided  the  level  remains 
constant. 

211.  Direction  of  the  jet  from  lateral  orifices. — From  the  principle  of 
the  equal  transmission  of  pressure,  water  issues  from  an  orifice  in  the  side  of  a 
vessel  with  the  same  velocity  as  from 
an  aperture  in  the  bottom  of  a  vessel 
at  the  same  depth.  Each  particle  of 
a  jet  issuing  from  the  side  of  a  vessel 
begins  to  move  horizontally  with  the 
velocity  above  mentioned,  but  it  is  at 
once  drawn  downward  by  the  force 
of  gravity  in  the  same  manner  as  a 
bullet,  fired  from  a  gun,  with  its  axis 
horizontal.  It  is  well  known  that 


Fig.  182. 


the  bullet  describes  a  parabola  (50) 

with  a  vertical  axis,  the  vertex  being 

the  muzzle  of  the  gun.     Now  since 

each   particle  of  the  jet  moves  in  the  same  curve,  the  jet  itself  takes  the 

parabolic  form,  as  shown  in  fig.  182. 

In  every  parabola  there  is  a  certain  point   called  the  focus,  and   the 
distance  from  the  vertex  to  the  focus  fixes  the  magnitude  of  a  parabola  in 


174  On  Gases.  [211- 

much  the  same  manner  as  the  distance  from  the  centre  to  the  circumference 
fixes  the  magnitude  of  a  circle.  Now  it  can  easily  be  proved  that  the  focus 
is  as  much  below,  as  the  surface  of  the  water  is  above,  the  orifice.  Accord- 
ingly the  jets  formed  by  water  coming  from  orifices  at  different  depths  below 
the  surface  take  different  forms  as  shown  in  fig.  182. 

212.  Height  of  the  jet. — If  a  jet  issuing  from  an  orifice  in  a  vertical  direc- 
tion has  the  same  velocity  as  a  body  would  have  which  fell  from  the  surface 
of  the  liquid  to  that  orifice,  the  jet  ought  to  rise  to  the  level  of  the  liquid.     I 
does  not,  however,  reach  this  ;  for  the  particles  which  fall  hinder  it.     But  by 
inclining  the  jet  at  a  small  angle  with  the  vertical,  it  reaches  about  —  of 
the  theoretical  height,  the  difference  being  due  to  friction  and  to  the  resist- 
ance of  the  air.     By  experiments  of  this  nature  the  truth  of  Torricelli's  law 
has  been  demonstrated. 

213.  Quantity  of  efflux.     Vena  contracta. — If  we  suppose  the  sides  of 
a  vessel  containing  water  to  be  thin,  and  the  orifice  to  be  a  small  circle  whose 
area  is  A,  we  might  think  that  the  quantity  of  water  E  discharged  in  a  second 
would  be  given  by  the  expression  A\/2g/i,  since  each  particle  has,  on  the 
average,  a  velocity  equal  to  *j2gh,  and  particles  issue  from  each  point  of  the 
orifice.     But  this  is  by  no  means  the  case.     This  may  be  explained  by  re- 
ference to  fig.  179,  in  which  AB  represents  an  orifice  in  the 
bottom  of  a  vessel — what  is  true  in  this  case  being  equally 
true  of  an  orifice  in  the  side  of  the  vessel.     Every  particle 
above  AB  endeavours  to  pass  out  of  the  vessel,  and  in  so 
doing  exerts  a  pressure  on  those  near  it.     Those  that  issue 
near  A  and  B  exert  pressures  in  the  directions  MM  and  NN  ; 
those  near  the  centre  of  the  orifice  in  the  direction  RQ,  those 
in  the  intermediate  parts  in  the  directions  PQ,  PQ.     In  con- 
sequence,  the  water  within    the    space    POP    is    unable  to 

Fig.  183.  escape,  and  that  which  does  escape,  instead  of  assuming  a 
cylindrical  form,  at  first  contracts,  and  takes  the  form  of  a 
truncated  cone.  It  is  found  that  the  escaping  jet  continues  to  contract,  until 
at  a  distance  from  the  orifice  about  equal  to  the  diameter  of  the  orifice.  This 
part  of  the  jet  is  called  the  vena  co?itracta.  It  is  found  that  the  area  of  its 
smallest  section  is  about  f  or  0-62  of  that  of  the  orifice.  Accordingly,  the 
true  value  of  the  efflux  per  second  is  given  approximately  by  the  formula 

E  =  o-62Av/2^ 

or  the  actual  value  of  E  is  about  0*62  of  its  theoretical  amount. 

214.  Influence  of  tubes  on  the  quantity  of  efflux. — The  result  given 
in  the  last  article  has  reference  to  an  aperture  in  a  thin  wall.  If  a  cylindrical 
or  conical  efHux  tube  or  ajutage  is  fitted  to  the  aperture,  the  amount  of  the 
efflux  is  considerably  increased,  and  in  some  cases  falls  but  a  little  short  of 
its  theoretical  amount. 

A  short  cylindrical  ajutage,  whose  length  is  from  two  to  three  times 
its  diameter,  has  been  found  to  increase  the  efHux  per  second  to  about 
0-82  A -v/2^.  In  this  case,  the  water  on  entering  the  ajutage  forms  a  con- 
tracted vein  (fig.  184),  just  as  it  would  do  on  issuing  freely  into  the  air; 
but  afterwards  it  expands,  and,  in  consequence  of  the  adhesion  of  the  water 
to  the  interior  surface  of  the  tube,  has,  on  leaving  the  ajutage,  a  section 


-215] 


Quantity  of  Efflux. 


175 


greater  than  that  of  the  contracted  vein.  The  contraction  of  the  jet  within 
the  ajutage  causes  a  partial  vacuum.  If  an  aperture  is  made  in  the  ajutage, 
near  the  point  of  greatest  contraction,  and  is  fitted  with  a  vertical  tube,  the 
other  end  of  which  dips  into  water  (fig.  184,)  it  is 
found  that  wa'er  rises  in  the  vertical  tube,  thereby 
proving  the  formation  of  a  partial  vacuum. 

If  the  ajutage  has  the  form  of  a  conic  frustrum 
whose  larger  end  is  at  the  aperture,  the  efflux  in 
a  second  may  be  raised  to  0-92  A  \/2£-//,  provided 
the  dimensions  are  properly  chosen.  If  the 
smaller  end  of  a  frustrum  of  a  cone  of  suitable 
dimensions  be  fitted  to  the  orifice,  the  efflux  may 
be  still  further  increased,  and  fall  very  little  short 
of  the  theoretical  amount. 

When  the  ajutage  has  more  than  a  certain 
length,  a  considerable  diminution  takes  place  in 
the  amount  of  the  efflux  :  for  example,  if  its  length 
is  48  times  its  diameter,  the  efflux  is' reduced  too*63Av/2^'//.  This  arises  from 
the  fact,  that,  when  water  passes  along  cylindrical  tubes,  the  resistance  in- 
creases with  the  length  of  the  tube  ;  for  a  thin  layer  of  liquid  is  attracted  to 
the  walls  by  adhesion,  and  the  internal  flowing  liquid  rubs  against  this. 
The  resistance  which  gives  rise  to  this  result  is  called  hydraulic  friction  :  it 
is  independent  of  the  material  of  the  tube,  provided  it  be  not  roughened  ; 
but  depends  in  a  considerable  degree  on  the  viscosity  of  the  liquid  ;  for 
instance,  ice-cold  water  experiences  a  greater  resistance  than  lukewarm 
water. 

According  to  Prony,  the  mean  velocity  v  of  water  in  a  cast-iron  pipe,  ot 
the  length  /,  and  the  diameter  d,  under  the  pressure  /,  is  in  metres 


-**  A/?' 


By  means  of  hydraulic  pressure  Tresca  has  submitted  solids  such  as 
silver,  lead,  iron  and  steel,  powders  like  sand,  soft  plastic  substances  such  as 
clay,  and  brittle  bodies  like  ice,  to  such  enormous  pressures  as  100,000  kilo- 
grammes, and  has  found  that  they  then  behave  like  fluid  bodies.  His  ex- 
periments show  also  that  these  bodies  transmit  pressure  equally  in  all 
directions,  when  this  pressure  is  considerable  enough. 

215.  Efflux  through  capillary  tubes. — This  was  investigated  by 
Poisseuille  by  means  of  the  apparatus  represented  in  fig.  185,  in  which  the 
capillary  tube  AB  is  sealed  to  a  glass  tube  on  which  a  bulb  is  blown.  The 
volume  of  the  space  between  the  marks  M  and  N  is  accurately  determined, 
and  the  apparatus  having  been  filled  with  the  liquid  under  examination  by 
suction,  the  apparatus  is  connected  at  the  end  M,  with  a  reservoir  of  com- 
pressed air,  in  which  the  pressure  is  measured  by  means  of  a  mercury  mano- 
meter. The  time  is  then  noted  which  is  required  for  the  level  of  the  liquid 
to  sink  from  M  to  N,  the  pressure  remaining  constant.  Poisseuille  thus  found 
that  q,  the  quantity  which  flows  out  in  a  given  time,  is  represented  by  the 
formula 


176 


On  Gases. 


[215- 


where/  is  the  pressure,  d  the  diameter,  and  /  the  length  of  the  tube,  while  k 
is  a  constant,  which   varies  with  the  nature  of  the  liquid  ;  and  is  greatly 

influenced  by  the  tempera- 
ture. An  increase  from  o° 
to  60°  C  increases  the  quan- 
tity threefold. 

216.  Form  of  the  jet. — 
After  the  contracted  vein, 
the  jet  has  the  form  of  a  solid 
rod  for  a  short  distance,  but 
then  begins  to  separate  into 
drops,  which  present  a  pecu- 
liar appearance.  They  seem 
to  form  a  series  of  ventral 
and  nodal  segments  (fig. 
1 86).  The  ventral  segments 
Fig.  185.  consist  of  drops  extended  in 

a  horizontal  direction,  and 
the  nodal  segments  in  a  longitudinal  direction. 

And  as  the  ventral  and  nodal  segments  have  respectively  a  fixed  position, 
each  drop  must  alternately  become  elongated  and  flattened  while  it  is  falling 
(fig.  187).  Between  any  two  drops  there  are  smaller  ones,  so  that  the  whole 
jet  has  a  tube-like  appearance. 

If  the  jet  is  momentarily  illuminated  by  the  electric  spark  its  structure  is 
well  seen  ;  the  drops  appear  then  to  be  stationary,  and  separate  from  each 
other. 

If  the  aperture  is  not  circular  the  form  of  the  jet  undergoes  curious 
changes. 

217.  Hydraulic  tourniquet. — If  water  be  contained  in  a  vessel,  and  an 
aperture  be  made  in  one  of  the  sides,  the  pressure  at  this  point  is  removed, 
for  it  is  expended  in  sending  out  the  water :  but  it  remains  on  the  other  side  ; 
and  if  the  vessel  were  movable  in  a  horizontal  direction,  it  would  move  in  a 
direction  opposite  that  of  the  issuing  jet.  This  is  illustrated  by  the  appa- 
ratus known  as  the  hydraulic  tourniquet  or  Barkers  mill  (fig.  188).  It  con- 
sists of  a  glass  vessel,  M,  containing  water,  and  capable  of  moving  about  its 
vertical  axis.  At  the  lower  part  there  is  a  tube,  C,  bent  horizontally  in  oppo- 
site directions  at  the  two  ends.  If  the  vessel  were  full  of  water  and  the  tubes 
closed,  the  pressure  on  the  sides  of  C  would  balance  each  other,  being  equal 
and  acting  in  contrary  directions  ;  but,  being  open,  the  water  runs  out,  the 
pressure  is  not  exerted  on  the  open  part,  but  only  on  the  opposite  side,  as 
shown  in  the  figure  A.  And  this  pressure,  not  being  neutralised  by  an  oppo- 
site pressure,  imparts  a  rotatory  motion  in  the  direction  of  the  arrow,  the 
velocity  of  which  increases  with  the  height  of  the  liquid  and  the  size  of  the 
aperture. 

The  same  principle  may  be  illustrated  by  the  following  experiment.  A 
tall  cylinder  containing  water  and  provided  with  a  lateral  stopcock  near  the 
bottom  is  placed  on  a  light  shallow  dish  on  water,  so  that  it  easily  floats. 
On  opening  the  stopcock  so  as  to  allow  water  to  flow  out,  the  vessel  is  ob- 
served to  move  in  a  direction  diametrically  opposite  to  that  in  which  the 


-218]  Hydraulic.  Tourniquet.  177 

water  is  issuing.  Similarly,  if  a  vessel  containing  water  be  suspended  by  a 
string,  on  opening  an  aperture  in  one  of  the  sides,  the  water  will  jet  out,  and 
the  vessel  be  deflected  away  from  the  vertical  in  the  opposite  direction. 

Segner's  water-wheel  and  the  reaction  machine  depend  on  this  principle. 
So  also  do  rotating  fire-works  ;  that  is,  an  unbalanced  reaction  from  the 
heated  gases  which  issue  from  openings  in  them,  gives  them  motion  in  the 
opposite  direction. 

218.  "Water- wheels.  Turbines. — When  water  is  continuously  flowing 
from  a  higher  to  a  lower  level,  it  may  be  used  as  a  motive  power.  The 
motive  power  of  water  is  utilised  by  means  of  mater-wheels ;  that  is,  by 
wheels  provided  with  buckets  or  float-boards  at  the  circumference,  and  on 
which  the  water  acts  either  by  pressure  or  by  impact. 


Fig.  1 86. 


7$ 


w 
I 

1 

Fig.  187. 


Water-wheels  turn  in  a  vertical  plane  round  a  horizontal  axis,  and  are  of 
two  principal  kinds,  undershot  and  overshot. 

In  undershot  wheels  the  float-boards  are  at  right  angles  to  the  circum- 
ference of  the  wheel.  The  lowest  float-boards  are  immersed  in  the  water 
which  flows  with  a  velocity  depending  on  the  height  of  the  fall.  Such 
wheels  are  applicable  where  the  quantity  of  water  is  great,  but  the  fall  in- 
considerable. Overshot  wheels  are  used  with  a  small  quantity  of  water  which 
has  a  high  fall,  as  with  small  mountain  streams.  On  the  circumference  of  the 
wheel  there  are  buckets  of  a  peculiar  shape.  The  water  falls  into  the  buckets 
on  the  upper  part  of  the  wheel,  which  is  thus  moved  by  the  weight  of  the 
water,  and  as  each  bucket  arrives  at  the  lowest  point  of  revolution  it  discharges 
all  the  water,  and  ascends  empty. 

The  turbine  is  a  horizontal  water-wheel,  and  is  similar  in  principle  to  the 


1/8  On  Gases.  [218- 

hydraulic  tourniquet  (217).  But  instead  of  the  horizontal  tubes  there  is  a 
horizontal  drum,  containing  curved  vertical  walls  ;  the  water,  in  issuing  from 
the  turbine,  pressing  against  these  walls,  exerts  a  reaction,  and  turns  the 
whole  wheel  about  a  vertical  axis.  Turbines  have  the  advantage  of  being 
of  small  bulk  for  their  power,  and  equally  efficient  for  the  highest  and  the 
lowest  falls. 

In  places  in  which  a  high-pressure  water  supply  is  available,  a  form  of 
water  motor  has  of  late  come  into  use.  The  water  is  led  from  pipes  into  a 
cylinder,  in  which  is  a  piston.  By  means  of  a  special  arrangement  called  the 
distributor,  which  will  be  more  fully  described  under  the  steam  engine,  the 
water  is  alternately  led  above  and  below  the  piston,  and  therefore  alternately 
presses  it  up  and  down.  This  motion  of  the  piston  is  transmitted  by  suitable 
mechanical  contrivances  to  the  rest  of  the  machine. 

Instruments  of  this  kind  are  made  which,  with  a  pressure  of  two  atmo- 
spheres and  a  cylinder  whose  diameter  is  4  c.m.,  give  about  |  of  a  horse 
power  with  a  consumption  of  about  530  gallons  of  water  in  an  hour. 

Water-power  is  usually  represented  by  the  weight  of  the  water  multiplied 
into  the  height  of  the  available  fall  ;  or  it  may  also  be  represented  by  half 
the  product  of  the  mass  into  the  square  of  the  velocity.  Both  measurements 
give  the  same  result  (61). 

The  water  power  of  the  Niagara  Falls  is  calculated  to  be  equal  to  four 
and  a  half  millions  of  horse-power. 

The  total  theoretical  effect  of  a  water-power  is  never  realised  ;  for  the 
water,  after  acting  on  the  wheel,  still  retains  some  velocity,  and  therefore  does 
not  impart  the  whole  of  its  velocity  to  the  wheel  ;  in  many  cases  water  flows 
past  without  acting  at  all ;  if  the  water  acts  by  impact,  vibrations  are  pro- 
duced which  are  transmitted  to  the  earth  and  lost  ;  the  same  effect  is  pro- 
duced by  the  friction  of  water  over  an  edge  of  the  sluice,  in  the  channel 
which  conveys  it,  or  against  the  wheel  itself,  as  well  as  by  the  friction  of  this 
latter  against  the  axle.  A  wheel  working  freely  in  a  stream,  as  with  the  corn 
mills  on  the  Rhine  near  Mainz,  does  not  utilise  more  than  20  per  cent,  of  the 
theoretical  effect,  while  one  of  the  more  perfect 
forms  of  turbines  will  work  up  to  over  80  per  cent. 
Water  engines  in  this  respect  exceed  steam  en- 
gines, which  on  the  average  do  not  use  more  than 
10  per  cent,  of  the  power  represented  by  the  coal 
they  burn. 

219.  Mariottes  bottle,  its  use. — Mariotte's 
bottle  presents  many  curious  effects  of  the  pressure 
of  the  atmosphere,  and  furnishes  a  means  of  obtain- 
ing a  constant  flow  of  water.  It  consists  of  a  large 
narrow-mouthed  bottle  in  the  neck  of  which  there 
is  a  tightly-fitting  cork  (fig.  189).  Through  this  a 
tube  passes  open  at  both  ends.  In  the  sides  of  the 
bottle  there  are  three  tubulures,  each  with  a  narrow 
orifice,  and  which  can  be  closed  at  will. 

The  bottle  and  the  tube  being  quite  filled  with 

water,  let  us  consider  what  will  be  the  effect  of  opening  successively  one 
of  the  tubulures,  a,  b,  and  c,  supposing,  as  represented  in  the  figure,  that  the 
lower  extremity  of  g  is  between  the  tubulures  b  and  c. 


-219]  Mariotte's  Bottle.  179 

i.  If  the  tubulure  b  is  open  the  water  flows  out,  and  the  surface  sinks  in 
the  tube  g  until  it  is  on  the  same  level  as  b  when  the  flow  stops.  This  flow 
arises  from  the  excess  of  pressure  at  the  point  e  over  that  at  b.  The  pressure 
at  c  is  the  same  as  the  pressure  of  the  atmosphere.  But  when  once  the  level 
is  the  same  at  b  and  at  e,  the  efflux  ceases,  for  the  atmospheric  pressure  on 
all  points  of  the  same  horizontal  layer, -be,  is  the  same  (100). 

ii.  If  now  the  tubulure  b  is  closed,  and  a  opened,  no  efflux  takes  place  ; 
on  the  contrary,  air  enters  by  the  orifice  a,  and  water  ascends  in  the  tube  g, 
as  high  as  the  layer  ad,  and  then  equilibrium  is  established. 

iii.  If  the  orifices  a  and  b  are  closed,  and  c  opened,  an  efflux  having  con- 
stant velocity  takes  place,  as  long  as  the  level  of  the  water  is  not  below  the 
open  end,  /,  of  the  tube.  Air  enters  bubble  by  bubble  at  /,  and  takes  the 
place  of  the  water  which  has  flowed  out. 

In  order  to  show  that  the  efflux  at  the  orifice  c  is  constant,  it  is  necessary 
to  demonstrate  that  the  pressure  on  the  horizontal  layer  ch  is  always  equal  to 
that  of  the  atmosphere  in  addition  to  the  pressure  of  the  column  hi.  Now 
suppose  that  the  level  of  the  water  has  sunk  to  the  layer  ad.  The  air  which 
has  penetrated  into  the  flask  supports  a  pressure  equal  to  that  of  the  atmo- 
sphere diminished  by  that  of  the  column  of  liquid ^i,  or  H  —pn.  In  virtue  of 
its  elasticity  this  pressure  is  transmitted  to  the  layer  ch.  But  this  layer  fur- 
ther supports  the  weight  of  a  column  of  water,  pm,  so  that'  the  pressure  at ;;/ 
is  really  pm  +  H  —  pn,  or  H  +  mn,  that  is  to  say,  H  +  ///. 

In  the  same  manner  it  may  be  shown  that  this  pressure  is  the  same  when 
the  level  sinks  to  b,  and  so  on  as  long  as  the  level  is  higher  than  the  aperture 
/.  The  pressure  on  the  layer  ch  is  therefore  constant,  and  consequently  the 
velocity  of  the  efflux.  But  when  once  the  level  is  below  the  point  /,  the 
pressure  decreases,  and  with  it  the  velocity. 

To  obtain  a  constant  flow  by  means  of  Mariotte's  bottle,  it  is  filled  with 
water,  and  the  orifice  which  is  below  the  tube  /  is  opened.  The  rapidity  of 
the  flow  is  proportional  to  the  square  root  of  the  height  ///. 


l8o  Acoustics.  [220- 


BOOK    V. 

ACOUSTICS. 
CHAPTER    I. 

PRODUCTION,   PROPAGATION,   AND   REFLECTION   OF   SOUND. 

220.  Province    of  acoustics. — The  study  of  sounds,  and  that  of  the 
vibrations  of  elastic  bodies,  form  the  province  of  acoustics. 

Music  considers  sounds  with  reference  to  the  pleasurable  feelings  they  are 
calculated  to  excite.  Acoustics  is  concerned  with  the  questions  of  the  pro- 
duction, transmission,  and  comparison  of  sounds  ;  to  which  may  be  added, 
the  physiological  question  of  the  perception  of  sounds. 

221.  Sound  and  noise. — Sound  is  a  peculiar  sensation  excited  in  the 
organ  of  hearing  by  the  vibrator)''  motion  of  bodies,  when  this  motion  is 
transmitted  to  the  ear  through  an  elastic  medium. 

All  sounds  are  not  identical ;  they  present  differences  by  which  they  may 
be  distinguished,  compared,  and  their  relations  determined. 

Sounds  are  distinguished  from  noises.  Sound  properly  so  called,  or 
musical  sound,  is  that  which  produces  a  continuous  sensation,  and  the  musical 
value  of  which  can  be  estimated  ;  while  noise  is  either  a  sound  of  too  short 
a  duration  to  be  determined,  like  the  report  of  a  cannon  ;  or  else  it  is  a  con- 
fused mixture  of  many  discordant  sounds,  like  the  rolling  of  thunder  or  the 
noise  of  the  waves.  Nevertheless  the  difference  between  sound  and  noise  is 
by  no  means  precise  ;  Savart  has  shown  that  there  are  relations  of  height  in 
the  case  of  noise,  as  well  as  in  that  of  sound  :  and  there  are  said  to  be  cer- 
tain ears  sufficiently  well  organised  to  determine  the  musical  value  of  the 
sound  produced  by  a  carriage  rolling  on  the  pavement. 

222.  Cause  of  sound. — Sound  is  always  the  result  of  rapid  oscillations 
imparted  to  the  molecules  of  elastic  bodies,  when  the  state  of  equilibrium  of 
these  bodies  has  been  disturbed  either  by  a   shock  or  by  friction.     Such 
bodies  tend  to  regain  their  first  position  of  equilibrium,  but  only  reach  it  after 
performing,  on  each  side  of  that  position,  very  rapid  vibratory  movements, 
the  amplitude  of  which  quickly  decreases.    A  body,  which  produces  a  sound 
is  called  a  sonorous  or  sounding  body. 

As  understood  in  England  and  Germany,  a  vibration  comprises  a  motion 
to  and  fro  ;  in  France,  on  the  contrary,  a  vibration  means  a  movement  to  or 
fro.  The  French  vibrations  are  with  us  semi-vibrations,  an  oscillation  or  vibra- 


© 

x-^-^\ 


-224]  Propagation  of  Sound.  1 8 1 

tion  is  the  movement  of  the  vibrating  molecule  in  only  one  direction  ;  a  double 
or  complete  vibration  comprises  the  oscillation  both  backwards  and  forwards. 
Vibrations  of  sounding  bodies  are  very  readily  observed.  If  a  light  powder  is 
sprinkled  on  a  body  which  is  in  the  act  of  yielding  a  musical  sound,  a  rapid 
motion  is  imparted  to  the  powder 
which  renders  visible  the  vibrations 
of  the  body ;  and  in  the  same 
manner,  if  a  stretched  cord  be 
smartly  pulled  and  let  go,  its  vibra- 
tions are  apparent  to  the  eye. 

A  bell-jar  is  held  horizontally 
in  one  hand  (fig.  190),  and  made 
to  vibrate  by  being  struck  with  the 

other ;  if  then  a  piece  of  metal  is  placed  in  it,  it  is  rapidly  raised  by  the 
vibrations  of  the  side  ;  touching  the  bell-jar  with  the  hand,  the  sound  ceases, 
and  with  it  the  motion  of  the  metal. 

223.  Sounds  not  propagated  in  vacuo. — The  vibrations  of  elastic  bodies 
can  only  produce  the  sensation  of  sound  in  us  by  the  intervention  of  a 
medium  interposed  between  the  ear  and  the 
sonorous  body  and  vibrating  with  it.  This 
medium  is  usually  the  air,  but  all  gases, 
vapours,  liquids,  and  solids  also  transmit 

sounds. 

The  following  experiment  shows  that  the 

presence  of  a  ponderable  medium  is  neces- 
sary for  the  propagation  of  sound.     A  small 

metal  bell,  which  is  continually  struck  by  a 

small    hammer   by  means  of  clockwork,  or 

else  an  ordinary'  musical  box,  is  placed  under 

the   receiver  of  an  air-pump  (fig.    191).     As 

long  as  the  receiver  is  full  of  air  at  the  ordi- 
nary pressure,  the  sound  is  transmitted,  but 

in    proportion    as    the  air  rs    exhausted  the 

sound  becomes  feebler,  and  is  imperceptible 

in  a  vacuum. 

To  ensure  the  success  of  the  experiment, 

the  bellwork  or  the  musical  box  must  be  placed 

on   wadding ;    for   otherwise    the   vibrations 

would  be  transmitted  to  the  air  through  the 

plate  of  the  pump. 

224.  Sound  is   propagated   in   all   elastic  bodies.— If,   in  the  above 

experiment,  after  the  vacuum  has  been  made,  any  vapour  or  gas  be  admitted, 

the  sound  of  the  bell  will  be  heard,  showing  that  sound  is  propagated  in  this 

medium  as  in  air. 

Sound  is  also  propagated  in  liquids.     When  two  bodies  strike  against 

each  other  under  water  the  shock  is  distinctly  heard.     And  a  diver  at  the 

bottom  of  the  water  can  hear  the  sound  of  voices  on  the  bank. 

The  conductibility  of  solids  is  such,  that  the  faint  scratching  of  a  pen  at 

the  end  of  a  long  piece  of  wood  is  heard  at  the  other  end.     The  earth  con- 


Fig.  191. 


1 82  Acoustics.  [224- 

ducts  sound  so  well,  that  at  night,  when  the  ear  is  applied  to  the  ground,  the 
stepping  of  horses,  or  any  other  noise  at  a  great  distance,  is  heard. 

225.  Propagation  of  sound  in  the  air. — In  order  to  simplify  the  theory 
of  the  propagation  of  sound  in  the  air,  we  shall  first  consider  the  case  in 
which  it  is  propagated  in  a  cylindrical  tube  of  indefinite  length.  Let  MN, 
fig.  192,  be  a  tube  filled  with  air  at  a  constant  pressure  and  temperature,  and 


hr 


Fig.  192. 

let  P  be  a  piston  oscillating  rapidly  from  A  to  a.  When  the  piston  passes 
from  A  to  a  it  compresses  the  air  in  the  tube.  But  in  consequence  of  the 
great  compressibility,  the  condensation  of  the  air  does  not  take  place  at  once 
throughout  the  whole  length  of  the  tube,  but  solely  within  a  certain  length, 
#  H,  which  is  called  the  condensed  wave. 

If  the  tube  MN  be  supposed  to  be  divided  into  lengths  equal  to  #H,  and 
each  of  these  lengths  divided  into  layers  parallel  to  the  piston,  it  may  be 
shown  by  calculation,  that  when  the  first  layer  of  the  wave  aH  comes  to  rest, 
the  motion  is  communicated  to  the  first  layer  of  the  second  wave  HH',  and 
so  on  from  layer  to  layer  in  all  parts  of  H'H",  H"H'".  The  condensed 
wave  advances  in  the  tube,  each  of  its  parts  having  successively  the  same 
degree  of  velocity  and  condensation. 

When  the  piston  returns  in  the  direction  ^A,  a  vacuum  is  produced 
behind  it,  which  causes  an  expansion  of  the  air  in  contact  with  its  posterior 
face.  The  next  layer  expanding  in  turn  brings  the  first  to  its  original  state 
of  condensation,  and  so  on  from  layer  to  layer.  Thus  when  the  piston  has 
returned  to  A,  an  expanded  wave  is  produced  of  the  same  length  as  the  con- 
densed wave,  and  directly  following  it  in  the  tube  where  they  are  propagated 
together,  the  corresponding  layers  of  the  two  waves  possessing  equal  and 
contrary  velocities. 

The  whole  of  a  condensed  and  expanded  wave  forms  an  undulation  ;  that 
is,  an  undulation  comprehends  that  part  of  the  column  of  air  affected  during 
the  backward  and  forward  motion  of  the  piston.  The  length  of  an  undula- 
tion is  the  space  which  sound  traverses  during  a  complete  vibration  of  the 
body  which  produces  it.  This  length  is  less  in  proportion  as  the  vibrations 
are  more  rapid. 

It  is  important  to  remark  that  if  we  consider  a  single  row  of  particles, 
which  when  at  rest  occupy  a  line  parallel  to  the  axis  of  the  cylinder,  for 
instance,  those  along  AH"  (fig.  192),  we  shall  find  they  will  have  respectively 
at  the  same  instant  all  the  various  velocities  which  the  piston  has  had  suc- 
cessively while  oscillating  from  A  to  a  and  back  to  A.  So  that  if  in  fig.  38 
AH'  represents  the  length  of  one  undulation,  the  curved  line  H'PQA  will 
represent  the  various  velocities  which  all  the  points  in  the  line  AH'  have 
simultaneously  :  for  instance,  at  the  instant  the  piston  has  returned  to  A,  the 
particle  at  M  will  be  moving  to  the  right  with  a  velocity  represented  by 


-226]  Intensity  of  Sound.  183 

CM,  the  particle  at  N  will  be  moving  to  the  left  with  a  velocity  represented 
by  PN,  and  so  on  of  the  other  particles. 

When  an  undulatory  motion  is  transmitted  through  a  medium,  the 
motions  of  any  two  particles  are  said  to  be  in  the  same  phase  when  those 
particles  move  with  equal  velocities  in  the  same  direction  ;  the  motions 
are  said  to  be  in  opposite  phases  when  the  particles  move  with  the  same 
velocities  in  opposite  directions.  It  is  plain,  from  an  inspection  of  fig.  38, 
that  when  any  two  particles  are  separated  by  a  distance  equal  to  half  an  un- 
dulation, their  motions  are  always  in  opposite  phases,  but  if  their  distance 
equals  the  length  of  a  complete  undulation  their  motions  are  in  the  same 
phase. 

A  little  consideration  will  show  that  in  the  condensed  wave  the  condensa- 
tion will  be  greatest  at  the  middle  of  the  wave,  and  likewise  that  the  expanded 
li'ai'c  will  be  most  rarefied  at  its  middle. 

It  is  an  easy  transition  from  the  theory  of  the  motion  of  sonorous  waves 
in  a  cylinder  to  that  of  their  motion  in  an  unenclosed  medium.  It  is  simply 
necessary  to  apply,  in  all  directions,  to  each  molecule  of  the  vibrating  body, 
what  has  been  said  about  a  piston  movable  in  a  tube.  A  series  of  spherical 
waves  alternately  condensed  and  rarefied  is  produced  around  each  centre  of 
disturbance.  As  these  waves  are  contained  within  two  concentrical  spherical 
surfaces,  whose  radii  gradually  increase,  while  the  length  of  the  undulation 
remains  the  same,  their  mass  increases  with  the  distance  from  the  centre  of 
disturbance,  so  that  the  amplitude  of  the  vibration  of  the  molecules  gradually 
lessens,  and  the  intensity  of  the  sound  diminishes. 

It  is  these  spherical  waves,  alternately  condensed  and  expanded,  which 
in  being  propagated  transmit  sound.  If  many  points  are  disturbed  at  the 
same  time,  a  system  of  waves  is  produced  around  each  point.  But  all  these 
waves  are  transmitted  one  through  the  other  without  modifying  either  their 
lengths  or  their  velocities.  Sometimes  condensed  or  expanded  waves  coincide 
with  others  of  the  same  nature  to  produce  an  effect  equal  to  their  sum  ;  some- 
times they  meet  and  produce  an  effect  equal  to  their  difference.  If  the  sur- 
face of  still  water  be  disturbed  at  two  or  more  points,  the  co-existence  of 
waves  becomes  sensible  to  the  eye. 

226.  Causes  which  influence  the  intensity  of  sound. — Many  causes 
modify  the  force  or  the  intensity  of  sound.  These  are,  the  distance  of 
the  sounding  body,  the  amplitude  of  the  vibrations,  the  density  of  the  air  at 
the  place  where  the  sound  is  produced,  the  direction  of  the  currents  of  air, 
and,  lastly,  the  neighbourhood  of  other  sounding  bodies. 

i.  The  intensity  of  sound  is  inversely  as  the  sqitare  of  the  distance  of  the 
sonorous  body  from  the  ear.  This  law  has  been  deduced  by  calculation,  but 
it  may  be  also  demonstrated  experimentally.  Let  us  suppose  several  sounds 
of  equal  intensity — for  instance,  bells  of  the  same  kind,  struck  by  hammers 
of  the  same  weight,  falling  from  equal  heights.  If  four  of  these  bells  are 
placed  at  a  distance  of  20  yards  from  the  ear,  and  one  at  a  distance  of  10 
yards,  it  is  found  that  the  single  bell  produces  a  sound  of  the  same  intensity 
as  the  four  bells  struck  simultaneously.  Consequently,  for  double  the 
distance  the  intensity  of  the  sound  is  only  one  fourth.  A  method  of  com- 
paring the  intensities  of  different  sounds  will  be  described  afterwards  (289). 

The  distance  at  which  sounds  can  be  heard  depends  on  their  intensity. 


1 84 


Acoustics. 


[226- 


The  report  of  a  volcano  at  St.  Vincent  was  heard  at  Demerara,  300  miles  off, 
and  the  firing  at  Waterloo  was  heard  at  Dover. 

ii.  The  intensity  of  the  sound  increases  luith  the  amplitude  of  the  vibrations 
of  the  sonorous  body.  The  connection  between  the  intensity  of  the  sound 
and  the  amplitude  of  the  vibrations  is  readily  observed  by  means  of  vibrating 
cords.  For  if  the  cords  are  somewhat  long,  the  oscillations  are  perceptible 
to  the  eye,  and  it  is  seen  that  the  sound  is  feebler  in  proportion  as  the  ampli- 
tude of  the  oscillations  decreases. 

iii.  The  intensity  of  sound  depends  on  the  density  of  the  air  in  the  place  in 
which  it  is  produced.  As  we  have  already  seen  (222),  when  an  alarum  moved 
by  clockwork  is  placed  under  the  bell-jar  of  an  air-pump,  the  sound  becomes 
weaker  in  proportion  as  the  air  is  rarefied. 

In  hydrogen,  which  is  about  ^  the  density  of  air,  sounds  are  much 
feebler,  although  the  pressure  is  the  same.  In  carbonic  acid,  on  the  con- 
trary, whose  density  is  1*529,  sounds  are  more  intense.  On  high  moun- 
tains, where  the  air  is  much  rarefied,  it  is  necessary  to  speak  with  some 
effort  in  order  to  be  heard,  and  the  discharge  of  a  gun  produces  only  a  feeble 
sound. 

The  ticking  of  a  watch  is  heard  in  water  at  a  distance  of  23  feet,  in  oil  of 
1  6},  in  alcohol  of  13,  and  in  air  of  only  10  feet. 

iv.  The  intensity  of  sound  is  modified  by  the  motion  of  the  atmosphere, 
and  the  direction  of  the  wind.  In  calm  weather  sound  is  always  better 
propagated  than  when  there  is  wind  ;  in  the  latter  case,  for  an  equal  dis- 
tance, sound  is  more  intense  in  the  direction  of  the  wind  than  in  the  con- 
trary direction. 

v.  Lastly,  sound  is  strengthened  by  the  proximity  of  a  sonorous  body.  A 
string  made  to  vibrate  in  free  air  has  but  a  very  feeble  sound  ;  but  when  it 

vibrates  above  a  sound- 
ing box,  as  in  the  case  of 
the  violin,  guitar,  or  vio- 
loncello, its  sound  is 
much  more  intense.  This 
arises  from  the  fact  that 
the  box  and  the  air  which 
it  contains  vibrate  in 
unison  with  the  string. 
Hence  the  use  of  sound- 
ing-boxes in  stringed  in- 
struments. 

227.  Apparatus  to 
strengthen  sound.  — 
The  apparatus  repre- 
sented in  fig.  193  was 
used  by  Savart  to  show 
the  influence  of  boxes  in 
strengthening  sound.  It 
consists  of  a  hemisphe- 


rical brass  vessel  A,  which  is  set  in  vibration  by  means  of  a  violin  bow. 
Near  it  there  is  a  hollow  cardboard  cylinder,  B,  closed  at  the  further  end. 
By  means  of  a  handle  this  cylinder  can  be  turned  on  its  support,  so  as  to 


-229]  Regnault  's  Experiments.  185 

be  inclined  at  any  given  degree  towards  the  vessel.  The  cylinder  is  fixed 
on  a  slide  C,  by  which  means  it  can  be  placed  at  any  distance  from  A. 
When  the  vessel  is  made  to  vibrate,  the  strengthening  of  the  sound  is  very 
remarkable.  But  the  sound  loses  almost  all  its  intensity  if  the  cylinder  is 
turned  away,  and  it  becomes  gradually  weaker  when  the  cylinder  is  removed 
to  a  greater  distance,  showing  that  the  strengthening  is  due  to  the  vibration 
of  the  air  in  the  cylinder. 

The  cylinder  B  is  made  to  vibrate  in  unison  with  the  brass  vessel  by  ad- 
justing it  to  a  certain  depth,  which  is  effected  by  making  one  part  slide  into 
the  other. 

Yitruvius  states  that,  in  the  theatres  of  the  ancients,  resonant  brass  vessels 
were  placed  to  strengthen  the  voices  of  the  actors. 

228.  Influence  of  tubes  on  the  transmission  of  sound. — The  law  that 
the  intensity  of  sound  increases  in  inverse  proportion  to  the  square  of  the 
distance  does  not  apply  to  the  case  of  tubes,  especially  if  they  are  straight 
and  cylindrical.     The  sonorous  waves  in  that  case  are  not  propagated  in  the 
form  of  increasing  concentrical  spheres,  and  sound  can  be  transmitted  to  a 
great  distance  without  any  perceptible  alteration.     Biot  found  that  in  one 
of  the  Paris  water  pipes,  1040  yards  long,  the  voice  lost  so  little  of  its  intensity, 
that  a  conversation  could  be  kept  up  at  the  ends  of  a  tube  in  a  very  low 
tone.     The  weakening  of  sound  becomes,  however,  perceptible  in  tubes  of 
large  diameter,  or  where  the  sides  are  rough.     This  property  of  transmitting 
sounds  was  first  used  in  England  for  speaking  tubes.     They  consist  of  caout- 
chouc tubes  of  small  diameter  passing  from  one  room  to  another.     If  a  person 
speaks  at  one  end  of  the  tube,  he  is  distinctly  heard  by  a  person  with  his  ear 
at  the  other  end. 

From  Biot's  experiments  it  is  evident  that  a  communication  might  be 
made  between  two  towns  by  means  of  speaking  tubes.  The  velocity  of  sound 
is  1125  feet  in  a  second  at  16-6  C.,  so  that  a  distance  of  50  miles  would  be 
traversed  in  four  minutes. 

229.  Regrnault's  experiments.— Theoretically,  a  sound  wave  should  be 
propagated  in  a  straight  cylindrical  tube  with  a  constant  intensity.     Regnault 
found   that   under   these   circumstances   the   intensity  of  sound   gradually 
diminishes  with  the  distance,  and  that  the  distance  at  which  it  ceases  to  be 
audible  is  nearly  proportional  to  the  diameter  of  the  tube. 

He  produced  sound  waves  of 'equal  strength  by  means  of  a  small  pistol 
charged  with  a  gramme  of  powder  and  fired  at  the  open  ends  of  tubes  of 
various  diameters,  and  he  then  ascertained  the  distance  at  which  the  sound 
could  no  longer  be  heard,  or  at  which  it  ceased  to  act  on  what  he  calls  a 
sensitive  membrane.  This  was  a  very  flexible  membrane  which  could  be 
fixed  across  the  tube  at  various  distances,  and  was  provided  with  a  small  metal 
disc  in  its  centre.  When  the  membrane  began  to  vibrate,  this  disc  struck 
against  a  metallic  contact,  and  thereby  closed  a  voltaic  circuit,  which  traced 
on  a  chronograph  the  exact  moment  at  which  the  membrane  received  the 
sound  wave. 

Experimenting  in  this  manner,  Regnault  found  that  the  report  of  a  pistol 
charged  as  stated  is  no  longer  audible  at  a  distance  of 

1 1 59  metres  in  a  tube  of o>tni 08  diameter 

38io        „  „  o""3oo 

9540        „  „  o""ioo        „ 


1 86  Acoustics.  [229- 

The  sound  wave  of  which  these  numbers  represent  the  limit  of  distance  at 
which  it  is  no  longer  heard,  still  acts  on  the  membrane  at  the  distances  of 
4156,  1 1, 430  and  19,851  metres  respectively. 

According  to  Regnault  the  principal  cause  of  this  diminution  of  intensity 
is  the  loss  of  vis  viva  against  the  sides  of  the  tube  ;  he  found  also  that  sounds 
of  high  pitch  are  propagated  in  tubes  less  easily  than  those  of  low  ones  ;  a 
bass  would  be  heard  at  a  greater  distance  than  a  treble  voice. 

230.  Velocity  of  sound  in  gases. — Since  the  propagation  of  sonorous 
waves  is  gradual,  sound  requires  a  certain  time  for  its  transmission  from  one 
place  to  another,  as  is  seen  in  numerous  phenomena.  For  example,  the 
sound  of  thunder  is  only  heard  some  time  after  the  flash  of  lightning  has  been 
seen,  although  both  the  sound  and  the  light  are  produced  simultaneously  ; 
and  in  like  manner  we  see  a  mason  in  the  act  of  striking  a  stone  before 
hearing  the  sound. 

The  velocity  of  sound  in  air  has  often  been  the  subject  of  experimental 
determination. 

The  most  accurate  of  the  direct  measurements  was  made  by  Moll  and 
Van  Beck  in  1823.  Two  hills,  near  Amsterdam,  Kooltjesberg  and  Zeven- 
boomen,  were  chosen  as  stations  :  their  distance  from  each  other  as  deter- 
mined trigonometrically  was  57,971  feet,  or  nearly  eleven  miles.  Cannons 
were  fired  at  stated  intervals  simultaneously  at  each  station,  and  the  time 
which  elapsed  between  seeing  the  flash  and  hearing  the  sound  was  noted  by 
chronometers.  This  time  could  be  taken  as  that  which  the  sound  required 
to  travel  between  the  two  stations  ;  for  it  will  be  subsequently  seen  that 
light  takes  an  inappreciable  time  to  traverse  the  above  distance.  In- 
troducing corrections  for  the  barometric  pressure,  temperature,  and  hygro- 
metric  state,  and  eliminating  the  influence  of  the  wind,  Moll  and  Van  Beck's 
results  as  recalculated  by  Schroder  van  der  Kolk  give  109278  feet  as  the 
velocity  of  sound  in  one  second  in  dry  air  at  o°  C.  and  under  a  pressure  of 
760  mm. 

Kendall,  in  a  North  Pole  expedition,  found  that  the  velocity  of  sound  at 
a  temperature  of— 40°  was  314  metres. 

The  velocity  of  sound  at  zero  may  be  taken  at  1093  feet  or  333  metres. 
This  velocity  increases  with  the  increase  of  temperature  ;  it  may  be  calcu- 
lated for  an  temperature  t°  from  the  formula, 

v=  1093  \f  (i  +0-003665/) 

where  1093  is  the  velocity  in  feet  at  o°  C.,  and  0*003665  the  coefficient  of  ex- 
pansion for  i°  C.  This  amounts  to  an  increase  of  nearly  two  feet  for  every 
degree  Centigrade.  For  the  same  temperature  it  is  independent  of  the  density 
of  the  air,  and  consequently  of  the  pressure.  It  is  the  same,  for  the  same 
temperature  with  all  sounds,  whether  they  be  strong  or  weak,  deep  or  acute. 
Biot  found,  in  his  experiments  on  the  conductivity  of  sound  in  tubes,  that 
when  a  well-known  air  was  played  on  a  flute  at  one  end  of  a  tube  1040  yards 
long,  it  was  heard  without  alteration  at  the  other  end,  from  which  he  con- 
cluded that  the  velocity  of  different  sounds  is  the  same.  For  the  same 
reason  the  tune  played  by  a  band  is  heard  at  a  great  distance  without  altera- 
tion, except  in  intensity,  which  could  not  be  the  case  if  some  sounds  travelled 
more  rapidly  than  others. 


-231]  Velocity  of  Sound  in  Gases.  187 

This  cannot,  however,  be  admitted  as  universally  true.  Earnshaw,  by  a 
mathematical  investigation  of  the  laws  of  the  propagation  of  sound,  concludes 
that  the  velocity  of  a  sound  depends  on  its  strength  ;  and,  accordingly,  that 
a  violent  sound  ought  to  be  propagated  with  greater  velocity  than  a  gentler 
one.  This  conclusion  is  confirmed  by  an  observation  made  by  Captain 
Parry  on  his  Arctic  expedition.  During  artillery  practice  it  was  found,  by 
persons  stationed  at  a  considerable  distance  from  the  guns,  that  the  report  of 
the  cannon  was  heard  before  the  command  of  fire  given  by  the  officer.  And 
more  recently,  Mallet  made  a  series  of  experiments  on  the  velocity  with  which 
sound  is  propagated  in  rocks,  by  observing  the  times  which  elapsed  before 
blastings,  made  at  Holynead,  were  heard  at  a  distance.  He  found  that  the 
larger  the  charge  of  gunpowder,  and  therefore  the  louder  the  report,  the  more 
rapid  was  the  transmission.  With  a  charge  of  2000  pounds  of  gunpowder, 
the  velocity  was  967  feet  in  a  second,  while  with  a  charge  of  12,000  it  was 
1  2  10  feet  in  the  same  time. 

Jacques  made  a  series  of  experiments  by  firing  different  weights  of  powder 
from  a  cannon  and  observing  the  velocity  of  the  report  at  different 
distances  from  the  gun  by  means  of  an  electrical  arrangement.  He  thus 
found  that,  nearest  the  gun,  the  velocity  is  least,  increasing  to  a  certain 
maximum  which  is  considerably  greater  than  the  average  velocity.  The 
velocity  is  also  greater  with  the  heavier  charge.  Thus  with  a  charge  of 
U  pound  the  velocity  was  1187,  and  with  a  charge  of  ^  pound  it  was 
1032  at  a  distance  of  from  30  to  50  feet  ;  while  at  a  distance  of  70  to 
80  it  was  1267  and  1120;  and  at  90  to  100  feet  it  was  1262  and  1114 
respectively. 

Bravais  and  Martins  found,  in  1844,  that  sound  travelled  with  the  same 
velocity  from  the  base  to  the  summit  of  the  Faulhorn,  as  from  the  summit  to 
the  base. 

231.  Calculation  of  the  velocity  of  sound  in  gases.  —  From  theoretical 
considerations  Newton  gave  a  rule  for  calculating  the  velocity  of  sound  in 
gases,  which  may  be  represented  by  the  formula 


in  which  i>  represents  the  velocity  of  the  sound,  or  the  distance  it  travels  in 
a  second,  e  the  elasticity  of  the  gas,  and  d  its  density. 

This  formula  expresses  that  the  velocity  of  the  propagation  of  sound  in 
gases  is  directly  as  the  square  root  of  the  elasticity  of  the  gas,  and  inversely 
as  the  square  root  of  its  density.  It  follows  that  the  velocity  of  sound  is  the 
same  under  any  pressure  ;  for  although  the  elasticity  increases  with  increased 
pressure,  according  to  Boyle's  law,  the  density  increases  in  the  same  ratio. 
At  Quito,  where  the  mean  pressure  is  only  21*8  inches,  the  velocity  is  the 
same  as  at  the  sea  level,  provided  the  temperature  is  the  same. 

Now  the  measure  of  the  elasticity  of  a  gas  is  the  pressure  to  which  it  is 
subjected  :  hence,  if  g  be  the  force  of  gravity.  //  the  barometric  height  reduced 
to  the  temperature  zero,  and  8  the  density  of  mercury,  also  at  zero,  then  for 
a  gas  under  the  ordinary  atmospheric  pressure,  and  for  zero,  e  =gh§  '.  New- 
ton's formula  accordingly  becomes 


1 88  Acoustics.  [231- 

Now  if  we  suppose  the  temperature  of  a  gas  to  increase  from  o°  to  /°,  its 
volume  will  increase  from  unity,  at  zero,  to  i  +  at  at  /,  a  being  the  coefficient 
of  expansion  of  the  gas.  But  the  density  varies  inversely  as  the  volume, 
therefore  d becomes  d-*-(i  +  at}.  Hence 


Substituting  in  this  formula  the  values  in  centimetres  and  grammes, 
£•=981,  ^  =  76,  ^/=crooi293,  we  get  for  the  value  v  a  number  29,795  centi- 
metres =  297-95  metres,  which  is  considerably  less  than  the  experimental 
result.  Laplace  assigned  as  a  reason  for  this  discrepancy  the  heat  produced 
by  pressure  in  the  condensed  waves  ;  and,  by  considerations  based  on  this 
idea,  Foisson  and  Biot  found  that  Newton's  formula  ought  to  be -written 

v=    *  /  £L-  (i  +  at}   -, ;  c  being  the  specific  heat  of  the  gas  for  a  constant 

pressure,  and  c'  its  specific  heat  for  a  constant  volume  (see  Book  VI.).  The 
average  value  of  this  constant  is  1-4,  and  if  the  formula  be  modified  by  the 
introduction  of  the  value  \/i'4  the  calculated  numbers  agree  with  the 
experimental  results. 

The  physical  reason  for  introducing  the  constant  *  /  c-  into  the  equation 

for  the  velocity  of  sound  may  be  understood  from  the  following  considera- 
tions: — We  have  already  seen  (225)  that  sound  is  propagated  in  air  by  a 
series  of  alternate  condensations  and  rarefactions  of  the  layers.  At  each 
condensation  heat  is  evolved,  and  this  heat  increases  the  elasticity,  and  thus 
the  rapidity,  with  which  each  condensed  layer  acts  on  the  next  ;  but  in  the 
rarefaction  of  each  layer,  the  same  amount  of  heat  disappears  as  was  deve- 
loped by  the  condensation,  and  its  elasticity  is  diminished  by  the  cooling.  • 
The  effect  of  this  diminished  elasticity  of  the  cooled  layer  is  the  same  as  if 
the  elasticity  of  an  adjacent  wave  had  been  increased,  and  the  rapidity  with 
which  this  latter  would  expand  upon  the  dilated  wave  would  be  greater. 
Thus,  while  the  average  temperature  of  the  air  is  unaltered,  both  the  heating 
which  increases  the  elasticity,  and  the  chilling  which  diminishes  it,  concur  in 
increasing  the  velocity. 

Knowing  the  velocity  of  sound,  we  can  calculate  approximately  the  distance 
at  which  it  is  produced.  Light  travels  with  such  velocity  that  the  flash  or 
the  smoke  accompanying  the  report  of  a  gun  may  be  considered  to  be  seen 
simultaneously  with  the  explosion.  Counting  then  the  number  of  seconds 
which  elapse  between  seeing  the  flash  and  hearing  the  sound,  and  multiply- 
ing this  number  by  1125,  we  get  the  distance  in  feet  at  which  the  gun  is 
discharged.  In  the  same  way  the  distance  of  thunder  may  be  estimated. 

232.  Velocity  of  sound  in  various  gases. — Approximately  the  same 
results  have  been  obtained  for  the  velocity  of  sound  in  air  by  another  method, 
by  which  the  velocity  in  other  gases  could  be  determined.  As  the  wave 
length  X  is  the  distance  which  sound  travels  during  the  time  of  one  oscillation, 

that  is,  —of  a  second,  the  velocity  of  sound  or  the  distance  traversed  in  a 
n 

second  is  v  =  n\.  Now  the  length  of  an  open  pipe  is  half  the  wave  length 
of  the  fundamental  note  of  that  pipe  ;  and  that  of  a  closed  pipe  is  a  quarter 


-233]  Velocity  of  Sound  m  various  Gases.  189 

of  the  wave  length  (275).  Hence,  if  we  know  the  number  of  vibrations  of 
the  note  emitted  by  any  particular  pipe,  which  can  be  easily  ascertained  by 
means  of  a  syren,  and  we  know  the  length  of  this  pipe,  we  can  calculate  i>. 
Taking  the  temperature  into  account,  Wertheim  found  in  this  way  1086 
feet  for  the  velocity  of  sound  in  air  at  zero. 

Further,  since  in  different  gases  which  have  the  same  elasticity,  but  differ 
in  density,  the  velocity  of  sound  varies  inversely  as  the  square  root  of  the 
density,  knowing  the  velocity  of  sound  in  air,  we  may  calculate  it  for  other 
gases  :  thus  in  hydrogen  it  will  be 


This  number  cannot  be  universally  accurate,  for  the  coefficient  —    differs 

somewhat  in'  different  gases.  And  when  pipes  were  sounded  with  different 
gases,  and  the  number  of  vibrations  of  tire  notes  multiplfed  with  twice  the 
length  of  the  pipe,  numbers  were  obtained  which  differed  from  those  cal- 
culated by  the  above  formula.  When,  however,  the  calculation  was  made, 

introducing  for  each  gas  the  special  value  of  c-  ,  the  theoretical  results  agreed 

c\ 
very  well  with  the  observed  ones. 

By  the  above  method  the  following  values  have  been  obtained  :  — 

Carbonic  acid          .         .         .         .         .  856  ft.  in  a  second. 

Oxygen   ........     104°  » 

Air  .........     1093 

Carbonic  oxide        .         .         »         .         .         .1106  „ 

Hydrogen        .         .         .         .         .         .         .4163  „ 

233.  Doppler's  principle.  —  \Yhen  a  sounding  body  approaches  the  ear, 
the  tone  perceived  is  somewhat  higher  than  the  true  one  ;  but  if  the  source 
of  sound  recedes  from  the  ear,  the  tone  perceived  is  lower.  The  truth  of 
this,  which  is  known  as  Doppler's  principle,  will  be  apparent  from  the  follow- 
'ing  considerations  :  —  When  the  source  of  sound  and  the  ear  are  at  rest,  the 
ear  perceives  n  waves  in  a  second  ;  but  if  the  ear  approaches  the  sound,  or 
the  sound  approaches  the  ear,  it  perceives  more  ;  just  as  a  ship  meets  more 
waves  when  it  ploughs  through  them  than  if  it  is  at  rest.  Conversely,  the  ear 
receives  a  smaller  number  when  it  recedes  from  the  source  of  sound.  The 
effect  in  the  first  case  is  as  if  the  sounding  body  emitted  more  vibrations  in 
a  second  than  it  really  does,  and  in  the  second  case  fewer.  Hence  in  the 
first  case  the  note  appears  higher  ;  in  the  second  case  lower. 

If  the  distance  which  the  ear  traverses  in  a  second  towards  the  source  of 
sound  (supposed  to  be  stationary)  is  s  feet,  and  the  wrave  length  of  the  par- 

ticular  tone  is  X  feet,  then  there  are  —waves  in  a  second;  or  also  —  ,   for 

A  C 

\   =  c,  where  c  is  the  velocity  of  sound  (230).     Hence  the  ear  receives  not 

only  the  ;/  original  waves,  but  also   _f  in  addition.     Therefore  the  number 
of  vibrations  which  the  ear  actually  perceives  is 


190  Acoustics.  [233- 

or  an  ear  which  approaches  a  tone  ;  and  by  similar  reasoning  it  is 


for  an  ear  receding  from  a  tone. 

Doppler's  principle  is  also  established  by  laboratory  experiments. 
Rollmann  fixed  a  long  rod  on  a  turning  machine,  at  the  end  of  which  was  a 
large  glass  bulb  with  a  slit  in  it,  which  sounded  like  a  humming  top,  when  a 
tangential  current  of  air  was  blown  against  the  slit.  The  uniform  and 
sufficiently  rapid  rotation  of  the  sphere,  developed  such  a  current  and  pro- 
duced a  steady  note,  the  pitch  of  which  was  higher  or  lower  in  each  rotation 
according  as  the  bulb  came  nearer,  or  receded  from,  the  observer. 

To  test  Doppler's  theory  Buys  Ballot  stationed  trumpeters  on  the  Utrecht 
Railway,  and  also  upon  locomotives,  and  had  the  height  of  the  approaching 
or  receding  tones  compared  with  stationary  ones  by  musicians.  He  thus 
found  both  the  principle  and  the  formula  fully  confirmed.  The  observation 
may  often  be  made  as  a  fast  train  passes  a  station  in  which  an  electrical 
alarum  is  sounding.  Independently  of  the  difference  in  loudness,  an  attentive 
ear  can  detect  a  difference  in  pitch  on  approaching  or  on  leaving  the  station. 

234.  Velocity  of  sound  in  liquids.  —  The  velocity  of  sound  in  water. 
was  investigated  in  1827  by  Colladon  and  Sturm.  They  moored  two  boats 
at  a  known  distance  in  the  Lake  of  Geneva.  The  first  supported  a  bell 
immersed  in  water,  and  a  bent  lever  provided  at  one  end  with  a  hammer 
which  struck  the  bell,  and  at  the  other  with  a  lighted  wick,  so  arranged  that 
it  ignited  some  powder  the  moment  the  hammer  struck  the  bell.  To  the 
second  boat  was  affixed  an  ear-trumpet,  the  bell  of  which  was  in  water, 
while  the  mouth  was  applied  to  the  ear  of  the  observer,  so  that  he  could 
measure  the  time  between  the  flash  of  light  and  the  arrival  of  sound  by  the 
water.  By  this  method  the  velocity  was  found  to  be  4708  feet  in  a  second 
at  the  temperature  8'i°,  or  four  times  as  great  as  in  air. 

The  velocity  of  sound,  which  is  different  in  different  liquids,  can  be  cal- 
culated by  a  formula  analogous  to  that  given  above  (230)  as  applicable  to 

gases,  that  is  v  =  A  /^-r  ;  in  which  g^  A,  and  d  have  their  previous  signi- 

V    ?4 

ficance  ;  while  p.  is  the  coefficient  of  the  compressibility  for  the  liquid  in 
question  —  that  is,  its  diminution  in  volume  by  a  pressure  of  one  atmosphere  — 
and  d  is  the  density.  In  this  way  were  obtained  the  numbers  given  in  the 
following  table.  As  in  the  case  of  gases,  the  velocity  varies  with  the  tem- 
perature, which  is  therefore  appended  in  each  case  :  — 

River  water  (Seine)        .        .        .  I3°C.  =•  4714  ft.  in  a  second. 

»  »  '  »  ....  30  =  5013  „ 

Artificial  sea-water  .  .  .  .  20  =  4761  „ 

Solution  of  common  salt  .  .18  =5132  „ 

„  „  chloride  of  calcium  .  23  =  6493  „ 

Absolute  alcohol  ....  23  ^  3854  ,, 

Turpentine  .....  24  «  3976  „ 

Ether  ......  =  3801  „ 

It  will  be  seen  how  close  is  the  agreement  .between  the  two  values  for 


-235]  Velocity  of  Sound  in  Solids.  191 

the  velocity  of  sound  in  water  ;  the  only  case  in  which  they  have  been 
directly  compared.  There  is  considerable  uncertainty  about  the  values  for 
other  liquids,  owing  to  the  uncertainty  of  the  values  for  their  compressibility. 

235.  Velocity  of  sound  in  solids.  —  As  a  general  rule,  the  elasticity  of 
solids,  as  compared  with  the  density,  is  greater  than  that  of  liquids,  and 
consequently  the  propagation  of  sound  is  more  rapid. 

The  difference  is  well  seen  in  an  experiment  by  Biot,  who  found  that  when 
a  bell  was  struck  by  a  hammer,  at  one  end  of  an  iron  tube  3120  feet  long, 
two  sounds  were  distinctly  heard  at  the  other  end.  The  first  of  these  was 
transmitted  by  the  tube  itself  with  a  velocity  x  ;  and  the  second  by  the  en- 
closed air  with  a  known  velocity  a.  The  interval  between  the  sounds  was 
2  -5  seconds.  The  value  of  x  obtained  from  the  equation 

3I20_3I20 

a          x 

shows  that  the  velocity  of  sound  in  the  tube  is  nearly  9  times  as  great  as 
that  in  air. 

To  this  class  of  phenomena  belongs  the  fact  that  if  the  ear  is  held  against 
a  rock  in  which  a  blasting  is  being  made  at  a  distance,  two  distinct  reports 
are  heard  —  one  transmitted  through  the  rock  to  the  ear,  and  the  other  trans- 
mitted through  the  air.  The  conductivity  of  sound  in  solids  is  also  well 
illustrated  by  the  fact  that  in  manufacturing  telegraph  wires  the  filing  at  any 
particular  part  can  be  heard  at  distances  of  miles  by  placing  one  end  of  the 
wire  in  the  ear.  The  toy  telephone  also  is  based  on  this  fact. 

The  velocity  of  sound  in  wire  has  also  been  determined  theoretically  by 

Wertheim  and  others,  by  the  formula  v  =  A  /-  in  which  /z  is  the  modulus 

V  d 

of  elasticity  ^89),  while  d  is  the  mass  in  unit  volume,  which  is  equal  to  the 
specific  gravity,  or  the  weight  of  unit  volume,  divided  by  the  acceleration  of 

gravity,  or  y 

o 

This  may  be  illustrated  from  a  determination  by  Wertheim  of  the 
velocity  of  sound  in  a  specimen  of  annealed  steel  wire,  the  specific  gravity  s 
of  which  was  7*631  and  its  modulus  21,000  (87).  That  is,  a  weight  of  2  1  ,000 
kilogrammes  would  double  unit  length  of  a  wire  I  sq.  mm.  in  cross  section,  if 
this  were  possible,  without  exceeding  the  limit  of  elasticity.  This  is  equal  to 
2,100,000,000  grammes  on  a  wire  one  sq.  cm.  in  cross  section.  Hence 

2IaXXX98l=  51958.  cm.  =  ,7047  feet. 


The  following  table  gives  the  velocity  in  various  bodies,  expressed  in  feet 
per  second  :  — 
Caoutchouc 
Wax 
Lead 
Gold 
Silver 
Pine 
Copper 
Oak. 


'?/ 
23Q4 

Elm  .... 

I  3ci6 

4030 
5717 
8553 
IO9OO 

1  1  666 
14156 

Fir  . 
Steel  wire 
Walnut  . 
Cedar 
Iron  .... 

.  15688 
•  15470 
•  15095 
.  16503 
.  16822 

1 92  Acoustics.  [235- 

In  the  case  of  wood  the  velocity  in  the  direction  of  the  fibres  is  greater 
than  across  them. 

Mallet  has  investigated  the  velocity  of  the  transmission  of  sound  in 
various  rocks,  and  finds  that  it  is  as  follows  : — 

Wet  sand 825  ft,  in  a  second 

Contorted,  stratified  quartz  and  slate  rock     *         ,  Io88  „ 

Discontinuous  granite    .         .         .         .  .  1306  „ 

Solid  granite 1664  „ 

A  direct  experimental  method  of  determining  the  velocity  of  sound  in 
solids,  gases,  and  vapours  will  be  described  farther  on  (277). 

If  a  medium  through  which  sound  passes  is  heterogeneous,  the  waves  of 
sound  are  reflected  on  the  different  surfaces,  and  the  sound  becomes  rapidly 
enfeebled.  Thus  a  soft  earth  conducts  sound  badly,  while  a  hard  ground 
which  forms  a  compact  mass  conducts  it  well. 

236.  Reflection  of  sound.— So  long  as  sound  waves  are  not  obstructed 
in  their  motion  they  are  propagated  in  the  form  of  concentric  spheres  ;  but 
when  they  meet  with  an  obstacle,  they  follow  the  general  law  of  elastic 
bodies  ;  that  is,  they  return  upon  themselves,  forming  new  concentric  waves, 
which  seem  to  emanate  from  a  second  centre  on  the  other  side  of  the  obstacle. 
This  phenomenon  constitutes  the  reflection  of  sound* 

Fig.  194  represents  a  series  of  incident  waves  reflected  from  an  obstacle, 
PO.  Taking,  for  example,  the  incident  wave  M  C  D  N,  emitted  from  the 


Fig.  194- 

centre  A,  the  corresponding  reflected  wave  is  represented  by  the  arc,  CKD, 
of  a  circle,  whose  centre  a  is  as  far  behind  the  obstacle  PO  as  A  is  before  it 

If  any  point,  C,  of  the  reflecting  surface  be  joined  to  the  sonorous  centre, 
and  if  the  perpendicular  CH  be  let  fall  on  the  surface  of  this  body,  the  angle! 
ACH  is  called  the  angle  of  incidence,  and  the  angle  BCH,  formed  by  the 
prolongation  of  «C,  is  the  angle  of  reflection. 

The  reflection  of  sound  is  subject  to  the  two  following  laws  : — 

I.  The  angle  of  reflection  is  equal  to  the  angle  of  incidence. 

II.  The  incident  sonorous  ray  and  the  reflected  ray  are  in  the  same  plane 
perpendicular  to  tJte  reflecting  surface. 


-237]  Echoes  and  ^Resonances.  193 

From  these  laws  it  follows  that  the  wave  which  in  the  figure  is  propagated 
in  the  direction  AC,  takes  the  direction  CB  after  reflection,  so  that  an  ob- 
server placed  at  B  hears,  besides  the  sound  proceeding  from  the  point  A,  a 
second  sound,  which  appears  to  come  from  C. 

The  laws  of  the  reflection  of  sound  are  the  same  as  those  for  light  and 
radiant  heat,  and  may  be  demonstrated  by  similar  experiments.  One  of  the 
simplest  of  these  is  made  with  conjugate  mirrors  (see  chapter  on  Radiant 
Heat)  ;  if  in  the  focus  of  one  of  these  mirrors  a  watch  is  placed,  the  ear  placed 
in  the  focus  of  the  second  mirror  hears  the  ticking  very  distinctly,  even  when 
the  mirrors  are  at  a  distance  of  12  or  13  yards. 

237.  Echoes  and  resonances. — An  echo  is  the  repetition  of  a  sound  in 
the  air,  caused  by  its  reflection  from  some  obstacle. 

A  very  sharp  quick  sound  can  produce  an  echo  when  the  reflecting 
surface  is  55  feet  distant ;  but  for  articulate  sounds  at  least  double  that 
distance  is  necessary,  for  it  may  be  easily  shown  that  no  one  can  pronounce 
or  hear  distinctly  more  than  five  syllables  in  a  second.  Now,  as  the  velo- 
city of  sound  at  ordinary  temperatures  may  betaken  at  1125  feet  in  a  second, 
in  a  fifth  of  that  time  sound  would  travel  225  feet.  If  the  reflecting  surface 
is  112-5  feet  distant,  in  going  and  returning  sound  would  travel  through  225 
feet.  The  time  which  elapses  between  the  articulated  and  the  reflected 
sound  would,  therefore,  be  a  fifth  of  a  second,  the  two  sounds  would  not 
interfere,  and  the  reflected  sound  would  be  distinctly  heard.  A  person 
speaking  with  a  loud  voice  in  front  of  a  reflector,  at  a  distance  of  112-5  feet* 
can  only  distinguish  the  last  reflected  syllable  :  such  an  echo  is  said  to  be 
monosyllabic.  If  the  reflector  were  at  a  distance  of  two  or  three  times  112-5 
feet,  the  echo  would  be  dissyllabic,  trisyllabic,  and  so  on. 

When  the  distance  of  the  reflecting  surface  is  less  than  112-5  feet  tne 
direct  and  the  reflected  sound  are  confounded.  They  cannot  be  heard 
separately,  but  the  sound  is  strengthened.  This  is  what  is  often  called  reso- 
nance, and  is  often  observed  in  large  rooms.  Bare  walls  are  very  reso- 
nant ;  but  tapestry  and  hangings,  which  are  bad  reflectors,  deaden  the 
sound. 

Multiple  echoes  are  those  which  repeat  the  same  sound  several  times  : 
this  is  the  case  when  two  opposite  surfaces  (for  example,  two  parallel  walls) 
successively  reflect  sound.  There  are  echoes  which  repeat  the  same  sound 
20  or  30  times.  An  echo  in  the  chateau  of  Simonetta,  in  Italy,  repeats  a 
sound  30  times.  At  Woodstock  there  is  one  which  repeats  from  17  to  20 
syllables. 

As  the  laws  of  reflection  of  sound  are  the  same  as  those  of  light  and 
heat,  curved  surfaces  produce  acoustic  foci  like  the  luminous  and  calorific 
foci  produced  by  concave  reflectors.  If  a  person  standing  under  the  arch  of 
a  bridge  speaks  with  his  face  turned  towards  one  of  the  piers,  the  sound  is 
reproduced  near  the  other  pier  with  such  distinctness  that  a  conversation 
can  be  kept  up  in  a  low  tone,  which  is  not  heard  by  any  one  standing  in  the 
intermediate  spaces. 

There  is  a  square  room  with  an  elliptical  ceiling,  on  the  ground  floor  of 
the  Conservatoire  des  Arts  et  Metiers,  in  Paris,  which  presents  this  pheno- 
menon in  a  remarkable  degree  when  persons  stand  in  the  two  foci  of  the 
ellipse. 


194  Acoustics.  [237- 

In  the  whispering  gallery7  of  St.  Paul's,  the  faintest  sound  is  thus  conveyed 
from  one  side  to  the  other  of  the  dome,  but  it  is  not  heard  at  any  intermediate 
points.  Placing  himself  close  to  the  upper  wall  of  the  Colosseum,  a  circular 
building  130  feet  in  diameter,  Wheatstone  found  a  word  to  be  repeated  a 
great  many  times.  A  single  exclamation  sounded  like  a  peal  of  laughter 
while  the  tearing  of  a  piece  of  paper  resembled  the  patter  of  hail. 

Whispering  galleries  are  formed  of  smooth  walls  having  a  continuous 
curved  form.  The  mouth  of  the  speaker  is  presented  at  one  point,  and 
the  ear  of  the  hearer  at  another  and  distant  point.  In  this  case,  the 
sound  is  successively  reflected  from  one  point  to  the  other  until  it  reaches 
the  ear. 

It  is  not  merely  by  solid  surfaces,  such  as  walls,  rocks,  ships'  sails,  &c., 
that  sound  is  reflected.  It  is  also  reflected  by  clouds,  and  it  has  even  been 
shown  by  direct  experiment  that  a  sound  in  passing  from  a  gas  of  one  density 
into  another  is  reflected  at  the  surface  of  separation  as  it  would  be  against 
a  solid  surface.  Now  different  parts  of  the  earth's  surface  are  unequally 
heated  by  the  sun,  owing  to  the  shadows  of  trees,  evaporation  of  water,  and 
other  causes,  so  that  in  the  atmosphere  there  are  numerous  ascending 
and  descending  currents  of  air  of  different  density.  Whenever  a  sonorous 
wave  passes  from  a  medium  of  one  density  into  another  it  undergoes  partial 
reflection,  which,  though  not  strong  enough  to  form  an  echo,  distinctly 
weakens  the  direct  sound.  This  is  doubtless  the  reason,  as  Humboldt  re- 
marks, why  sound  travels  further  at  night  than  at  daytime  ;  even  in  the  South 
American  forests,  where  the  animals,  which  are  silent  by  day,  fill  the  atmo- 
sphere in  the  night  with  thousands  of  confused  sounds. 

It  has  generally  been  considered  that  fog  in  the  atmosphere  is  a  great' 
deadener  of  sound  ;  it  being  a  mixture  of  air  and  globules  of  water,  at  each 
of  the  innumerable  surfaces  of  contact  a  portion  of  the  vibration  is  lost. 
The  evidence  as  to  the  influence  of  this  property  is  conflicting ;  recent  re- 
searches of  Tyndall  show  that  a  white  fog,  or  snow,  or  hail,  are  not  important 
obstacles  to  the  transmission  of  sound,  but  that  aqueous  vapour  is.  Expe- 
riments made  on  a  large  scale,  in  order  to  ascertain  the  best  form  of  fog 
signals,  gave  some  remarkable  results. 

On  some  days  which  optically  were  quite  clear,  certain  sounds  could  not 
be  heard  at  a  distance  far  inferior  to  that  at  which  they  could  be  heard  even 
during  a  thick  haze.  Tyndall  ascribes  this  result  to  the  presence  in  the 
atmosphere  of  aqueous  vapour,  which  forms  in  the  air  innumerable  striae 
that  do  not  interfere  with  its  optical  clearness,  but  render  it  acoustically 
turbid,  the  sound  being  reflected  by  this  invisible  vapour  just  as  light  is  by 
the  visible  cloud. 

These  conclusions  first  drawn  from  observations  have  been  verified  by 
laboratory  experiments.  Tyndall  has  shown  that  a  medium  consisting  of 
alternate  layers  of  light  and  heavy  gas  deadens  sound,  and  also  that  a 
medium  consisting  of  alternate  strata  of  heated  and  ordinary  air  exerts  a 
similar  influence.  The  same  is  the  case  with  an  atmosphere  containing  the 
vapours  of  volatile  liquids.  So  long  as  the  continuity  of  air  is  preserved, 
sound  has  great  power  of  passing  through  the  interstices  of  solids  ;  thus  it 
will  pass  through  twelve  folds  of  a  dry  silk  handkerchief,  but  is  stopped  by  a 
single  layer  if  it  is  wetted. 


-239]  Speaking  Trumpet.     Ear  Trumpet.  195 

It  has  long  been  known  that  sound  is  pfropagated  in  a  direction  against 
that  of  the  wind  with  less  velocity  than  with  the  wind.  This  is  probably 
due  to  a  refraction  of  sound  on  a  large  scale.  The  velocity  of  wind  along 
the  ground  is  always  considerably  less  than  at  a  greater  height ;  thus,  the 
velocity  at  a  height  of  8  feet  has  been  observed  to  be  double  what  it  is  at  a 
height  of  one  foot  above  the  ground.  Hence,  the  front  of  a  condensed  wave 
(fig.  192),  which  was  originally  vertical,  becomes  tilted  upwards  and  with  the 
lower  part  forward  ;  and,  as  the  direction  of  the  wave  motion  is  at  right  angles 
to  the  front  of  the  wave,  the  effect  of  the  coalescence  of  a  number  of  these 
rays  thus  directed  upwards,  is  to  produce  an  increase  of  the  sound.  The 
ray  which  travels  with  the  wind  will  for  similar  reasons  be  refracted  down- 
wards. 

238.  Refraction  of  sound. — It  will  be  found  in  the  sequel  that  refraction 
is  the  change  of  direction  which  light  and  heat  experience  on  passing  from 
one  medium  to  another.     It  has  been  shown  by  Hajech  that  the  laws  of  the 
refraction  of  sound  are  the  same  as  those  for  light  and  heat  :  he  used  tubes 
filled  with  various  gases  and  liquids,  and  closed  by  membranes  ;  the  mem- 
brane at  one  end  was  at  right  angles  to  the  axis  of  the  tube,  while  the  other 
made  an  angle  with  it.     When  these  tubes  were  placed  in  an  aperture  in  the 
wall  between  two  rooms,  a  sound  produced  in  front  of  the  tube  in  one  room, 
that  of  a  tuning-fork  for  instance,  was   heard   in   directions  in  the  other 
varying  with  the  nature  of  the  substance  with  which  the  tube  was  filled. 
Accurate  measurements  showed  that  the  law  held  that  the  sines  of  the  angle 
of  incidence  and  of  refraction  are  in  a  constant  ratio,  which  is  equal  to  the 
ratio  of  the  velocity  of  sound  in  the  two  media. 

Sondhauss  has  confirmed  the  analogy  of  the  refraction  of  sound  waves 
to  those  of  light  and  heat.  He  constructed  lenses  of  gas  by  cutting  equal 
segments  out  of  a  large  collodion  balloon,  and  fastening  them  on  the  two 
sides  of  a  sheet  iron  ring  a  foot  in  diameter,  so  as  to  form  a  double  convex 
lens  about  4  inches  thick  in  the  centre.  This  was  filled  with  carbonic  acid, 
and  a  watch  was  placed  in  the  direction  of  the  axis  :  the  point  was  then 
sought  on  the  other  side  of  the  lens  at  which  the  sound  was  most  distinctly 
heard.  It  was  found  that  when  the  ear  was  removed  from  the  axis,  the 
sound  was  scarcely  perceptible  ;  but  that  at  a  certain  point  on  the  axial  line 
it  was  very  distinctly  heard.  Consequently,  the  sound  waves  in  passing 
from  the  lens  had  converged  towards  the  axis,  their  direction  had  been 
changed  ;  in  other  words,  they  had  been  refracted. 

The  refraction  of  sound  may  be  easily  demonstrated  by  means  of  one  of 
the  very  thin  india-rubber  balloons  used  as  children's  toys,  inflated  by 
carbonic  acid.  If  the  balloon  be  filled  with  hydrogen,  no  focus  is  detected  ; 
it  acts  like  a  concave  lens,  and  the  divergence  of  the  rays  is  increased, 
instead  of  their  being  converged  to  the  ear. 

239.  Speaking:  trumpet.     Bar  trumpet. — These  instruments  are  based 
both  on  the  reflection  of  sound  and  on  its  conductibility  in  tubes. 

The  speaking  trumpet,  as  its  name  implies,  is  used  to  render  the  voice 
audible  at  great  distances.  It  consists  of  a  slightly  conical  tin  or  brass  tube 
(fig.  195),  very  much  wider  at  one  end  (which  is  called  the  belt),  and  provided 
with  a  mouthpiece  at  the  other.  The  larger  the  dimensions  of  this  instrument 
the  greater  is  the  distance  at  which  the  voice  is  heard.  Its  action  is  usually 

K2 


Acoustics.  [239- 

ascribed  to  the  successive  reflections  of  sonorous  waves  from  the  sides  of 
the  tube,  by  which  the  waves  tend  more  and  more  to  pass  in  a  direction 
parallel  to  the  axis  of  the  instrument.  It  has,  however,  been  objected  to 


Fig-  195- 

this  explanation,  that  the  sounds  emitted  by  the  speaking  trumpet  are 
not  stronger  solely  in  the  direction  of  the  axis,  out  in  all  directions  ;  that  the 
bell  would  not  tend  to  produce  parallelism  in  the  sonorous  wave,  whereas 
it  certainly  exerts  considerable  influence  in  strengthening  the  sound.  It  must 
be  said  that  no  satisfactory  explanation  has  been  given  of  the  effect  of  the  bell. 

The  ear  trumpet  is  used  by  persons  who  are  hard  of  hearing.  It  is 
essentially  an  inverted  speaking  trumpet,  and  consists  of  a  conical  metallic 
tube,  one  of  whose  extremities,  terminating  in  a  bell,  receives  the  sound,  while 
the  other  end  is  introduced  into  the  ear.  This  instrument  is  the  reverse  of 
the  speaking  trumpet.  The  bell  serves  as  a  mouthpiece  ;  that  is,  it  receives 
the  sound  coming  from  the  mouth  of  the  person  who  speaks.  These  sounds 
are  transmitted  by  a  series  of  reflections  to  the  interior  of  the  trumpet,  so 
that  the  waves  which  would  become  greatly  developed,  are  concentrated  on 
the  auditory  apparatus,  and  produce  a  far  greater  effect  than  divergent  waves 
would  have  done. 

240.  Stethoscope. — One  of  the  most  useful  applications  of  acoustical 
principles  is  the  stethoscope.  Figs.  196,  197  represent  an  improved  form  of 
this  instrument  devised  by  Konig.  Two  sheets  of  caoutchouc,  c  and  <?,  are 
fixed  to  the  circular  edge  of  a  hollow  metal  hemisphere  ;  the  edge  is  provided 


Fig.  196. 


Fig.  197. 


with  a  stopcock,  so  that  the  sheets  can  be  inflated,  and  then  present  the  ap- 
pearance of  a  double  convex  lens,  as  represented  in  section  in  fig.  196.  To 
a  tubulure  on  the  hemisphere  is  fixed  a  caoutchouc  tube  terminated  by  horn 
or  ivory,  ^,  which  is  placed  in  the  ear  (fig.  197). 

When  the  membrane  of  the  stethoscope  is  applied  to  the  chest  of  a  sick 
person  the  beating  of  the  heart  and  the  sounds  of  respiration  are  transmitted 
to  the  air  in  the  chamber  c  «,  and  from  thence  to  the  ear  by  means  of  the 
flexible  tube.  If  several  tubes  are  fixed  to  the  instrument,  as  many  observers 
may  simultaneously  auscultate  the  same  patient. 


-242]  Savarts  Apparatus.  197 


CHAPTER   II. 

MEASUREMENT  OF  THE  NUMBER  OF  VIBRATIONS. 

241.  Savart's  apparatus. — Savarfs  toothed  wheel,  so  called  from  the 
name  of  its  inventor,  is  an  apparatus  by  which  the  absolute  number  of  vibra- 
tions corresponding  to  a  given  note  can  be  determined.  It  consists  of  a 
solid  oak  frame  in  which  there  are  two  wheels,  A  and  B  (fig.  198) ;  the  larger 


Fig.  198. 

wheel,  A,  is  connected  with  the  toothed  wheel  by  means  of  a  strap  and  a 
multiplying  wheel,  thereby  causing  the  toothed  wheel  to  revolve  with  great 
velocity ;  a  card,  E,  is  fixed  on  the  frame,  and,  in  revolving,  the  toothed 
wheel  strikes  against  it,  and  causes  it  to  vibrate.  The  card  being  struck  by 
each  tooth,  makes  as  many  vibrations  as  there  are  teeth.  At  the  side  of  the 
apparatus  there  is  an  indicator,  H,  which  gives  the  number  of  revolutions  of 
the  wheel,  and  consequently  the  number  of  vibrations  in  a  given  time. 

When  the  wheel  is  moved  slowly,  the  separate  shocks  against  the  card 
are  distinctly  heard ;  but  if  the  velocity  is  gradually  increased,  the  sound 
becomes  higher  and  higher.  Having  obtained  the  sound  whose  number  of 
vibrations  is  to  be  determined,  the  revolution  of  the  wbeel  is  continued  with 
the  same  velocity  for  a  certain  number  of  seconds.  The  number  of  turns  of 
the  toothed  wheel  B  is  then  read  off  on  the  indicator,  and  this  multiplied  by 
the  number  of  teeth  in  the  wheel  gives  the  total  number  of  vibrations. 
Dividing  this  by  the  corresponding  number  of  seconds,  the  quotient  gives 
the  number  of  vibrations  per  second  for  the  given  sound. 

242.  Syren. — The  syren  is  an  apparatus  which,  like  Savart's  wheel,  is 
used  to  measure  the  number  of  vibrations  of  a  body  in  a  given  time.  The 


198 


Acoustics. 


[242- 


name  '  syren '  was  given  to  it  by  its  inventor,  Cagniard  Latour,  because  it 
yields  sounds  under  water. 

It  is  made  entirely  of  brass.  Fig.  199  represents  it  fixed  on  the  table  of 
a  bellows,  by  which  a  continuous  current  of  air  can  be  sent  through  it.  Figs. 
200  and  201  show  the  internal  details.  The  lower  part  consists  of  a  cylin- 
drical box,  O,  closed  by  a  fixed  plate,  B.  On  this  plate  a  vertical  rod,  T,  rests, 
to  which  is  fixed  a  disc,  A,  moving  with  the  rod.  In  the  plate  B  there  are 
equidistant  circular  holes,  and  in  the  disc  A  are  an  equal  number  of  holes  of 
the  same  size,  and  the  same  distance  from  the  centre  as  those  of  the  plate. 
These  holes  are  not  perpendicular  to  the  disc  ;  they  are  all  inclined  to  the 
same  extent  in  the  same  direction  in  the  plate,  and  are  inclined  to  the  same 
extent  in  the  opposite  direction  in  the  disc,  so  that  when  they  are  opposite 


Fig.  199. 


Fig.  20 1. 


each  other  they  have  the  appearance  represented  in  ;;/;/,  fig.  200.  Conse- 
quently, when  a  current  of  air  from  the  bellows  reaches  the  hole  ;;?,  it  strikes 
obliquely  against  the  sides  of  the  hole  «,  and  imparts  to  the  disc  A  a  rotatory 
motion  in  the  direction  //A. 

For  the  sake  of  simplicity,  let  us  first  suppose  that  in  the  movable  disc 
A  there  are  eighteen  holes,  and  in  the  fixed  plate  B  only  one,  which  faces 
one  of  the  upper  holes.  The  wind  from  the  bellows  striking  against  the 
sides  of  the  latter,  the  movable  disc  begins  to  rotate,  and  the  space  between 
two  of  its  consecutive  holes  closes  the  hole  in  the  lower  plate.  But  as  the 
disc  continues  to  turn  from  its  acquired  velocity,  two  holes  are  again  opposite 
each  other,  a  new  impulse  is  produced,  and  so  on.  During  a  complete 
revolution  of  the  disc  the  lower  hole  is  eighteen  times  open  and  eighteen 
times  closed.  A  series  of  effluxes  and  stoppages  is  thus  produced,  which 
makes  the  air  vibrate,  and  ultimately  produces  a  sound  when  the  successive 
impulses  are  sufficiently  rapid.  If  the  fixed  plate,  like  the  moving  disc,  had 
eighteen  holes,  each  hole  would  separately  produce  the  same  effect  as  a 
separate  one,  the  sound  would  be  eighteen  times  as  intense,  but  the  number 
of  vibrations  would  not  be  increased. 


-244]  Limit  of  Perceptible  Sounds.  199 

In  order  to  know  the  number  of  vibrations  corresponding  to  the  sound 
produced,  it  is  necessary  to  know  the  number  of  revolutions  of  the  disc  A  in 
a  second.  For  this  purpose  an  endless  screw  on  the  rod  T  transmits  the 
motion  to  a  wheel,  «,  with  100  teeth.  On  this  wheel,  which  moves  by  one 
tooth  for  every  turn  of  the  disc,  there  is  a  catch  P,  which  at  each  complete 
revolution  moves  one  tooth  of  a  second  wheel,  b  (fig.  201).  On  the  axis  of 
these  wheels  there  are  two  needles,  which  move  round  dials  represented  in 
fig.  199.  One  of  these  indices  gives  the  number  of  turns  of  the  disc  A,  the 
other  the  number  of  hundreds  of  turns.  By  means  of  two  screws,  D  and  C, 
the  wheel  a  can  be  uncoupled  from  the  endless  screw. 

Since  the  pitch  of  the  sound  rises  in  proportion  to  the  velocity  of  the  disc 
A,  the  wind  is  forced  until  the  desired  sound  is  produced.  The  same  current 
is  kept  up  for  a  certain  time — two  minutes,  for  example — and  the  number  of 
turns  read  off.  This  number  multiplied  by  18,  and  divided  by  120,  gives 
the  number  of  vibrations  in  a  second. 

With  the  same  velocity  the  syren  gives  the  same  sound  in  air  as  in  water  ; 
the  same  is  the  case  with  all  gases  ;  and  it  appears,  therefore,  that  any  given 
sound  depends  on  the  number  of  vibrations,  and  not  on  the  nature  of  the 
sounding  body. 

The  buzzing  and  humming  noise  of  certain  insects  is  not  vocal,  but  is 
produced  by  very  rapid  flapping  of  the  wings  against  the  air  or  the  body. 
The  syren  has  been  ingeniously  applied  to  count  the  velocity  of  the  undula- 
tions thus  produced,  which  is  effected  by  bringing  it  into  unison  with  the  sound. 
It  has  thus  been  found  that  the  wings  of  a  gnat  flap  at  the  rate  of  1 5,000 
times  in  a  second. 

If  a  report  is  produced  in  a  space  with  two  parallel  walls  at  no  great 
distance  apart,  the  sound  is  regularly  reflected  from  one  to  the  other  and 
reaches  the  ear  at  regular  intervals  ;  that  is,  the  echo  acts  as  a  tone. 

243.  Bellows. — In  acoustics  a  bellows  is  an  apparatus  by  which  wind 
instruments,  such  as  the  syren  and  organ  pipes,  are  worked.     Between  the 
four  legs  of  a  table  there  is  a  pair  of  bellows,  S  (fig.  202),  which  is  worked 
by  means  of  a  pedal,  P.     D  is  a  reservoir  of  flexible  leather,  in  which  is 
stored  the  air  forced  in  by  the  bellows.    If  this  reservoir  is  pressed  by  means 
of  weights  on  a  rod,  T,  moved  by  the  hand,  the  air  is  driven  through  a  pipe, 
E,  into  a  chest,  C,  fixed  on  the  table.     In  this  chest  there  are  small  holes 
closed  by  leather  valves,  which  can  be  opened  by  pressing  on  keys  in  front 
of  the  box.     The  syren  or  sounding  pipe  is  placed  in  one  of  these  holes. 

244.  Xiimit  of  perceptible  sounds. — Before  Savart's  researches,  physicists 
assumed  that  the  ear  could  not  perceive  a  sound  when  the  number  of  vibra- 
tions was  below  16  for  deep  sounds,  or  above  9,000  for  acute  sounds.     But 
he  showed  that  these  limits  were  too  close,  and  that  the  faculty  of  perceiving 
sounds  depends  rather  on  their  intensity  than  on  their  height ;  so  that  when 
extremely  acute  sounds  are  not  heard,  it  arises  from  the  fact  that  they  have 
not  been  produced  with  sufficient  intensity  to  affect  the  organ  of  hearing. 

By  increasing  the  diameter  of  the  toothed  wheel,  and  consequently  the 
amplitude  and  intensity  of  the  vibrations,  Savart  pushed  the  limit  of  acute 
sounds  to  24,000  vibrations  in  a  second. 

For  deep  sounds  he  substituted  for  the  toothed  wheel  an  iron  bar  about 
two  feet  long,  which  revolved  on  a  horizontal  axis  between  two  thin  wooden 


2OO  Acoustics.  [244- 

plates,  about  0-08  of  an  inch  from  the  bar.     As  often  as  the  bar  passed,  a 
grave   sound  was  produced,  due  to  the  displacement  of  the   air.     As  the 

motion  was  accelerated,  the 
sound  became  continuous,  very 
grave  and  deafening.  By  this 
means  Savart  found,  that  with 
7  to  8  vibrations  in  a  second, 
the  ear  perceived  a  distinct  but 
very  deep  sound. 

Despretz,  however,  who  in- 
vestigated the  same  subject, 
disputed  Savart's  results  as  to 
the  limits  of  deep  sounds,  and 
considers  that  no  sound  is 
audible  that  is  made  by  less 
than  1 6  vibrations  per  second. 
Helmholtz  holds  that  the  per- 
ception of  a  sound  begins  at  30 
vibrations,  and  only  has  a  defi- 
nite musical  value  when  the 
number  is  more  than  40.  Below 
30  the  impression  of  a  number 
of  separate  beats  is  produced. 
On  the  other  hand  acute  sounds 
are  audible  up  to  those  corre- 
sponding to  38,000  vibrations 
in  a  second. 

Fig.  202.  The  discordant  results  ob- 

tained by  these  and  other  ob- 
servers for  the  limit  of  audibility  of  higher  notes  are  no  doubt  due  to  the 
circumstance  that  different  observers  have  different  capacities  for  the  per- 
ception of  sounds.  Preyer  has  investigated  this  subject  by  means  of  experi- 
mental methods  of  greater  precision  than  any  that  have  hitherto  been  applied 
for  this  purpose.  The  minimum  limit  for  the  normal  ear  he  found  to  lie 
between  16  and  24  single  vibrations  in  a  second  ;  the  maximum  limit  reached 
41,000  ;  but  many  persons  with  average  powers  of  hearing  were  found  to  be 
absolutely  deaf  to  tones  of  16,000,  12,000,  or  even  fewer  vibrations. 

245.  Duhamel's  graphic  method. — When  the  '  syren'  or  Savart's  wheel 
is  used  to  determine  the  exact  number  of  vibrations  corresponding  to  a  given 
sound,  it  is  necessary  to  bring  the  sound  which  they  produce  into  unison 
with  the  given  sound,  and  this  cannot  be  done  exactly  unless  the  experimenter 
have  a  practised  ear.  DuhameFs  graphic  method  is  very  simple  and  exact, 
and  free  from  this  difficulty.  It  consists  in  fixing  a  fine  point  to  the  body 
emitting  the  sound,  and  causing  it  to  trace  the  vibrations  on  a  properly 
prepared  surface. 

The  apparatus  consists  of  a  wood  or  metal  cylinder,  A  (fig.  203),  fixed  to 
a  vertical  axis,  O,  and  turned  by  a  handle.  The  lower  part  of  the  axis  is  a 
screw  working  in  a  fixed  nut,  so  that,  according  as  the  handle  is  turned  from 
left  to  right,  or  from  right  to  left,  the  cylinder  is  raised  or  depressed.  Round 
the  cylinder  is  rolled  a  sheet  of  paper  covered  with  an  inadhesive  film  of 


-245] 

lampblack. 


Graphic  Method. 


201 


On  this  film  the  vibrations  register  themselves.  This  is  effected 
as  follows.  Suppose  the  body  emitting  the  note  to  be  a  steel  rod.  It  is  held 
firmly  at  one  end,  and  carries,  at  the  other,  a  fine  point  which  grazes  the 
surfaces  of  the  cylinder.  If  the  rod  is  made  to  vibrate  and  the  cylinder  is 
at  rest,  the  point  would  describe  a  short  line  ;  but  if  the  cylinder  is  turned, 
the  point  produces  an  undulating  trace,  containing  as  many  undulations  as 
the  point  has  made  vibrations.  Consequently  the  number  of  vibrations  can 


Fig.  203. 

be  counted.     It  remains  only  to  determine  the  time  in  which  the  vibrations 
were  made. 

There  are  several  ways  of  doing  this.  The  simplest  is  to  compare  the 
curve  traced  by  the  vibrating  rod  with  that  traced  by  a  tuning-fork  (251), 
which  gives  a  known  number  of  vibrations  per  second  —  for  example,  500. 
One  prong  of  the  fork  is  furnished  with  a  point,  which  is  placed  in  contact 
with  the  lampblack.  The  fork  and  the  rod  are  then  set  vibrating  together, 
and  each  produces  its  own  undulating  trace.  When  the  paper  is  unrolled, 
it  is  easy,  by  counting  the  number  of  vibrations  each  has  made  in  the  same 
distance,  to  determine  the  number  of  vibrations  made  per  second  by  the 
elastic  rod.  Suppose,  for  instance,  that  the  tuning-fork  made  1  50  vibrations, 
while  the  rod  made  165  vibrations.  Now  we  already  know  that  fhe  tuning- 
fork  makes  one  vibration  in  the  ^  part  of  a  second,  and  therefore  150 
vibrations  in  |§§  of  a  second.  But  in  the  same  time  the  rod  makes  165 

vibrations  ;    therefore  it  makes  one  vibration  in  the  -  =?  —      of  a  second, 


and  hence  it  makes  per  second  ^? 


-  — 
500  x  165 

or  550  vibrations. 


202  Acoustics.  [246- 


CHAPTER   III. 

THE  PHYSICAL  THEORY   OF   MUSIC. 

246.  Properties  of  musical  tones. — A  simple  musical  tone  results  from 
a  continuous  rapid  isochronous  vibration,  provided  the  number  of  the  vibra- 
tions falls  within  the  very  wide  limits  mentioned  in  the  last  chapter  (244). 
Musical  tones  are  in  most  cases  compound.  The  distinction  between  a 
simple  and  a  compound  musical  tone  will  be  explained  later  in  the  chapter. 
The  tone  yielded  by  a  tuning-fork  furnished  with  a  proper  resonance-box  is 
simple ;  that  yielded  by  a  wide-stopped  organ  pipe,  or  by  a  flute,  is  nearly 
simple ;  that  yielded  by  a  musical  string  is  compound. 

Musical  tones  have  three  leading  qualities,  namely,  pitch,  intensity,  and 
timbre  or  colotir. 

i.  The  pitch  of  a  musical  tone  is  determined  by  the  number  of  vibrations 
per  second  yielded  by  the  body  producing  the  tone. 

ii.  The  intensity  of  the  tone  depends  on  the  extent  of  the  vibrations.  It 
is  greater  when  the  extent  is  greater,  and  less  when  it  is  less.  It  is,  in  fact, 
proportional  to  the  square  of  the  extent  or  amplitude  of  the  vibrations  which 
produce  the  tone. 

iii.  The  timbre  or  stamp  is  that  peculiar  quality  of  tone  which  distinguishes 
a  note  when  sounded  on  one  instrument  from  the  same  note  when  sounded 
on  another.  Thus  when  the  C  of  the  treble  stave  is  sounded  on  a  violin, 
and  on  a  flute,  the  two  notes  will  have  the  same  pitch  ;  that  is,  are  produced 
by  the  same  number  of  vibrations  per  second,  and  they  may  have  the  same 
intensity,  and  yet  the  two  tones  will  have  very  distinct  qualities  ;  that  is, 
their  timbre  is  different.  The  cause  of  the  peculiar  timbre  of  tones  will  be 
considered  later  in  the  chapter. 

247.  Musical  intervals. — Let  us  suppose  that  a  musical  tone,  which  for 
the  sake  of  future  reference  we  will  denote  by  the  letter  C,  is  produced  by 
m  vibrations  per  second  ;  and  let  us  further  suppose  that  any  other  musical 
tone,  X,  is  produced  by  n  vibrations  per  second,  n  being  greater  than  m  ; 
then  the  interval  from  the  note  C  to  the  note  X  is  the  ratio  n  ;  m,  the  interval 
between  two  notes,  being  obtained  by  division,  not  by  subtraction.  Although 
two  or  more  tones  may  be  separately  musical,  it  by  no  means  follows  that 
when  sounded  together  they  produce  a  pleasant  sensation.  On  the  con- 
trary, unless  they  are  concordant,  the  result  is  harsh,  and  usually  unpleasing. 
We  have,  therefore,  to  inquire  what  notes  are  fit  to  be  sounded  together. 
Now  when  musical  tones  are  compared,  it  is  found  that  if  they  are  separated 
by  an  interval  of  2  :  1,4:  I,  &c.,  they  so  closely  resemble  one  another  that 
they  may  for  most  purposes  of  music  be  considered  as  the  same  tone.  Thus, 
suppose  c  to  stand  for  a  musical  note  produced  by  2m  vibrations  per  second, 


-248] 


The  Musical  Scale.  203 


then  C  and  c  so  closely  resemble  one  another  as  to  be  called  in  music  by 
the  same  name.  The  interval  from  C  to  c  is  called  an  octave,  and  c  is 
said  to  be  an  octave  above  C,  and  conversely  C  an  octave  below  c.  If  we 
now  consider  musical  sounds  that  do  not  differ  by  an  octave,  it  is  found  that 
if  we  take  three  notes,  X,  Y,  and  Z,  resulting  respectively  from  p,  q,  and  r 
vibrations  per  second,  these  three  notes  when  sounded  together  will  be  con- 
cordant if  the  ratio  of  p  :  q  :  r  equals  4:5:6.  Three  such  notes  form  a 
harmonic  triad,  and  if  sounded  with  a  fourth  note,  which  is  the  octave  of 
X,  constitute  what  is  called  in  music  a  major  chord.  Any  of  the  notes  of  a 
chord  may  be  altered  by  one  or  more  octaves  without  changing  its  distinc- 
tive character ;  for  instance,  C,  E,  G,  and  c  are  a  chord,  and  C,  c,  e,  g  form 
the  same  chord. 

If,  however,  the  ratio  p  :  q  :  r  equals  10  :  12  :  15,  the  three  sounds  are 
slightly  dissonant,  but  not  so  much  so  as  to  disqualify  them  from  producing 
a  pleasing  sensation.  When  these  three  notes  and  the  octave  to  the  lower 
are  sounded  together  they  constitute  what  in  music  is  called  a  minor  chord. 

248.  The  musical  scale. — The  series  of  sounds  which  connects  a  given 
note  C,  with  its  octave  c,  is  called  the  diatonic  scale  or  gamut.  The  notes 
composing  it  are  indicated  by  the  letters  C,  D,  E,  F,  G,  A,  B.  The  scale 
is  then  continued  by  taking  the  octaves  of  these  notes,  namely,  e,  d,  e,f,g,  a,  b, 
and  again  the  octaves  of  these  last,  and  so  on. 

The  notes  are  also  known  by  names,  viz.,  do  or  ut,  re,  mi,  fa,  sol,  la,  si, 
do.  The  relations  existing  between  the  notes  are  these  : — C,  E,  G  form 
a  major  triad,  G,  B,  d  form  a  major  triad,  and  F,  A,  c  form  a  major  triad. 
C,  G,  and  F  have,  for  this  reason,  special  names,  being  called  respectively 
the  tonic,  do?ninant,  and  sub-dominant,  and  the  three  triads  the  tonic, 
dominant,  and  sub-dominant  triads  or  chords  respectively.  Consequently, 
the  numerical  relations  between  the  notes  of  the  scale  will  be  given  by  the 
three  proportions — 


C  :  E 

G 

"4 

5 

6 

G  :  B 

2D 

::4 

5. 

6 

F  :  A 

2C 

I  \  4 

5 

6 

Hence  if  m  denotes  the  number  of  double  vibrations  corresponding  to 
the  note  C,  the  number  of  vibrations  corresponding  to  the  remaining  notes 
will  be  given  by  the  following  table — 

do        re        mi       fa        sol        la        si        do 
CDEFGAB^r 


\m       f; 


The  intervals  between  the  successive  notes  being  respectively — 
C  to  D     D  to  E     E  to  F     F  to  G     G  to  A    A  to  B     B  to  c 

»  10  16 .  '  9  10  1»  16 

8  9  15  8  9  8  15 

It  will  be  observed  here  that  there  are  three  kinds  of  intervals,  f,  ^  and 
j5  ;  of  these  the  two  former  are  called  a  tone,  the  last  a  semitone,  because  it 
is  about  half  as  great  as  the  interval  of  a  tone.  The  two  tones,  however,  are 
not  identical,  but  differ  by  an  interval  of  ||,  which  is  called  a  comma.  Two 
notes  which  differ  by  a  comma  can  be  readily  distinguished  by  an  educated 
ear.  The  interval  between  the  tonic  and  any  note  is  denominated  by  the 


2O4  Acoustics.  [248- 

position  of  the  latter  note  in  the  scale  ;  thus  the  interval  from  C  to  G  is  a 
fifth.  The  scale  we  have  now  considered  is  called  the  major  scale,  as 
being  formed  of  major  triads.  If  the  minor  triad  were  substituted  for  the 
major,  a  scale  would  be  formed  that  could  be  strictly  called  a  minor  scale. 
As  scales  are  usually  written,  howrever,  the  ascending  scale  is  so  formed  that 
the  tonic  bears  a  minor  triad,  the  dominant  and  sub-dominant  bear  major 
triads,  while  in  the  descending  scale  they  all  bear  minor  triads.  Practically, 
in  musical  composition,  the  dominant  triad  is  always  major.  If  the 
ratios  given  above  are  examined,  it  will  be  found  that  in  the  major  scale 
the  interval  from  C  to  E  equals  f ,  while  in  the  minor  scale  it  equals  \. 
The  former  interval  is  called  a  major  third,  the  latter  a  minor  third.  Hence 
the  major  third  exceeds  the  minor  third  by  an  interval  of  ff .  This  interval 
is  called  a  semitone,  though  very  different  from  the  interval  above  called  by 
that  name. 

A  complete  discussion  of  the  number  of  notes,  and  the  intervals  between 
them,  will  be  found  in  an  article  by  Mr.  A.  J.  Ellis,  in  vol.  xiii.  of  the  Pro- 
ceedings of  the  Royal  Society  (p.  93),  '  On  a  perfect  Musical  Scale.' 

249.  On  semitones  and  on  scales  with  different  key  notes. — It  will 
be  seen  from  the  last  article  that  the  term  '  semitone '  does  not  denote  a 
constant  interval,  being  in  one  case  equivalent  to  jf  and  in  another  to  f  |. 
It  is  found  convenient  for  the  purposes  of  music  to  introduce  notes  inter- 
mediate to  the  seven  notes  of  the  gamut  ;  this  is  done  by  increasing  or 
diminishing  these  notes  by  an  interval  of  ff.  When  a  note  (say  C)  is  in- 
creased by  this  interval,  it  is  said  to  be  sharpened,  and  is  denoted  by  the 
symbol  C&  ,  called  '  C  sharp  ; '  that  is,  Cff  -»-C  =ff.  When  it  is  decreased  by 
the  same  interval,  it  is  said  to  be  flattened,  and  is  represented  thus — B  b, 
called  '  B  flat  ; '  that  is,  B  -*-  Bb  =  ff.  If  the  effect  of  this  be  examined,  it  will 
be  found  that  the  number  of  notes  in  the  scale  from  C  up  to  c  has  been  in- 
creased from  seven  to  twenty-one  notes,  all  of  which  can  be  easily  distin- 
guished by  the  ear.  Thus  reckoning  C  to  equal  I,  we  have — 

C         CB          Db         D         D8          Eb         E     &c. 

T  ?5  27  9  75  6  5  P,r 

24  25  8  64  54          VJLV" 

Hitherto  we  have  made  the  note  C  the  tonic  or  key  note.  Any  other  of 
the  twenty-one  distinct  notes  above  mentioned,  e.g.  G,  or  F,  or  Ctf ,  &c., 
may  be  made  the  key  note,  and  a  scale  of  notes  constructed  with  reference 
to  it.  This  will  be  found  to  give  rise  in  each  case  to  a  series  of  notes,  some 
of  which  are  identical  with  those  contained  in  the  series  of  which  C  is  the 
key  note,  but  most  of  them  different.  And  of  course  the  same  would  be  true 
for  the  minor  scale  as  well  as  for  the  major  scale,  and  indeed  for  other  scales 
which  may  be  constructed  by  means  of  the  fundamental  triads. 

250.  On  musical  temperament. — The  number  of  notes  that  arise  from 
the  construction  of  the  scales  described  in  the  last  article  is  so  great  as  to 
prove  quite  unmanageable  in  the  practice  of  music  ;  and  particularly  for 
music  designed  for  instruments  with  fixed  notes,  such  as  the  pianoforte  or 
harp.  Accordingly,  it  becomes  practically  important  to  reduce  the  number 
of  notes,  which  is  done  by  slightly  altering  their  just  proportions.  This 
process  is  called  temperament.  By  tempering  the  notes,  however,  more  or 
less  dissonance  is  introduced,  and  accordingly  several  different  systems  of 


-251]  The  Tuning-fork.  205 

temperament  have  been  devised  for  rendering  this  dissonance  as  slight  as 
possible.  The  system  usually  adopted  is  called  the  system  of  equal  tempera- 
ment. It  consists  in  the  substitution  between  C  and  c  of  eleven  notes  at 
equal  intervals,  each  interval  being,  of  course,  the  twelfth  root  of  2,  or  1-05946. 
F>\  this  means  the  distinction  between  the  semitones  is  abolished,  so  that, 
for  example,  Cfl  and  Db  become  the  same  note.  The  scale  of  twelve 
notes  thus  formed  is  called  the  chromatic  scale.  It  of  course  follows  that 
major  triads  become  slightly  dissonant.  Thus,  in  the  diatonic  scale,  if  we 
reckon  C  to  be  i,  E  is  denoted  by  1-25003,  and  G  by  1-50000:  On  the  system 
of  equal  temperament,  if  C  is  denoted  by  I,  E  is  denoted  by  1*25992,  and  G 
by  1-49831. 

If  individual  intervals  are  made  pure  while  the  errors  are  distributed  over 
the  others,  such  a  system  is  called  that  of  unequal  temperament.  Of  this 
class  is  Kirnberger's,  in  which  nine  of  the  tones  are  pure. 

Although  the  system  of  equal  temperament  has  the  advantage  of  afford- 
ing, with  as  small  a  number  of  notes  as  possible,  the  greatest  variety  of  tones, 
yet  it  has  the  disadvantage  that  no  chord  of  an  equally-tempered  instrument, 
such  as  the  piano,  is  quite  pure.  And  as  musical  education  mostly  has  its 
basis  on  the  piano,  even  singers  and  instrumentalists  usually  give  equally- 
tempered  intervals.  Only  in  the  case  of  string  quartet  players,  who  have 
freed  themselves  from  school  rules,  and  in  that  of  vocal  quartet  singers,  who 
sing  much  without  accompaniment,  does  the  natural  pure  temperament  assert 
itself,  and  thus  produce  the  highest  musical  effect. 

251. — Tiie  number  of  vibrations  producing  each  note.  The  tuning- 
fork. — Hitherto  we  have  denoted  the  number  of  vibrations  corresponding  to 
the  note  C  by  ;;/,  and  have  not  assigned  any 
numerical  value  to  that  symbol.  In  the  theory 
of  music  it  is  frequently  assumed  that  the  middle 
C  corresponds  to  256  double  vibrations  in  a 
second.  This  is  the  note  which,  on  a  pianoforte 
of  seven  octaves,  is  produced  by  the  white  key 
on  the  left  of  the  two  black  keys  close  to  the 
centre  of  the  keyboard.  This  number  is  con- 
venient as  being  continually  divisible  by  two, 
and  is  therefore  frequently  used  in  numerical 
illustrations.  It  is,  however,  arbitrary.  An 
instrument  is  in  tune  provided  the  intervals 
between  the  notes  are  correct,  when  c  is  yielded 
by  any  number  of  vibrations  per  second  not 
differing  much  from  256.  Moreover,  two  instru- 
ments are  in  tune  with  one  another,  if,  being 
separately  in  tune,  they  have  any  one  note,  for 
instance  C,  yielded  by  the  same  number  of  vibra- 
tions. Consequently,  if  two  instruments  have 
one  note  in  common,  they  can  then  be  brought 
into  tune  jointly  by  having  their  remaining  notes  F'g-  2°4- 

separately  adjusted  with  .reference  to  the  fundamental  note.  A  tuning-fork 
or  diapason  is  an  instrument  yielding  a  constant  sound,  and  is  used  as  a 
standard  for  tuning  musical  instruments.  It  consists  of  an  elastic  steel  rod, 


206  Acoustics.  [251- 

bent  as  represented  in  fig.  204.  It  is  made  to  vibrate  either  by  drawing  a 
bow  across  the  ends,  or  by  striking  one  of  the  legs  against  a  hard  body,  or 
by  rapidly  separating  the  two  prongs  by  means  of  a  steel  rod  as  shown  in 
the  figure.  The  vibration  produces  a  note  which  is  always  the  same  for  the 
same  tuning-fork.  The  note  is  strengthened  by  fixing  the  tuning-fork  on  a 
box  open  at  one  end,  called  a  resonance  box. 

The  standard  tuning-fork  in  any  country  represents  its  accepted  concert 
pitch. 

It  has  been  remarked  for  some  years  that  not  only  has  the  pitch  of  the 
tuning-fork  been  getting  higher  in  the  large  theatres  of  Europe,  but  also 
that  it  is  not  the  same  in  London,  Paris,  Berlin,  Vienna,  Milan,  &c.  This  is 
a  source  of  great  inconvenience  both  to  composers  and  singers,  and  a  com- 
mission was  appointed  in  1859  to  establish  in  France  a  tuning-fork  of  uniform 
pitch,  and  to  prepare  a  standard  which  would  serve  as  an  invariable  type. 
In  accordance  with  the  recommendations  of  that  body,  a  normal  tuning-fork 
has  been  established,  which  is  compulsory  on  all  musical  establishments 
in  France,  and  a  standard  has  been  deposited  in  the  Conservatory  of  Music 
in  Paris.  It  performs  437*5  double  vibrations  per  second,  and  gives  the 
standard  note  a  or  /#,  or  the  a  in  the  treble  stave  (252).  Consequently,  with 
reference  to  this  standard,  the  middle  c  or  do  would  result  from  261  double 
vibrations  per  second. 

In  England  a  committee,  appointed  by  the  Society  of  Arts,  recommended 
that  a  standard  tuning-fork  should  be  one  constructed  to  yield  528  double 
vibrations  in  a  second  and  that  this  should  represent  </  in  the  treble  stave. 
This  number  has  the  advantage  of  being  divisible  by  2  down  to  33,  and  is  in 
fact  the  same  as  the  normal  tuning-fork  adopted  in  Stuttgardt  in  1834,  which 
makes  440  vibrations  in  the  second,  and,  like  the  French  one,  corresponds 
to  a  in  the  same  stave. 

252.  Musical  notation.      Musical  range. — It    is   convenient   to  have 

some  means  of  at  once  naming  any  particular  note  in  the  whole  range  of 

musical  sounds  other  than  by  stating  its  number  of  vibrations.     Perhaps  a 

>    convenient  practice  is  to  call  the  octave,  of  which  the  C  is  produced  by  an 

>L*-eight-foot  organ  pipe,  by  the  capital  letters  C,  D,  E,  F,  G,  A,  B  ;  the  next 

higher  octave  by  the  corresponding  small  letters,  c,  d,  e,f,g,a,b\  and  to 

designate  the  octaves  higher  than  this  by  the  index  placed  over  the  letter 

thus,  </,  d',  e',  f,  g',  a\  £',  and  the  higher  series  in  a  similar  manner.     The 

same  principle  may  be  applied  to  the  notes  below  C  ;  thus  the  octave  below 

C  is  C,,  and  the  next  lower  one  C,,. 

Hence  we  have  the  series 

C,,     C,     C    c    c'    Sf    c"f    <*». 

In  musical  writing  the  notes  are  expressed  by  signs  which  indicate  the 
length  of  time  during  which  the  note  is  to  be  played  or  sung,  and  are  written 
on  a  series  of  lines  called  a  stave.  Thus 


d  e  f 

stands  for  the  octave  in  the  treble  clef ;  of  which  the  top  note  is  the  standard 
c'  and  the  bottom  is  the  middle  c.     When  the  five  lines  are  insufficient  they 


-254]  Compound  Musicaf  Notes  and  Harmonics.  207 

are  continued  above  and  below  the  stave  by  what  are  called  ledger  lines. 
In  order  to  avoid  confusion,  a  bass  clef  is  used  for  the  lower  notes ;  and  it 


may  be  remarked  that     Tfc^         -  and  §|-  -  stand  for  the  same  note 

y^j    ~ -^i~_"V-  r  ~~_ 

tj   * 

•(251)  which  is  the  middle  c. 

The  deepest  note  of  orchestral  instruments  is  the  E,  of  the  double  bass, 
which  makes  41^  vibrations,  taking  the  key  note  as  making  440  vibrations 
in  a  second.  Some  organs  and  pianofortes  go  as  low  as  C//x  with  32 
vibrations  in  a  minute,  some  grand  pianos  even  as  low  as  A/x/  with  27^  vibra- 
tions. But  the  musical  character  of  all  these  notes  below  Ey  is  imperfect, 
for  we  are  near  the  limit  at  which  the  ear  can  combine  the  separate  vibra- 
tions to  a  musical  note  (244).  These  notes  can  only  be  used  musically  with 

i  their  next  higher  octave,  to  which  they  impart  a  certain  character  of  depth 
and  richness. 

In  the  other  direction,  pianofortes  go  to  a{v  with  3520  or  even  ?  with 

;   4224  vibrations  in  a  second.     The  highest  note  of  the  orchestra  is  probably 

;  the  d*  of  the  piccolo  flute,  which  makes  4752  vibrations.  And  although  the 
ear  can  distinguish  sounds  which  are  still  higher,  they  have  no  longer  a 
pleasurable  character.  And  while  the  notes  which  are  distinguishable  by 
the  ear,  range  between  16  and  38,000  vibrations,  or  II  octaves  ;  those  which 
are  musically  available,  range  from  about  40  to  4000  vibrations,  or  within  7 

i   octaves. 

253.  Wave  length  of  a  given  note.    Amplitude  of  oscillation.— Know- 
|  ing  the  number  of  vibrations  which  a  sounding  body  makes  in  a  second,  the 

corresponding  wave  length  is  easily  calculated.  For  since  sound  travels  at 
:  about  1120  feet  in  a  second,  if  a  body  only  made  one  vibration  in  a  second 

its  wave  length  would  be  1120  feet ;  if  it  made  two,  the  wave  length  would 

Jbe  half  of  1120  feet ;  if  it  made  three,  the  third  and  so  on — that  is,  that  the 
\  wave  length  of  any  note  is  the  quotient  obtained  by  dividing  the  velocity  of 
\  sound  by  the  number  of  vibrations;  and  this  whatever  the  height  of  the 

sound,  since  the  velocity  is  the  same  for  high  and  low  notes. 

Hence,  calling  v  the  velocity  of  sound,  /  the  wave  length,  n  the  number 

of  vibrations  in  a  second,  we  have  v  =  ln^  from  which  n=  -  -  ;  that   is,   that 

,  the  number  of  vibrations  is  inversely  as  the  wave  length. 

The  amplitude  of  oscillation  which  is   required   for  the  production  of 
'  audible  sounds  is  very  small.     Lord  Rayleigh  determined  it  in  the  case  of  the 
i  waves  due  to  a  pipe  which  sounded  the  note  /iv,  and  which  could  be  heard 
at  a  distance  of  820  metres.     He  found  that  the  amplitude  of  the  oscillation 
of  these  waves  could  not  be  greater  than  the  one  ten-millionth  of  a  milli- 
metre. 

254.  On  compound  musical  tones  and  harmonics. — When  any  given 
1  note  (say  C)  is  sounded  on  most  musical  instruments,  not  that  tone  alone  is 
1  produced,  but  a  series  of  tones,  each  being  of  less  intensity  than  the  one 

preceding  it.  If  C,  which  may  be  called  the  primary  tone,  is  denoted  by 
unity,  the  whole  series  is  given  by  the  numbers  r,  2,  3,  4,  5,  6,  7,  &c. ;  in 
other  words,  first  the  primary  C  is  sounded,  then  its  octave  becomes  audible, 
then  the  fifth  to  that  octave,  then  the  second  octave,  then  the  third,  fifth, 
and  a  note  between  the  sixth  and  seventh  to  the  second  octave,  and  so  on. 


. 

208  Acoustics.  [254- 

These  secondary  tones  are  called  the  harmonics  of  the  primary  tone.  Though 
feeble  in  comparison  with  the  primary  tone,  they  may,  with  a  little  practice, 
be  heard,  when  the  primary  tone  is  produced  on  most  musical  instruments  ; 
when,  for  instance,  one  of  the  lower  notes  is  sounded  on  the  pianoforte. 

255.  Helmholtz  s  analysis  of  sound. — For  the  purpose  of  experimentally 
proving  the  presence  of  the  harmonics  as  distinct  tones,  Professor  Helmholtz 
devised  an  instrument  which  he  called  a  resonance  globe.  The  principle  may 
be  illustrated  by  the  following  experiment  : — If  an  empty  glass  cylinder 
be  taken  and  a  vibrating  tuning-fork  be  held  over  the  mouth  of  the 
vessel,  the  column  of  air  will  not  be  set  in  vibration  unless  the  column  of  air 
be  of  a  certain  definite  length  ;  such,  indeed,  that  the  wave  length  of  the 
fundamental  note  corresponds  to  the  wave  length  of  the  note  produced  by 
the  tuning-fork.  Now  by  pouring  in  water  we  can  regulate  the  length  of  the 
column  of  air,  and  by  trial  can  hit  off  the  exact  length  ;  when  this  is  attained 
the  note  of  the  tuning-fork  will  be  heard  to  be  powerfully  reinforced  (227). 
A  resonance  globe  (fig.  205)  is  a  glass  globe  tuned  to  a  particular  note, 


Fig    205.  Fig,  206. 

furnished  with  two  openings,  one  of  which,  «,  turned  towards  the  origin  of 
sound,  and  the  other,  #,  by  means  of  an  indiarubber  tube,  is  applied  to  the 
ear.  If  the  tone  proper  to  the  resonance  globe  exists  among  the  harmonics 
of  the  compound  tone  that  is  sounded  it  is  strengthened  by  the  globe,  and 
thereby  rendered  distinctly  audible.  Further,  other  things  being  the  same, 
the  note  proper  to  a  given  globe  depends  on  the  diameter  of  the  globe  and 
that  of  the  uncovered  opening.  Consequently,  by  means  of  a  series  of  such 
globes,  the  whole  series  of  harmonics  in  a  given  compound  tone  can  be 
rendered  distinctly  audible,  and  their  existence  put  beyond  a  doubt. 

Konig,  the  eminent  acoustical  instrument  maker,  has  made  an  important 
modification  in  the  resonance  globe,  to  which  he  has  given  the  form  repre- 
sented in  fig.  206.  The  resonator  is  cylindrical,  and  the  end  which  receives 
the  sound  can  be  drawn  out,  so  that  the  volume  may  be  increased  at  pleasure. 
As  the  sound  thereby  becomes  deeper,  the  same  resonator  may  be  tuned  to 
a  variety  of  notes.  On  the  tubulure  fits  a  caoutchouc  tube  by  which  the 
vibrations  may  be  transmitted  in  any  direction. 

256.  Ronig's  apparatus  for  the  analysis  of  sound.-— As  the  successive 
application  to  the  ear  of  various  resonators  is  both  slow  and  tedious,  Konig 
devised  a  remarkable  apparatus  in  which  a  series  of  resonators  act  on  mano- 
metric  flames  (288) ;  the  sounds  thus,  as  it  were,  become  visible,  and  may 
be  shown  to  a  large  auditory. 


-256]         Konigs  Apparatus  for  the  Analysis  of  Sound.  209 

It  consists  of  an  iron  frame  (fig.  207)  on  which  are  fixed  in  two  parallel 
lines  fourteen  resonators  tuned  so  as  to  give  the  notes  from  F,  to  c" — that  is 
to  say,  four  octaves  and  a  half ;  or  notes  of  which  the  highest  give  the  lower 
harmonics  of  the  primary.  On  the  right  is  a  chamber,  C,  which  is  supplied 
with  coal  gas  by  the  caoutchouc  tube,  D,  and  on  which  are  placed  eight 
gas  jets,  each  provided  with  a  manometric  capsule  (288).  Each  jet  is  con- 
nected with  the  chamber  C  by  a  special  caoutchouc  tube,  while  behind  the 
apparatus  a  second  tube  connects  the  same  jet  to  one  of  the  resonators 


Fi5.  207. 

On  the  right  of  the  jets  is  a  system  of  rotating  mirrors  identical  with  that 
described  in  article  288. 

These  details  being  understood,  suppose  the  largest  resonator  on  the  right 
tuned  to  resound  with  the  note  I,  and  seven  others  with  the  harmonics  of 
this  note.  Let  the  sound  I  be  produced  in  part  of  this  apparatus ;  if  it  is 
simple,  the  lower  resonator  alone  answers,  and  the  corresponding  flame  is 
alone  dentated  ;  but  if  the  fundamental  note  is  accompanied  by  one  or  more 
of  its  harmonics,  the  corresponding  resonators  speak  at  the  same  time,  which 


2io  Acoustics.  [257- 

is  recognised  by  the  dentation  of  their  flames  ;  and  thus  the  constituents  of 
each  sound  may  be  detected. 

257.  Synthesis  of  sounds. — Not  only  has  Helmholtz  succeeded  in  de- 
composing sounds  into  their  constituents  ;  he  has  verified  the  result  of  his 
analysis  by  performing  the  reverse  operation,  the  synthesis  ;  that  is,  he  has 
reproduced  a  given  sound  by  combining  the  individual  sounds  of  which  his 
resonators  had  shown  that  it  was  composed.  The  apparatus  which  he  used 
for  this  purpose  consists  of  eleven  tuning-forks,  the  first  of  which  yields  the 
fundamental  note  of  256  vibrations,  or  C,  nine  others  its  harmonics,  while  the 
eleventh  serves  as  make  and  break  to  cause  the  diapasons  to  vibrate  by  means 
of  electro-magnets.  Each  diapason  has  a  special  electro-magnet,  and  more- 
over a  resonator,  which  strengthens  it. 

All  these  diapasons  and  their  accessories  are  arranged  in  parallel  lines  of 
five  (fig.  208),  the  first  comprising  the  fundamental  note  and  its  uneven 


Fig.  208. 

harmonics,  3,  5,  7,  and  9 ;  the  second  the  even  harmonics,  2,  4,  6,  8,  and  10 ; 
beyond,  there  is  the  diapason  break  K  arranged  horizontally.  One  of  its 
prongs  is  provided  with  a  platinum  point  which  grazes  the  surface  of  mercury 
contained  in  a  small  cup,  the  bottom  of  which  is  connected,  by  a  copper 
wire,  with  an  electro-magnet  placed  in  front  of  the  diapason. 

The  apparatus  being  thus  arranged,  a  wire  from  a  voltaic  battery  is  con- 
nected with  the  binding  screw,  c,  and  this  with  the  electro-magnet,  E  ;  which 
in  turn  is  connected  with  those  of  the  nine  following  diapasons,  and  then 
with  the  diapason  K  itself.  So  long  as  the  diapason  does  not  vibrate,  the 
current  does  not  pass,  for  the  platinum  point  does  not  dip  in  the  mercury 
cup  which  is  connected  with  the  other  pole  of  the  battery.  But  when  the 


-258] 


\&»»f"r  *\te/ 

Results  of  Helmlwltz's  Researches. 


211 


diapason  is  made  to  vibrate  by  means  of  a  bow,  the  current  passes.  Owing 
to  their  elasticity,  the  limbs  of  the  tuning-fork  soon  revert  to  their  original 
position,  the  point  is  no  longer  in  the  mercury,  the  current  is  broken,  and 
so  on  at  each  double  vibration  of  the  diapason.  This  intermittence  of  the 
current  being  transmitted  to  all  the  other  electro-magnets,  they  are  alternately 
active  and  inactive.  Hence  they  communicate  to  all  the  diapasons  by  their 
attraction  the  same  number  of  vibrations.  This  is  the  case  with  the  diapason 
i,  which  is  tuned  in  unison  with  the  diapason  break  ;  but  the  diapason  3, 
being  tuned  to  make  three  times  as  many  vibrations,  makes  three  vibrations 
at  each  break  of  the  current ;  that  is  to  say,  the  electro-magnet  only  attracts 
it  at  every  third  vibration  ;  in  like  manner,  diapason  b  only  receives  a  fresh 
impulse  every  five  vibrations,  and  so  on. 

The  following  is  the  working  of  the  apparatus  : — The  resonator  of  each 
diapason  is  closed  by  a  clapper  O  (fig.  209),  so  that  the  sounds  made  by  the 
diapasons  are  scarcely  per- 
ceptible when  the  clappers 
are  lowered.  Each  of  these 
is  fixed  to  the  end  of  a  bent 
lever,  the  shorter  arm  of 
which  is  worked  by  a  cord 
<z,  which  is  connected  with 
one  of  the  keys  of  a  key- 
board placed  in  front  of  the 
apparatus  (fig.  208).  When 
a  key  is  depressed,  the  cord 
moves  the  lever,  which 
raises  the  clapper,  and  the 
resonator  then  acts  by 
strengthening  its  diapason. 
Hence  by  depressing  any 
keys  we  may  add  to  the 
fundamental  sounds  any  of 
the  nine  primary  harmonics,  and  thus  reproduce  the  sounds,  the  composition 
of  which  has  been  determined  by  analysis.  Thus  by  depressing  all  the 
keys  at  once  we  obtain  the  sound  of  an  open  pipe  in  unison  with  the  deepest 
diapason.  By  depressing  the  key  of  the  fundamental  notes  and  those  of  its 
uneven  harmonics,  we  obtain  the  sound  of  a  closed  pipe. 

258.  Results  of  Helmholtzs  researches — By  both  his  analytical  and 
synthetical  investigations  into  sounds  of  the  most  varied  kinds — those  from 
various  musical  instruments,  the  human  voice,  and  even  noises — Helmholtz 
has  fully  succeeded  in  explaining  the  different  timbre  or  quality  of  sounds.  It 
is  due  to  the  different  intensities  of  the  harmonics  which  accompany  the 
primary'  tones  of  these  sounds.  The  leading  results  of  these  researches  into 
the  colour  of  sounds  may  be  thus  stated  : — 

i.  Simple  tones,  as  those  produced  by  a  tuning-fork  with  a  resonance  box, 
and  by  wide  covered  pipes,  are  soft  and  agreeable  without  any  roughness, 
but  weak,  and  in  the  deeper  notes  dull. 

ii.  Musical  sounds  accompanied  by  a  series  of  harmonics,  say  up  to  the 
sixth,  in  moderate  strength,  are  full  and  musical.  In  comparison  with  simple 


Fig.  209. 


212  Acoustics.  [258- 

tones  they  are  grander,  richer,  and  more  sonorous.     Such  are  the  sounds  of 
open  organ  pipes,  of  the  pianoforte,  &c. 

iii.  If  only  the  uneven  harmonics  are  present,  as  in  the  case  of  narrow 
covered  pipes,  of  pianoforte  strings  struck  in  the  middle,  clarionets,  &c.,  the 
sound  becomes  indistinct  ;  and  when  a  greater  number  of  harmonics  are 
audible,  the  sound  acquires  a  nasal  character. 

iv.  If  the  harmonics  beyond  the  sixth  and  seventh  are  very  distinct,  the 
sound  becomes  sharp  and  rough.  If  less  strong,  the  harmonics  are  not 
prejudicial  to  the  musical  usefulness  of  the  notes.  On  the  contrary,  they 
are  useful  as  imparting  character  and  expression  to  the  music.  Of  this  kind 
are  most  stringed  instruments,  and  most  pipes  furnished  with  tongues,  &c. 
Sounds  in  which  harmonics  are  particularly  strong  acquire  thereby  a  pecu- 
liarly penetrating  character ;  such  are  those  yielded  by  brass  instruments. 

v.  To  form  a  given  vowel  sound  one  or  more  characteristic  notes  which 
are  always  the  same  must  be  added.  These  change  with  the  syllable  pro- 
nounced, but  depend  neither  on  the  height  of  the  note,  nor  on  the  person 
who  emits  them. 

259.  Production  of  vocal  sounds. — The  trachea  or  windpipe  is  a  tube 
which  terminates  at  one  end  in  the  lungs,  and  at  the  other  in  the  larynx 

which  is  the  true  organ  of  vocal  sound. 
Fig.  210  represents  a  horizontal  section  of 
this  organ.  It  consists  of  a  number  of  car- 
tilaginous structures  b  b  which  are  connected 
by  various  muscles,  by  which  great  variety  and 
control  in  the  motions  is  attainable.  These 
muscles  are  connected  with,  and  move,  two 
elastic  membranes  or  bands  with  broad  bases 
fixed  to  the  larynx, and  with  sharp  edges  cc\ 
these  are  called  the  vocal  chords.  Accord- 
ing to  the  pressure  of  the  muscles  these 
chords  are  more  or  less  tightly  stretched, 
and  the  space  between  them,  the  vocal  slit, 
is  narrower  or  wider  accordingly.  In  ordi- 
nary breathing,  air  passes  through  the  triangular  aperture  o  ;  but  when  in 
singing  this  is  closed,  the  vocal  chords  are  stretched  and  are  put  in  vibration 
by  the  current  of  air,  and  produce  tones  which  are  higher  the  more  tightly 
the  chords  are  stretched,  and  the  narrower  is  the  vocal  slit. 

The  notes  produced  by  men  are  deeper  than  those  of  women  or  boys, 
because  in  them  the  larynx  is  longer  and  the  vocal  chords  larger  and  thicker  ; 
hence,  though  equally  elastic,  they  vibrate  less  swiftly.  The  vocal  chords 
are  18  millimetres  long  in  men,  and  12  millimetres  long  in  women.  Chest 
notes  are  due  to  the  fact  that  the  whole  membrane  vibrates,  while  the  fal- 
setto is  produced  by  a  vibration  of  the  extreme  edges,  only.  The  ordinary 
compass  of  the  voice  is  within  two  octaves,  though  this  is  exceeded  by  some 
celebrated  singers,  Catalini,  for  instance,  is  said  to  have  had  a  range  of  3§ 
octaves. 

The  wave  length  of  the  sounds  emitted  by  a  man's  voice  in  ordinary  con- 
versation is  from  8  feet  to  12  feet,  and  that  of  women's  voice  is  from  2  feet  to 
4  feet,  in  a  second. 


-260] 


Interference  of  Sound. 


213 


The  sound  of  the  human  voice  is  very  complex  and  rich  in  harmonics,  for 
the  mouth  and  the  various  cavities  opening  into  the  mouth;  act  as  resonators  ; 
as  the  note  changes  with  their  extent,  with  the  degree  to  which  the  mouth  is 
opened  and  the  shape  given  to  it,  certain  harmonics  are  strengthened  or  not, 
and  thus  the  voice  acquires  a  different  timbre. 

260.  Perception  of  sounds.  Tne  ear. — The  organ  of  hearing  in  man 
consists  of  several  structures  ;  the  external  ear  (fig.  211)  by  which  the  sound 
is  collected  and  transmitted  through  the  auditory  passage  a  to  the  drum  or 
tympanum  /.  This  is  a  delicated  tightly  stretched  membrane  or  skin  which 
separates  the  outer  ear  from  the  middle  ear  or  tympanic  cavity.  This  is  a 
cavity  in  the  temporal  bone  in  which  are  several  small  bones  whose  dimen- 
sions are  considerably  exaggerated  in  the  figure.  One  of  these,  the  hammer 
d,  is  attached  at  one  end  to  the  drum,  and  at  the  other  is  jointed  to  the 
anvil  e  :  the  latter  is  connected  by  means  of  the  stirrup  bone  f,  to  the  oval 
window,  an  aperture  closed  by  a  fine  membrane  and  which  separates  the 
tympanic  cavity  from  the  labyrinth.  The  tympanic  cavity  is  also  connected 
by  the  Eustachian  tube  b  with  the  cavity  of  the  mouth,  so  that  the  air  in  it 
is  always  under  the  same  pressure. 

The  labyrinth  is  a  complicated  structure  filled  with  fluid  ;  it  is  entirely  of 
bone,  with  the  exception  of  the  oval  window  already  mentioned  and  the 
round  window  o.  The 
labyrinth  consists  of  three 
parts  :  the  vestibule,  which 
is  closed  by  the  oval  win- 
dow ;  the  three  semicir- 
cular canals  k ;  and  the 
spiral-shaped  cochlea  or 
snail  shell  s.  This  is 
separated  throughout  its 
entire  length  by  a  divi- 
sion partly  of  bony  pro- 
jection and  partly  of 
membrane ;  the  upper 
part  of  this  division  is 
connected  with  the  vesti- 
bule, and  therefore  with 
the  oval  window,  while 

the  lower  part  is  connected  with  the  round  window.  In  the  labyrinthine  fluid 
of  this  part  the  termination  of  the  auditory  nerve  is  spread,  the  other  end 
leading  to  the  brain. 

The  membranous  part  of  this  diaphragm  is  lined  with  about  3000 
extremely  minute  fibres  which  are  the  termination  of  the  acoustic  nerve  ;/. 
Each  of  these,  which  are  called  Corti's  fibres,  seems  to  be  tuned  for  a 
particular  note  as  if  it  were  a  small  resonator.  Thus  when  the  vibrations  of 
any  particular  note  reach  these  fibres,  through  the  intervention  of  the  stirrup 
bone  and  the  fluid  of  the  labyrinth,  one  fibre  or  set  of  fibres  only  vibrates  in 
unison  with  this  note,  and  is  deaf  for  all  others.  Hence  each  simple  note 
only  causes  one  fibre  to  vibrate,  while  compound  notes  cause  several  ;  just 
as  when  we  sing  with  a  piano,  only  the  fundamental  note  and  its  harmonics 


214  Acoustics.  [260- 

vibrate.  Thus,  however  complex  external  sounds  may  be,  these  microscopic 
fibres  can  analyse  it  and  reveal  the  constituents  of  which  it  is  formed. 

261.  Interference  of  sound.  —  If  two  waves  of  sound  of  the  same  length 
proceed  in  the  same  direction,  and  if  they  coincide  in  their  phases,  they 
strengthen  one  another  ;  if,  however,  their  phases  differ  by  half  a  wave  length 
they  neutralise  each  other,  and  silence  is  the  result.     This  is  called  the  inter- 

ference of  sound. 

It  may  be  illustrated  by  a  number  of  experiments,  of  which  that  repre- 
sented in  fig.  212  is  one  of  the  simplest  and  most  convenient.     Two  T-shaped 

glass  tubes  obac  and  nedf,  are 
connected  at  one  end  by  a  short 
indiarubber  tube  ad,  while 
at  the  other  ends  they  are 
connected  by  a  long  indiarub- 
ber tube  cqf.  The  end  o  pro- 
vided with  a  caoutchouc  tube 
is  held  in  one  ear,  the  other  ear 

F;  being  closed,  and  a  tuning-fork 

is  sounded  in  front  of  the  long 

free  tube  nrs.  If  the  length  of  the  indiarubber  tube  cqf  be  half  the  wave 
length  of  the  note  produced  by  the  fork,  the  sounds  will  reach  the  ear  in 
completely  opposite  phases  ;  they  will  accordingly  neutralise  each  other  and 
no  sound  will  be  heard.  But  if  this  indiarubber  tube  is  closed  by  pinching 
it,  the  note  is  at  once  heard.  If  the  tuning-fork  gives  the  note  cv  the  note 
it  produces  makes  528  vibrations  in  a  second,  and  the  length  of  the  tube 
should  be  34  centimetres. 

262.  Beats.  —  If  the  notes  are  different  and  are  not  quite  in  the  same 
phase,  they  alternately  weaken  and  strengthen  each  other  ;  they  are  said  to 

Fig.  213. 


Fig.  214. 

beat  with  one  another.  This  may  be  explained  as  follows  : — Suppose  AB,  in 
fig.  213,  to  be  a  row  of  particles  transmitting  the  sound  :  suppose  the  vibra- 
tions producing  the  one  tone  to  be  indicated  by  the  continuous  curved  line  ; 
then,  on  the  one  hand,  the  ordinates  of  the  different  points  of  AB  give  the 
velocities  with  which  those  points  are  simultaneously  moving,  and,  on  the 
other  hand,  each  point  will  have  successively  the  different  velocities  repre- 
sented by  the  successive  ordinates.  In  like  manner  let  the  dotted  line  show 
the  vibrations  which  produce  the  second  tone.  And,  for  the  sake  of  distinct- 
ness, suppose  the  number  of  vibrations  in  a  second  producing  the  former 
tone  to  be  to  that  producing  the  latter  in  the  ratio  of  3  :  2.  Now  let  us  con- 


-262]  Combinational  Tones.  2 1 5 

sider  any  point  which  when  at  rest  occupies  the  position  N  ;  draw  the  ordi- 
nate  cutting  the  former  curve  in  P  and  the  latter  in  Q.  If  the  tones  were 
sounded  separately,  the  velocity  of  N  at  a  given  distance  produced  by  the 
former  tone  would  be  PN,  and  that  of  N  at  the  same  instant  produced  by 
the  latter  tone  would  be  QN.  Consequently,  as  they  are  sounded  together, 
the  actual  velocity  of  N  at  the  given  instant  is  the  sum  of  these,  or  PN  +  QN. 
If  at  the  same  instant  we  consider  the  point  «,  its  velocity  will  consist  of  pn 
and  nq  jointly,  but,  as  these  are  in  opposite  directions,  its  actual  amount 
will  be  ^;/  —  nq.  Hence  the  actual  velocity  resulting  from  the  co-existence 
of  the  two  tones  will  be  indicated  by  the  curve  in  fig.  214,  whose  ordinates 
equal  the  (algebraical)  sum  of  the  corresponding  ordinates  of  the  two  curves 
in  fig.  213  ;  that  is,  if  AN,  An,  .  .  .  represent  equal  distances  in  both  figures, 
the  curve  is  described  by  taking  RN  equal  to  PN  +  QN,  rn  equal  topn  —  gn, 
and  so  on.  This  curve  shows  by  its  successive  ordinates  the  simultaneous 
velocities  of  the  different  particles  of  AB,  and  the  successive  velocities  com- 
municated to  the  drum  of  the  ear.  An  inspection  of  the  figure  will  show 
that  the  velocities  are  first  great,  then  small,  then  great,  and  so  on,  the 
drum  being  first  moved  rapidly  for  a  short  time,  then  for  a  short  time  nearly 
brought  to  rest,  and  so  on.  In  short,  the  effect  of  the  beating  of  tones  on 
the  ear,  as  compared  with  that  of  a  continuous  tone,  is  strictly  analogous 
to  the  effect  produced  on  the  eye  by  a  flickering,  as  compared  with  a  steady, 
light. 

It  may  be  proved  that  when  two  simple  tones  are  produced  by  m  and  n 
double  vibrations  per  second,  they  produce  m  —  n  beats  per  second;  thus,  if 
C  is  produced  by  128,  and  D  by  144,  double  vibrations  per  second,  they  will 
on  being  sounded  together  produce  16  beats  per  second.  It  has  been  ascer- 
tained that  the  beats  produced  by  two  tones  are  not  audible  unless  the  ratio 
m  :  n  is  less  than  the  ratio  6  :  5.  Hence,  in  the  case  represented  by  fig.  213, 
though  the  alternations  of  intensity  exist,  they  would  not  be  audible.  Also, 
if  the  tones  have  very  different  intensities,  the  intensity  of  the  beat  is  very 
much  disguised. 

It  is  found  that  when  beats  are  fewer  than  10  per  second  or  more  than  70 
per  second  they  are  disagreeable,  but  not  to  the  extent  of  producing  discord. 
Beats  from  10  to  70  per  second  may  be  regarded  as  the  source  of  all  discord 
in  music,  the  maximum  of  dissonance  being  attained  when  about  30  beats 
are  produced  in  a  second.  For  example,  if  c  and  B  are  sounded  together 
the  effect  is  very  discordant,  the  interval  between  those  notes  being  16  :  15, 
so  that  the  beats  are  audible,  and  the  number  of  beats  per  second  being  16. 
On  the  other  hand,  if  C,  E,  and  G  are  sounded  together  there  is  no  disso- 
nance ;  but  if  C,  E,  G,  B  are  sounded  together  the  discord  is  very  marked, 
since  C  produces  r,  which  is  discordant  with  B.  It  will  be  remarked  that 
C,  E,  G  is  a  major  triad,  while  E,  G,  B  is  a  minor  triad. 

A  compound  musical  tone,  being  composed  of  simple  tones  represented 
•by  i,  2,  3,  4,  5,  6,  7,  &c.,  does  not  give  rise  to  any  simple  tones  capable  of 
producing  an  audible  beat  up  to  the  seventh — the  sixth  and  seventh  are  the 
first  that  produce  an  audible  beat.  It  is  for  this  reason  that  there  is  no 
trace  of  roughness  in  a  compound  tone,  unless  the  seventh  harmonic  be 
audible. 

If  we  were  to  represent  graphically  a  compound  tone,  we  should  proceed 


216  Acoustics.  [262- 

to  construct  a  curve  out  of  simple  tones  of  different  intensities  in  the  same 
manner  as  fig.  214  is  constructed  from  two  simple  tones  of  equal  intensity 
represented  by  fig.  213.  It  is  evident  that  the  resulting  curve  will  take 
different  forms  according  to  the  presence  or  absence  of  different  harmonics 
and  their  different  intensities  ;  in  other  words,  the  colour  or  timbre  of  the 
notes  produced  by  different  instruments  will  depend  upon  the  form  of  the 
vibrations  producing  the  sound. 

Beats  not  too  fast  to  be  readily  counted  arise  between  adjacent  notes  in 
the  lower  octaves  of  large  organs.  They  are  also  met  with  in  the  sounds  of 
church  bells,  and  in  those  emitted  by  telegraph  wires  when  vibrating  power- 
fully in  a  strong  wind.  They  are  heard  very  distinctly  in  the  latter  case  by 
pressing  one  ear  against  a  telegraph-post  and  closing  the  other. 

By  means  of  beats  the  notes  emitted  by  two  musical  instruments  may  be 
brought  into  very  accurate  unison,  by  continuing  the  tuning  until  the  beats 
disappear.  In  order  to  make  tuning-forks  produce  the  normal  number  of 
440  vibrations,  an  auxiliary  tuning-fork  is  used  which  makes  436  vibrations  ; 
each  of  the  forks  under  experiment  must  then  give  4  beats  in  a  second,  which 
can  be  controlled  with  very  great  accuracy. 

263.  Combinational   tones. — Besides   the   beats    produced  when   two 
musical  notes  are  sounded  together,  there  is  another  and  distinct  pheno- 
menon, which  may  be  thus  described  : — Suppose  two  simple  tones  to  be  simul- 
taneously produced  by  vibrations  of  finite  extent,  and  of  n  and  m  vibrations 
per  second.     It  has  been  shown  by  Helmholtz  that  they  generate  a  series  of 
other  tones.     The  principal  one  of  these,  which  may  be  called  the  differen- 
tial tone,  is  produced  by  n  —  m  vibrations  per  second.     Its  intensity  is  usually 
very  small,  but  it  is  distinctly  audible  in  beats.     It  has  been  called  the  grave 
harmonic,  as  generally  its   pitch  is  much  lower  than  that   of  the  notes  by 
which  it  is  generated.     It  has  been  supposed  to  be  caused  by  the  beats  be- 
coming too  numerous  to  be  distinguished,  and  coalescing  into  a  continuous 
sound,  and  this  supposition  was  countenanced  by  the  fact  that  its  pitch  is 
the  same  as  the  beat  number.     The  supposition  is  shown  to  be  erroneous, 
first  by  the  existence  of  the  differential  tones  for  intervals  that  do  not  beat  ; 
and,  secondly,  by  the  fact  that,  under  certain  circumstances,  both  the  beats 
and  the  differential  tones  may  be  heard  together. 

264.  The   physical   constitution  of  musical  chords. — Let   us   suppose 
two  compound  tones  to  be  sounded  together,  say  C  and  G,  then  we  obtain 
two  series  of  tones  each  consisting  of  a  primary  and  its  harmonics,  namely, 
denoting  C  by  4,  the  two  series,  4,8,  12,  16,  .  .  .  and  6,  12,  18,  24,  &c.    Now, 
if,  instead  of  producing  the  two  notes  C  and  G,  we  had  sounded  the  octave 
below  C,  we  should  have  produced  the  series,  2,  4,  6,  8,   10,  12,  14,  16,  18, 
&c.     It  is  plain  that  the  two  former  series  when  joined  differ  from  the  last  in 
the  following  respects  : — (a)  The  primary  tone  2  is  omitted,     (b]  In  the  case 
of  the  last  series,  the  consecutive  tones  continually  decrease  in  intensity  ; 
whereas  in  the  two  former  series,  4  and  6  are  of  the  same  intensity,  8  is  of 
lower  intensity,  but  the  two  I2's  will  strengthen  each  other,  and  so  on.     (c] 
Certain  of  the  harmonics  of  the  primary  2  are  omitted  ;  for  example,  10,  14, 
&c.,  do  not  occur  in  either  of  the  two  former  series.     In  spite  of  these  dif- 
ferences, however,  the  two  compound  jiotes  affect  the  ear  in  a  manner  very 
closely  resembling  a  single  compound  tone  ;  in  short,  they  coalesce  into  a 


-264]         The  Physical  Constitution  of  Musical  Chords.  217 

single  tone  with  an  artificial  colour.  It  maybe  added  that  in  the  case  above 
taken  C  and  G  produce  as  a  combination  tone  2  (that  is  6-4),  so  that, 
strictly  speaking,  the  2  is  not  wanted  in  the  series  produced  by  C  and  G, 
only  it  exists  in  very  diminished  intensity.  The  same  explanation  will 
apply  to  all  possible  chords ;  for  example,  in  the  case  of  the  major  chord, 
C,  E,  G,  we  have  a  tone  of  artificial  colour  expressed  by  the  series  of  simple 
tones,  4,  5,  6,  8,  10,  12,  15,  16,  18,  &c.,  together  with  the  combination  tones, 
1,1,2.  It  will  be  remarked  that  in  the  whole  of  this  series  there  are  no  dis- 
sonant tones  introduced,  except  15,  16,  and  16,  18,  and  this  dissonance  will 
be  inappreciably  slight,  since  15  is  the  third  harmonic  of  5,  and  16  the 
fourth  harmonic  of  4,  so  that  their  intensities  will  be  different,  as  also  will  be 
the  intensities  of  16  and  18.  On  the  other  hand,  nearly  all  the  tones  which 
form  a  natural  compound  tone  are  present,  namely,  there  are  i,  2,  4,  5,  6,  8, 
10,  12,  &c.,  in  place  of  i,  2,  3,  4,  5,  6,  7,  8,  9,  10,  11,  12,  &c.  In  short,  the 
major  triad  differs  only  from  a  natural  compound  tone  in  that  it  consists  of 
a  series  of  simple  tones  of  different  intensities,  and  omits  those  which,  by 
beating  with  its  neighbouring  tone,  would  produce  dissonance  :  for  example, 
7,  which  would  beat  with  6  and  8  ;  9,  which  would  beat  with  8  and  10  ;  and 
n,  which  would  beat  with  loand  12.  It  is  this  circumstance  which  renders 
the  major  chord  of  such  great  importance  in  harmony.  If  the  constituents 
of  the  minor  chord  are  similarly  discussed,  namely,  three  compound  tones 
whose  primaries  are  proportional  to  10,  12,  15,  it  will  be  found  to  differ  from 
the  major  chord  in  the  following  principal  respects  :  (a)  The  primary  of  the 
natural  tone  to  which  it  approximates  is  very  much  deeper  than  that  of  the 
corresponding  major  chord,  (b]  It  introduces  the  differential  tones,  2,  3,  5, 
which  form  a  major  chord.  Now  it  has  already  been  remarked  that  when  a 
major  and  minor  chord  are  sounded  together,  they  are  distinctly  dissonant ; 
for  example,  when  C,  E,  G,  A  are  sounded  together.  Accordingly,  the  fact 
of  the  differential  tones  forming  a  major  chord,  shows  that  an  elementary 
dissonance  exists  in  every  minor  chord. 


218 


Acoustics. 


[265 


CHAPTER   IV. 

VIBRATIONS   OF   STRETCHED   STRINGS,   AND   OF   COLUMNS   OF   AIR. 

265.  Vibrations    of  strings. — By  a  string  is    meant    the    string   of   a 
musical  instrument,  such  as  a  violin,  which  is  stretched  by  a  certain  force, 
and   is    commonly   of   catgut    or   is  a   metal  wire.     The  vibrations  which 
strings  experience  may  be  either  transversal  or  longitudinal,  but  practically 
the  former  are  alone  important.     Transversal  vibrations  may  be  produced 
by  drawing  a  bow  across  the  string,  as  in  the  case  of  the  violin  :  or  by 
striking  the  string,  as  in  the  case  of  the  pianoforte  ;  or  by  pulling  it  trans- 
versely, and  then  letting  it  go  suddenly,  as  in  the  case  of  the  guitar  and 
harp. 

266.  Sonometer. — The  sonometer  is  an  apparatus  by  which  the  trans- 
verse vibrations  of  strings  may  be  studied.     It  is  also  called  the  monochord 


Fig.  215. 

because  it  has  generally  only  one  string.  In  addition  to  the  string,  it  con- 
sists of  a  thin  wooden  box  to  strengthen  the  sound  ;  on  this  there  are  two 
fixed  bridges,  A  and  D  (fig.  2 1 5),  over  which  and  over  the  pulley  n,  passes 
the  string,  which  is  usually  a  metal  wire.  This  is  fastened  at  one  end,  and 
stretched  at  the  other  by  weights,  P,  which  can  be  increased  at  will.  By 
means  of  a  third  movable  bridge,  B,  the  length  of  that  portion  of  the  wire 
which  is  to  be  put  in  vibration  can  be  altered  at  pleasure. 

267.  Laws  of  the  transverse  vibrations  of  strings. — If  /  be  the 
length  of  a  string — that  is,  the  vibrating  part  between  two  bridges,  A  and  B 
(fig.  215) — rthe  radius  of  the  string,  dfits  density,  P  the  stretching  weight, 
and  n  the  number  of  vibrations  per  second,  it  is  found  by  calculation  that 

n  =  ~  A  /_£;  TT  being  the  ratio  of  the  circumference  to  the  diameter,  g 
the  acceleration  of  gravity. 


-269]  Nodes  wid  Loops.  219 

The  above  formula  expresses  the  following  laws  : — 

I.  The  stretching  weight  or  tension  being  constant ',  the  number  of  vibra- 
tions in  a  second  is  inversely  as  the  length. 

I 1.  The  number  of  vibrations  in  a  second  is  inversely  as  the  diameter  of 
the  string. 

III.  The  number  of  vibrations  in  a  second  is  directly  as  the  square  root  of 
the  stretching  weight  or  tension. 

IV.  The  number  of  vibrations  in  a  second  of  a  string  is  inversely  as  the 
square  root  of  its  density. 

These  laws  are  applied  in  the  construction  of  stringed  instruments,  in 
which  the  length,  diameter,  tension,  and  material  of  the  strings  are  so 
chosen,  that  given  notes  may  be  produced  from  them. 

268.  Experimental  verification  of  the  laws  of  the  transverse  vibra- 
tion of  strings. — Law  of  the  lengths.  In  order  to  prove  this  law,  we  may 
call  to  mind  that  the  relative  numbers  of  vibrations  of  the  notes  of  the  gamut 
are 

CDEFGABc 


^435 

4323 


If  now  the  entire  length  of  the  sonometer  be  made  to  vibrate,  and  then,  by 
means  of  the  bridge  B,  the  lengths  f,  f ,  f,  f,  f,  T8B,  §,  which  are  the  inverse  of 
the  above  numbers,  be  successively  made  to  vibrate,  all  the  notes  of  the 
gamut  are  successively  obtained,  which  proves  the  first  law. 

I.'i-j  of  the  diameters.  This  law  is  verified  by  stretching  upon  the  sono- 
meter two  cords  of  the  same  material,  the  diameters  of  which  are  as  3  to  2, 
for  instance.  When  these  are  made  to  vibrate,  the  second  cord  gives  the 
fifth  above  the  other  ;  which  shows  that  it  makes  three  vibrations  while  the 
first  makes  two. 

Law  of  the  tensions.  Having  placed  on  the  sonometer  two  identical 
strings,  they  are  stretched  by  weights  which  are  as  4  :  9.  The  second  now 
gives  the  fifth  of  the  first,  from  which  it  is  concluded  that  the  numbers  of 
their  vibrations  are  as  2  :  3  ;  that  is,  as  the  square  roots  of  the  tensions.  If 
the  two  weights  are  as  1 6  to  25,  the  major  third  or  f  would  be  obtained. 

Law  of  the  densities.  Two  strings  of  the  same  radius,  but  different 
densities,  are  fixed  on  the  sonometer.  Having  been  subjected  to  the  same 
stretching  weight,  the  position  of  the  movable  bridge  on  the  denser  one  is 
altered  until  it  is  in  unison  with  the  other  string.  If  then  </and  d*  are  the 
densities  of  the  two  strings,  and  /  and  f  the  lengths  which  vibrate  in  unison 

we  find    ,=  ~=^.     But  as  we  know  from  the  first  law  that   f-  -,  we  have 

;/      \ '  a' 

=  — T-,  which  verifies  this  law. 
;/,      Vr/ 

It  must  be  added  that  a  string,  like  most  other  sounding  bodies,  never 
vibrates  exclusively  as  a  whole,  but  only  in  aliquot  parts  ;  so  that  the  funda- 
mental note  is  always  accompanied  by  overtones,  which,  however,  are  usually 
so  feeble  as  to  be  imperceptible  to  ordinary  ears  (254). 

269.  Nodes  and  loops. — Let  us  suppose  the  string  AD  (fig.  215)  to  begin 
vibrating,  the  ends  A  and  D  being  fixed,  and  while  it  is  doing  so,  let  a  point, 
B,  be  brought  to  rest  by  a  stop,  and  let  us  suppose  DB  to  be  one-third  part 

L  2 


FIG.  216. 


220  Acoustics.  [269- 

of  AD.  The  part  DB  must  now  vibrate  about  B  and  D  as  fixed  points  in 
the  manner  indicated  by  the  continuous  and  dotted  lines  ;  now  all  parts  of 
the  same  string  tend  to  make  a  vibration  in  the  same  time  ;  accordingly  the 
part  between  A  and  B  will  not  perform  a  single  vibration,  but  will  divide  into 
two  at  the  point  C,  and  vibrate  in  the  manner  shown  in  the  figure.  If  BD 
were  one-fourth  part  of  AD  (fig.  217),  the  part  AD  would  be  subdivided  at 
C  and  C'  into  three  vibrating  portions  each  equal  to  BD.  The  points  B,  C,  C' 
are  called  nodes  or  nodal  points ;  the  middle  point  of  the  part  of  the  string 
between  any  two  consecutive  nodes  is  called  a  loop  or  ventral  segment.  It 
will  be  remarked  that  the  ratio  of  BD  :  BA  must  be  that  of  some  two  whole 
numbers,  for  example,  i  :  2,  i  :  3,  2  :  3,  &c.,  otherwise  the  nodes  cannot  be 
formed,  since  the  two  portions  of  the  string  cannot  then  be  made  to  vibrate 
in  the  same  time,  and  the  vibrations  will  interfere  with  and  soon  destroy  one 
another. 

If  now  we  refer  to  fig.  216,  the  existence  of  the  node  at  C  can  be  easily 
proved  by  bending  some  light  pieces  of  paper,  and  placing  them  on  the  string, 

say  three  pieces,  one 
at  C  and  the  others 
respectively  midway 
between  B  and  C, 
and  between  C  and 
A.  The  one  at  C 
experiences  only  a 
very  slight  motion, 
and  remains  in  its 
place,  thereby  prov- 
ing the  existence  of 
a  node  at  C ;  the 
other  two  are  vio- 
lently shaken,  and 
in  most  cases  thrown  off  the  string. 

When  a  musical  string  vibrates  between  fixed  points  A  and  B,  its  motion 
is  not  quite  so  simple  as  might  be  inferred  from  the  above  description.  In 
point  of  fact,  partial  vibrations  are  soon  produced,  and  superimposed  upon 
the  primary  vibrations.  The  partial  vibrations  correspond  to  the  half,  third, 
fourth,  &c.,  parts  of  the  string.  It  is  by  these  partial  vibrations  that  the 
harmonics  are  produced  which  accompany  the  primary  note  due  to  the 
primary  vibrations  (268). 

270.  Wind  instruments. — In  the  cases  hitherto  considered  the  sound 
results  from  the  vibrations  of  solid  bodies,  and  the  air  only  serves  as  a  vehicle 
for  transmitting  them.  In  wind  instruments,  on  the  contrary,  when  the  sides 
of  the  tube  are  of  adequate  thickness,  the  enclosed  column  of  air  is  the  sound- 
ing body.  In  fact,  the  substance  of  the  tubes  is  without  influence  on  the 
primary  tone  ;  with  equal  dimensions,  it  is  the  same  whether  the  tubes  are  of 
glass,  of  wood,  or  of  metal.  These  different  materials  simply  do  no  more 
than  give  rise  to  different  harmonics,  and  thereby  impart  a  different  quality 
to  the  compound  tone  produced. 

In  reference  to  the  manner  in  which  the  air  in  tubes  is  made  to  vibrate 
wind  instruments  are  divided  into  month  instruments  and  reed  instruments. 


Fig.  217. 


-272] 


Reed  Instruments. 


221 


271.  Momth  instrument*. — In  mouth  instruments  all  parts  of  the  mouth- 
piece are  fixed.     Fig.  219  represents  the  mouthpiece  of  an  organ  pipe,  and 
fig.  218  that  of  a  whistle,  or  of  a  flageolet.     In  both 

figures,  the  aperture  ib  is  called  the  mouth  ;  ^it  is  here 
that  air  enters  the  pipe  ;  b  and  o  are  the  lips,  the  upper 
one  of  which  is  bevelled.  The  mouthpiece  is  fixed  at 
one  end  of  a  tube,  the  other  end  of  which  may  be  either 
opened  or  closed.  In  fig.  219  the  tube  can  be  fitted 
on  a  wind-chest  by  means  of  the  foot  P. 

When  a  rapid  current  of  air  enters  by  the  mouth, 
it  strikes  against  the  upper  lip,  and  a  shock  is  pro- 
duced which  causes  the  air  to  issue  from  bo  in  an 
intermittent  manner.  In  this  way,  pulsations  are  pro- 
duced which,  transmitted  to  the  air  in  the  pipe,  make 
it  vibrate,  and  a  sound  is  the  result.  In  order  that  a 
pure  note  may  be  produced,  there  must  be  a  certain 
relation  between  the  form  of  the  lips  and  the  mag- 
nitude of  the  mouth ;  the  tube  also  ought  to  have  a 
great  length  in  comparison  with  its  diameter.  The  Fis-  2l8-  *'«•  2I9- 
number  of  vibrations  depends  in  general  on  the  dimensions  of  the  pipe,  and 
the  velocity  of  the  current  of  air. 

272.  Rsei  instruments. — In  reed  instruments  a  simple  elastic  tongue 
sets  the  air  in  vibration.     The  tongue,  which  is  either  of  metal  or  of  wood,  is 
moved  by  a  current  of  air.     The  mouthpieces  of  the  oboe,  the  bassoon,  the 
clarionet,  the  child's  trumpet,  are  different  applications  of  the  reed,  which, 
it  may  be  remarked,  is  seen  in  its  simplest  form  in  the  Jew's  harp.     Some 
organ  pipes  are  reed  pipes,  others  are  mouth  pipes. 

Fig.  220  represents  a  model  of  a  reed  pipe  as  commonly  shown  in 
lectures.  It  is  fixed  on  the  wind-chest  Q  of  a  bellows,  and  the  vibrations 
of  the  reed  can  be  seen  through  a  piece  of  glass,  E,  fitting  into  the  sides. 
A  wooden  horn,  H,  strengthens  the  sound. 

Fig.  221  shows  the  reed,  out  of  the  pipe.  It  consists  of  four  pieces  :  ist, 
a  rectangular  wooden  tube  closed  below  and  open  above  at  o ;  2nd,  a 
copper  plate  cc  forming  one  side  of  the  tube,  and  in  which  there  is  a  longitu- 
dinal aperture,  through  which  air  passes  from  the  tube  MN  to  the  orifice  o  • 
3rd,  a  thin  elastic  plate,  /,  called  the  tongue,  which  is  fixed  at  its  upper  end, 
and  which  grazes  the  edge  of  the  longitudinal  aperture,  nearly  closing  it  ; 
4th,  a  curved  wire,  r,  which  presses  against  the  tongue,  and  can  be  moved 
up  and  down.  It  thus  regulates  the  length  of  the  tongue,  and  determines 
the  pitch  of  the  note.  It  is  by  this  wire  that  reed  pipes  are  tuned.  The 
reed  being  replaced  in  the  pipe  MN,  when  a  current  of  air  enters  by  the 
foot  P,  the  tongue  is  compressed,  it  bends  inwards,  and  affords  a  passage  to 
air,  which  escapes  by  the  orifice  o.  But,  being  elastic,  the  tongue  regains 
its  original  position,  and  performing  a  series  of  oscillations  successively 
opens  and  closes  the  orifice.  In  this  way  sonorous  waves  result  and  pro- 
duce a  note,  whose  pitch  increases  with  the  velocity  of  the  current. 

In  this  reed  the  tongue  vibrates  alternately  before  and  behind  the  aper- 
ture, and  just  escapes  grazing  the  edges,  as  is  seen  in  the  harmonium,  con- 
certina, &c. ;  such  a  reed  is  called  a  free  reed.  But  there  are  other  reeds 


222  Acoustics.  [272- 

called  beating  reeds,  in  which  the  tongue,  which  is  larger  than  the  orifice, 
strikes  against  the  edges  at  each  oscillation.      The  reed  of  the  clarionet, 

represented  in  fig.  222,  is  an  ex- 
ample of  this  ;  it  is  kept  in  its 
place  by  the  pressure  of  the  lips. 
The  reeds  of  the  hautboy  and 
bassoon  are  also  of  this  kind. 

273.  Of  the  tones  produced 
by  the  same  pipe. — Daniel  Ber- 
nouilli  discovered  that  the  same 
organ  pipe  can  be  made  to  yield  a 
succession  of  tones  by  properly 
varying  the  force  of  the  current 
of  air.  The  results  he  arrived  at 
may  be  thus  stated  : — 

i.  If  the  pipe  is  open  at  the 
end  opposite  to  the  mouthpiece, 
then,  denoting  the  primary  tone 
by  I,  we  can,  by  gradually  in- 
creasing the  force  of  the  current 
of  air,  obtain  successively  the 
tones,  2,  3,  4,  5,  &c.  ;  that  is  to 
say,  the  harmonics  of  the  primary 
tone. 

ii.  If  the  pipe  is  closed  at  the 
end  opposite  to  the  mouthpiece, 
then,  denoting  the  primary  tone 
by  i,  we  can,  by  gradually  increasing  the  force  of  the  current  of  air,  obtain 
successively  the  tones  3,  5,  7,  &c.  ;  that  is  to  say,  the  uneven  harmonics  of 
the  primary  tone. 

It  must  be  added  that  if  a  closed  and  an  open  pipe  are  to  yield  the  same 
primary  tone,  the  closed  pipe  must  be  half  the  length  of  the  open  pipe,  if  in 
other  respects  they  are  the  same. 

In  any  case  it  is  impossible  to  produce  from  the  given  pipe  a  tone  not 
included  in  the  above  series  respectively. 

Although  the  above  laws  are  enunciated  with  reference  to  an  organ  pipe, 
they  are  of  course  true  of  any  other  pipe  of  uniform  section. 

274.  On  the  nodes  and  loops  of  an  organ  pipe. — The  vibrations  of  the 
air  producing  a  musical  tone  take  place  in  a  direction  parallel  to  the  axis  of 
the  pipe — not  transversely  as  in  the  case  of  the  portions  of  a  vibrating  spring. 
In  the  former  case,  however,  as  well  as  in  the  latter,  the  phenomena  of  nodes 
and  loops  may  be  produced.  But  now  by  a  node  must  be  understood  a 
section  of  the  column  of  air  contained  in  the  pipe,  where  the  particles  remain 
at  rest,  but  where  there  are  rapid  alterations  of  condensation  and  rarefaction. 
By  a  loop  or  ventral  segment  must  be  understood  a  section  of  the  column  of 
air  contained  in  the  pipe  where  the  vibrations  of  the  particles  of  air  have  the 
greatest  amplitudes,  and  where  there  is  no  change  of  density.  The  sections 
of  the  column  of  air  are,  of  course,  made  at  right  angles  to  its  axis.  When 
the  column  of  air  is  divided  into  several  vibrating  portions,  it  is  found  that 


Fig.  220. 


Fig.  221 


Fig.  222. 


-274] 


Nodes  and  Loops  of  an  Organ  Pipe. 


223 


the  distance  between  any  two  consecutive  loops  is  constant,  and  that  it  is 
bisected  by  a  node.  We  can  now  consider  separately  the  cases  of  the  open 
and  closed  pipes. 

i.  In  the  case  of  a  stopped  pipe,  the  bottom  is  always  a  node,  for  the 
layer  of  air  in  contact  with  it  is  necessarily  at  rest,  and  only  undergoes 
variations  in  density.  At  the  mouthpiece,  on  the  contrary,  where  the  air  has 
a  constant  density,  that  of  the  atmosphere,  and  the  vibration  is  at  its  maxi- 
mum, there  is  always  a  loop.  In. any  stopped  pipe  there  is  at  least  one  node 
and  one  loop  (fig.  223) ;  the  pipe  then  yields  its  fundamental  note,  and  the 


i 


T 


V 


~7 


Fig.  223.        Fig.  224.         Fig.  225. 


Fig.  226.          Fig.  227.        Fig.  228. 


distance  VN  from  the  loop  to  the  node  is  equal  to  half  a  condensed  or 
rarefied  wave-length. 

If  the  current  of  air  be  forced,  the  mouthpiece  always  remains  a  loop, 
and  the  bottom  a  node,  the  column  divides  into  three  -equal  parts  (fig.  224), 
and  an  intermediate  node  and  loop  are  formed.  The  sound  produced  is  the 
first  harmonic.  When  the  second  harmonic  (5)  is  produced,  there  are  two 
intermediate  nodes  and  two  loops,  and  the  tube  is  then  subdivided  into  five 
equal  parts  (fig.  225),  and  so  on. 

ii.  In  the  case  of  the  open  pipe,  whatever  note  it  produces,  there  must  be 
a  loop  at  each  end,  since  the  enclosed  column  of  air  is  in  contact  with  the 
external  air  at  those  points.  When  the  primary  tone  is  produced,  there  will 
be  a  loop  at  each  end,  and  a  node  at  the  middle  section  of  the  pipe,  the  nodes 
and  loops  dividing  the  column  into  two  equal  parts  (fig.  226).  When  the 
first  harmonic  (2)  is  produced,  there  will  be  a  loop  at  each  end,  and  a  loop 
in  the  middle,  the  column  being  divided  into  four  equal  parts  by  the  alternate 
loops  and  nodes  (fig.  227).  When  the  second  harmonic  (3)  is  produced,  the 
column  of  air  will  be  divided  into  six  equal  parts  by  the  alternate  nodes  and 
loops,  and  so  on  (fig.  228).  It  will  be  remarked  that  the  successive  modes 
of  division  of  the  vibrating  column  are  the  only  ones  compatible  with  the 


224  Acoustics.  [274- 

alternate  recurrence  at  equal  intervals  of  nodes  and  loops,  and  with  the 
occurrence  of  a  loop  at  each  end  of  the  pipe. 

There  are  several  experiments  by  which  the  existence  of  nodes  and  hoops 
can  be  shown. 

(a)  If  a  fine  membrane  is  stretched  over  a  pasteboard  ring,  and  has 
sprinkled  on  it  some  fine  sand,  it  can  be  gradually  let  down  a  tube,  as  shown 
in  fig.  231.  Now  suppose  the  tube  to  be  producing  a  musical  note.  As  the 


Fig.  229. 


Fig.  230. 


Fig,  231. 


Fig.  232. 


membrane  descends,  it  will  be  set  in  vibration  by  the  vibrating  air.  But 
when  it  reaches  a  node  it  will  cease  to  vibrate,  for  there  the  air  is  at  rest. 
Consequently  the  grains  of  sand,  too,  will  be  at  rest,  and  their  quiescence 
will  indicate  the  position  of  the  node.  On  the  other  hand,  when  the  mem- 
brane reaches  a  loop — that  is,  a  point  where  the  amplitude  of  the  vibrations 
of  the  air  attains  a  maximum — it  will  be  violently  agitated,  as  will  be  shown 
by  the  agitation  of  the  grains  of  sand.  And  thus  the  positions  of  the  loops 
can  be  rendered  manifest. 

(£)  Again,  suppose  a  pipe  to  be  constructed  with  holes  bored  in  one  of 
its  sides,  and  these  covered  by  little  doors  which  can  be  opened  and  shut,  as 
shown  in  fig.  229.  Let  us  suppose  the  little  doors  to  be  shut  and  the  pipe  to 


-275]  Vibrations  produced  by  a  Musical  Pipe.  22$ 

be  caused  to  produce  such  a  note  that  the  nodes  are  at  N  and  N'  and  the 
loops  at  V,  V,  V".  At  the  latter  points  the  density  is  that  of  the  external 
air,  and  consequently  if  the  door  at  V  is  opened  no  change  is  produced  in 
the  note.  At  the  former  points  N  and  N'  condensation  and  rarefaction 
are  alternately  taking  place.  If  now  the  door  at  N'  is  opened,  this  alterna- 
tion of  density  is  no  longer  possible,  for  the  density  at  this  open  point  must 
be  the  same  as  that  of  the  external  air,  and  consequently  N'  becomes  a 
loop,  and  a  note  yielded  by  the  tube  is  changed.  The  change  of  notes,  pro- 
duced by  changing  the  fingering  of  the  flute,  is  one  form  of  this  experi- 
ment. 

(c)  Suppose  A,  in  fig.  230,  to  be  a  pipe  emitting  a  certain  note,  and  sup- 
pose P  to  be  a  plug,  fitting  the  tube,  fastened  to  the  end  of  a  long  rod  by 
which  it  can  be  forced  down  the  tube.     Now  when  the   plug  is  inserted, 
whatever  be  its  position,  there  will  be  a  node  in  contact  with  it.     Conse- 
quently, as  it  is  gradually  forced  down,  the  note  yielded  by  the  pipe  will 
keep  on  changing.     But  every  time  it  reaches  a  position  which  was  occupied 
by  a  node  before   its   insertion,  the   note   becomes   the  same  as  the  note 
originally  yielded.     For  now  the  column  of  air  vibrates  in  exactly  the  same 
manner  as  it  did  before  the  plug  was  put  in. 

(d)  Fig.  232  shows  another  mode  of  illustrating  the  same  point,  which  is 
identical  in  principle  with  Konig's  manometric  flames.     The  figure  repre- 
sents an  organ  pipe,  on  one  side  of  which  is  a  chest,  P,  filled  with  coal  gas, 
by  means  of  the  tirbe  S.     The  gas  from  the  chest  comes  out  in  three  jets,  A, 
B,  C,  and  is  then  ignited.     The  manner  in  which  the  gas  passes  from  the 
chest  to  the  point  of  ignition  is  shown  in  the  smallest  figure,  which  is  an 
enlarged  section  of  A.     A  circular  hole  is  bored  in  the  side  of  the  pipe  and 
covered  with  a  membrane,  r.     A  piece  of  wood  is  fitted  into  the  hole  so  as 
to  leave  a  small  space  between  it  and  the  membrane.     The  gas  passes  from 
the  chest,  in  the  direction  indicated  by  the  arrow,  into  the  space  between 
the  membrane  and  the  piece  of  wood,  and  so  out  of  the  tube, ;;/,  at  the  mouth 
of  which  it  is  ignited.      Now  suppose  the  pipe   to  be  caused  to  yield  its 
primary'  note,  then  as  it  is  an  uncovered  pipe  there  ought  to  be  a  node  at  B, 
its  middle  point.     Consequently  there  ought  to  be  rapid  changes  of  density 
at  B  ;  these  would  cause  the  membrane,  r,  to  vibrate,  and  thereby  blow  out 
flame,  ;;/,  and  this  is  what  actually  happens.     If  by  increasing  the  force  of 
the  wind  the  octave  to  the  primary  note  is  produced,  B  will  be  a  loop,  and 
A  and  C  nodes.     Consequently  the  flames  at  A  and  C  will  now  be  ex- 
tinguished as  is,  in  point  of  fact,  the  case.     But  at  B,  there  being  no  change 
of  density,  the  membrane  is  unmoved,  and  the  flame  continues   to   burn 
steadily. 

By  each  and  all  of  these  experiments  it  is  shown  that  in  a  given  pipe, 
whether  open  or  closed,  there  are  always  a  certain  number  of  nodes,  and 
midway  between  any  two  consecutive  nodes  there  is  always  a  loop  or  ventral 
segment. 

275.  Formulae  relative  to  the  number  of  vibrations  produced  by  a 
musical  pipe. — It  follows  from  what  has  been  said  that  the  column  of  air 
in  stopped  pipes  is  always  divided  by  the  nodes  and  loops  into  an  uneven 
number  of  parts  which  are  equal  to  each  other,  and  each  of  which  is  a  quarter 
of  a  complete  vibration  (figs.  223,  224,  and  225),  while  in  an  open  pipe  it  is 

L  3 


226  Acoustics.  [275- 

divided  into  an  even  number  of  such  parts  (figs.  226,  227,  228).  If  L  be  the 
length  of  the  pipe,  /  the  wave-length  of  the  sound  which  it  emits,  and  p  any 

whole  number,  then  for  stopped  pipes  we  have  L=  (2p  +  l)  — ;    and    for 

4 

open  pipes  L  =  2/—  -•£-.    Replacing  in  each  of  these  formulae  /by  its  value 

-  (253)  we  have  L  =  (zp+i)  V~  and  L=^';  from  which  for  stopped  pipes 

(26  -»-  i)z/        ,  f  <bv 

we   have  n  =  v  ^      -'--  ,  and  for  open  ones  n  =  *— . 
4^  2L 

If,  in  the  first  formula,  we  give  to /the  successive  values  o,  I,  2,  3,  4,  £c., 

we   have  n=  -— ,    -?-  ,    JL .  t^at  js  the  fundamental  sound  and  all  its  uneven 
4L     4L     4L  , 

harmonics  ;  and  in  the  formula  for  the  open  pipe  we  get  similarly  — ,  2  '    ^ 

2 L,    2L,    2 L, 

&c.,  that  is,  the  fundamental  note  and  all  its  harmonics  even  and  uneven. 
276.  Explanation  of  the  existence  of  nodes  and  loops  in  a  musical 

box.— The  existence  of  nodes  and  loops  ie  to  be  explained  by  the  co- 
existence in  the  same  pipe  of  two  equal  waves  travelling  in  contrary 
directions. 

Let  A  (fig.  233)  be  a  point  from  which  a  series  of  waves  sets  out  towards 
B,  and  let  the  length  of  these  waves,  whether  of  condensation  or  rarefaction, 


Fig.  233. 

be  AC,  CD,  DB.  And  let  B  be  the  point  from  which  the  series  of  exactly 
equal  waves  sets  out  towards  A.  It  must  be  borne  in  mind  that  in  the  case 
of  a  wave  of  condensation  originating  at  A  the  particles  move  in  the  direc- 
tion A  to  B,  but  in  a  wave  of  condensation  originating  at  B  they  move  in  the 
direction  B  to  A.  Now  let  us  suppose  that  condensation  at  C,  caused  by 
the  wave  from  A,  begins  at  the  same  instant  that  condensation  caused  by 
the  wave  from  B  begins  at  D.  Consequently,  restricting  our  attention  to 
the  particles  in  the  line  CD,  at  any  instant  the  velocities  of  the  particles  in 
CD  due  to  the  former  wave  will  be  represented  by  the  ordinates  of  the 
curve  SPRT,  while  those  due  to  the  wave  from  B  will  be  represented  by  the 
co-ordinates  of  the  curve  TQrS.  Then,  since  the  waves  travel  with  the  same 
velocity,  and  are  at  C  and  D  respectively  at  the  same  instant,  we  must  have 
for  any  subsequent  instant,  CR  equal  to  Dr.  If,  therefore,  N  is  the  middle 
point  between  C  and  D,  we  must  have  rN  equal  to  RN,  and  consequently 
PN  equal  to  QN  ;  that  is  to  say,  if  the  particle  at  N  transmitted  only  one 
vibration,  its  motion  at  each  instant  would  be  in  the  opposite  phase  to  that 
of  its  motion  if  it  transmitted  only  the  other  vibration.  In  other  words,  the 
particle  N  will  at  every  instant  tend  to  be  moved  with  equal  velocity  in 
opposite  directions  by  the  two  waves,  and  therefore  will  be  permanently  at 
rest.  That  point  is  therefore  a  node.  In  like  manner  there  is  a  node  at  N' 


-277]       Kitndfs  Determination  of  tJie  Velocity  of  Sound.         227 

midway  between  A  and  C,  and  also  at  N"  midway  between  B  and  D.  In 
regard  to  the  motion  of  the  remaining  particles,  it  is  plain  that  their  respec- 
tive velocities  will  be  the  (algebraical)  sum  of  the  velocities  they  would  at 
each  instant  receive  from  the  waves  separately.  Hence  at  the  instant  indi- 
cated by  the  diagram  they  are  given  by  the  ordinates  of  the  curve  HNK. 
This  curve  will  change  from  instant  to  instant,  and  at  the  end  of  the  time 
occupied  by  the  passage  of  a  wave  of  condensation  (or  of  rarefaction)  from 
C  to  D  will  occupy  the  position  shown  by  the  dotted  line  //N£.  Hence  it  is 
evident  that  particles  near  N  have  but  small  changes  of  velocity,  whilst  those 
near  C  and  D  experience  large  changes  of  velocity. 

If  the  curve  HK  were  produced  both  ways,  it  would  always  pass  through 
X'  and  N";  the  part,  however,  between  N  and  N'  would  sometimes  be  on 
one  side,  and  sometimes  on  the  other  side  of  AB.  Hence  all  the  particles 
between  N'  and  N  have,  simultaneously,  first  a  motion  in  the  direction  A  to 
B,  and  then  a  motion  in  the  direction  B  to  A,  those  particles  near  C  having 
the  greatest  amplitude  of  vibrations.  Hence  near  N  and  N'  there  will  be 
alternately  the  greatest  condensation  and  rarefaction. 

This  explanation  applies  to  the  case  in  which  AB  is  the  axis  of  an  open 
organ  pipe,  A  being  the  end  where  the  mouthpiece  is  situated.  The  waves 
from  B  have  their  origin  in  the  reflections  of  the  series  of  waves  from  A.  In 
the  particular  case  considered,  the  note  yielded  by  the  pipe  is  that  indicated 
by  3  ;  that  is,  the  fifth  above  the  octave  to  the  primary  note.  A  similar  ex- 
planation can  obviously  be  applied  to  all  other  cases,  and  whether  the  end 
be  opened  or  closed.  But  in  the  latter  case  the  series  of  waves  from  the 
closed  end  must  commence  at  a  point  distant  from  the  mouthpiece  by  a 
space  equal  to  one  half,  or  three  halves,  or  five  halves,  £c.,  of  the  length  of 
a  wave  of  condensation  or  expansion. 

277.  Kundt's  determination  of  the  velocity  of  sound. — Kundt  has 
devised  a  method  of  determining  the  velocity  of  sound  in  solids  and  in 
gases  which  can  be  easily  performed  by  means  of  simple  apparatus,  and  is 
capable  of  great  accuracy.  A  glass  tube,  BB,  about  two  yards  long  (fig.  226) 
and  two  inches  in  internal  diameter,  is  closed  at  one  end  by  a  movable 
stopper  b  ;  the  other  end  is  fitted  with  a  cork  KK,  which  tightly  grasps  a 
glass  tube,  AA',  of  smaller  dimensions.  This  is  closed  at  one  end  by  a 
piston,  #,  which  moves  with  gentle  friction  in  the  outer  tube  BB.  Then  by 
rubbing  the  free  end  of  the  tube,  AA',  with  a  wet  cloth,  it  produces  longitu- 
dinal vibrations,  and  these  transmit  their  motion  to  the  air  in  the  tube  ab. 
If  the  tube  ab  contain  some  lycopodium  powder,  this  is  set  in  active  vibra- 
tion and  then  arranges  itself  in  small  patches  in  a  certain  definite  order  as 
represented  in  the  figure  ;  the  nature  and  arrangement  of  which  depend  on 
the  vibrating  part  of  the  rod  and  the  tube, 

These  heaps  represent  the  nodes,  and  the  mean  distance  d  between  them 
can  be  measured  with  great  accuracy  ;  it  represents  the  distance  between 
two  nodes,  or,  half  a  wave-length  ;  that  is,  the  wave-length  of  the  sound  in 
air  is  id.  If  the  rod  has  the  length  s  and  is  grasped  in  the  middle  by  the 
cork  KK,  from  the  law  of  the  longitudinal  vibrations  of  rods  (281)  the  wave- 
length of  the  sound  it  then  emits  is  twice  its  length,  or  is.  That  is,  the 
wave-length  of  the  vibrating  column  of  air  is  to  that  in  the  rod  as  id  :  2s. 
As  the  velocity  of  sound  in  any  body  is  equal  to  the  wave-length  in  that 


228  Acoustics.  [277- 

body  multiplied  by  the  number  of  vibrations  in  a  second  ;  and  since  the 
number  of  vibrations  is  here  the  same  in  both  cases,  for  the  tone  is  the 
same,  the  velocity  of  sound  in  the  glass  is  to  the  velocity  of 
sound  in  air  as  2sn  :  2<//z,  that  is,  as  s  :  d.  Thus  when  the  glass 
tube  was  clamped  in  the  middle  by  KK,  so  that  the  length  ab 
was  equal  to  half  the  length  of  the  tube  A'A,  the  number  of  the 
ventral  segments  was  eight.  This  corresponds  to  a  ratio  of 
wave-length  of  i  to  16  :  in  other  words,  the  velocity  of  sound  in 
glass  is  1 6  times  that  in  air. 

The  method  is  capable  of  great  extension.  By  means  of 
the  stopcock  ?;/,  different  gases  could  be  introduced  instead  of 
air,  and  corresponding  differences  found  for  the  length  of  the 
ventral  segments  from  which,  by  a  simple  calculation,  the  cor- 
responding velocities  were  found.  Thus  the  velocities  of  sound 
in  carbonic  acid,  coal  gas,  and  hydrogen,  were  found  to  be 
respectively  0-8,  r6,  and  3*56  that  of  air,  or  nearly  as  the  inverse 
square  of  the  densities. 

So  also  by  varying  the  material  of  the  rod  AA',  different 
velocities  are  obtained.  Thus  the  velocity  in  steel  was  found  to 
be  15*24,  and  that  in  brass  io-87  that  of  air. 

Kundfs  figures  may  also  be  obtained  by  providing  glass 
tubes  a  yard  or  two  in  length  with  lycopodium  powder,  as  in 
the  above  experiment,  and  hermetically  sealing  them  at  both 
ends.  The  tubes  are  then  put  into  longitudinal  vibrations  ;  in- 
stead of  air  they  may  be  filled  with  hydrogen  or  any  other  gas. 
278.  Cbemical  harmonicon. — The  air  in  an  open  tube 
may  be  made  to  give  a  sound  by  means  of  a  luminous  jet  of 
hydrogen,  coal  gas,  £c.  When  a  glass  tube  about  12  inches 
long  is  held  over  a  lighted  jet  of  hydrogen  (fig.  235),  a  note  is 
produced,  which,  if  the  tube  is  in  a  certain  position,  is  the  funda- 
mental note  of  the  tube.  The  sounds,  doubtless,  arise  from 
the  successive  explosions  produced  by  the  periodic  combina- 
tions of  the  atmospheric  oxygen  with  the  issuing  jet  of  hydrogen. 
The  apparatus  is  called  the  chemical  harmonicon, 

The  note  depends  on  the  size  of  the  flame  and  the  length 
of  the  tube  :  with  a  long  tube,  by  varying  the  position  of  the  jet 
in  the  tube,  the  series  of  notes  in  the  ratio  i  :  2  :  3  :  4  :  5  is 
obtained. 

If,  while  the  tube  emits  a  certain  sound,  the  voice  or  the  syren  (242) 
be  gradually  raised  to  the  same  height,  as  soon  as  the  note  is  nearly  in 
unison  with  the  harmonicon,  the  flame  becomes  agitated,  jumps  up  and 
down,  and  is  finally  steady  when  the  two  sounds  are  in  unison.  If  the 
note  of  the  syren  is  gradually  heightened  the  pulsations  again  commence  ; 
they  are  the  optical  expressions  of  the  beats  (262)  which  occur  near  perfect 
unison. 

If,  while  the  jet  burns  in  the  tube  and  produces  a  note,  the  position  of 
the  tube  is  slightly  altered,  a  point  is  reached  at  which  no  sound  is  heard. 
If  now  the  voice,  or  the  syren,  or  the  tuning-fork,  be  pitched  at  the  note 
produced  by  the  jet,  it  begins  to  sing,  and  continues  to  sing  even  after  the 


[A 

Fig.  234. 


Wind  Instruments. 


229 


-280] 

syren  is  silent.     A  mere  noise,  or  shouting  at  an  incorrect  pitch,  affects  the 
flame,  but  does  not  cause  it  to  sing. 

279.  Stringed    instruments — Stringed    musical 
instruments  depend  on  the  production  of  transverse 
vibrations.     In  some,  such  as  the  piano,  the  sounds 
are  constant,  and  each- note  requires  a  separate  string  ; 
in  others,  such  as  the  violin  and  guitar,  the  sounds  are 
•varied  by  the  fingering,  and  can  be  produced  by  fewer 
strings. 

In  the  piano  the  vibrations  of  the  strings  are  pro- 
duced by  the  stroke  of  the  hammer,  which  is  moved 
by  a  series  of  bent  levers  communicating  with  the 
keys.  The  sound  is  strengthened  by  the  vibrations 
of  the  air  in  the  sounding  board  on  which  the  strings 
are  stretched.  Whenever  a  key  is  struck,  a  damper 
is  raised  which  falls  when  the  finger  is  removed  from 
the  key,  and  stops  the  vibrations  of  the  correspond- 
ing string.  By  means  of  ^  pedal  all  the  dampers  can 
be  simultaneously  raised,  and  the  vibrations  then 
last  for  some  time. 

The  harp  is  a  sort  of  transition  from  the  instru- 
ments with  constant  to  those  with  variable  sounds. 
Its  strings  correspond  to  the  natural  notes  of  the 
scale  :  by  means  of  the  pedals  the  lengths  of  the 
vibrating  parts  can  be  changed,  so  as  to  produce 
sharps  and  flats.  The  sound  is  strengthened  by 
the  sounding-box,  and  by  the  vibrations  of  all  the  strings  harmonic  with 
those  played. 

In  the  violin  and  guitar  each  string  can  give  a  great  number  of  sounds 
according  to  the  length  of  the  vibrating  part,  which  is  determined  by  the 
pressure  of  the  fingers  of  the  left  hand  while  the  right  hand  plays  the  bow, 
or  the  strings  themselves.  In  both  these  instruments  the  vibrations  are 
communicated  to  the  upper  face  of  the  sounding  box,  by  means  of  the  bridge 
over  which  the  strings  pass.  These  vibrations  are  communicated  from  the 
upper  to  the  lower  face  of  the  box,  either  by  the  sides  or  by  an  intermediate 
piece  called  the  sound  post.  The  air  in  the  interior  is  set  in  vibration  by 
both  faces,  and  the  strengthening  of  the  sound  is  produced  by  all  these 
simultaneous  vibrations.  The  value  of  the  instrument  consists  in  the  per- 
fection with  which  all  possible  sounds  are  intensified,  which  depends  essen- 
tially on  the  quality  of  the  wood,  and  the  relative  arrangement  of  the  parts. 

280.  Wind  instruments. — All  wind  instruments  may  be  referred  to  the 
different  types  of  sounding  tubes  which  have  been  described.     In  some,  such 
as  the  organ,  the  notes  are  _/&'<?</,  and  require  a  separate  pipe  for  each  note, 
in  others  the  notes  are  variable,  and  are  produced  by  only  one  tube  :  the 
flute,  horn,  £c.,  are  of  this  class. 

In  the  organ  the  pipes  are  of  various  kinds ;  namely,  mouth  pipes,  open 
and  stopped,  and  reed  pipes  with  apertures  of  various  shapes.  By  means  of 
stops  the  organist  can  produce  any  note  by  both  kinds  of  pipe. 

In  theyfote,  the  mouthpiece  consists  of  a  simple  lateral  circular  aperture  ; 


Fig.  235. 


230  Acoustics.  [280- 

the  current  of  air  is  directed  by  means  of  the  lips,  so  that  it  grazes  the  edge 
of  the  aperture.  The  holes  at  different  distances  are  closed  either  by  the 
fingers  or  by  keys ;  when  one  of  the  holes  is  opened,  a  loop  is  produced  in 
the  corresponding  layer  of  air,  which  modifies  the  distribution  of  nodes  and 
loops  in  the  interior,  and  thus  alters  the  note.  The  whistling  of  a  key  is 
similarly  produced. 

The  pandcEan  pipe  con'sists  of  tubes  of  different  sizes  corresponding  to  the 
different  notes  of  the  gamut. 

In  the  trumpet,  the  horn,  the  trombone,  cornet-a-piston,  and  ophicleide, 
the  lips  form  the  reed,  and  vibrate  in  the  mouthpiece.  In  the  horn,  different 
notes  are  produced  by  altering  the  distance  of  the  lips.  In  the  trombone, 
one  part  of  the  tube  slides  within  the  other,  and  the  performer  can  alter 
at  will  the  length  of  the  tube,  and  thus  produce  higher  or  lower  notes.  In 
the  cornet-a-piston  the  tube  forms  several  convolutions  ;  pistons  placed  at 
different  distances  can,  when  played,  cut  off  communication  with  other  parts 
of  the  tube,  and  thus  alter  the  length  of  the  vibrating  column  of  air. 


-281] 


Vibrations  of  Rods. 


231 


CHAPTER  V. 

VIBRATIONS  OF   RODS,   PLATES,   AND  MEMBRANES. 

281.  Vibrations  of  rods.  —  Rods  and  narrow  plates  of  wood,  of  glass, 
and  especially  of  tempered  steel,  vibrate  in  virtue  of  their  elasticity  ;  like 
strings  they  have  two  kinds  of  vibrations,  longitudinal  and  transverse.  The 
latter  are  produced  by  fixing  the  rods  at  one  end,  and  passing  a  bow  over 
the  free  part.  Longitudinal  vibrations  are  produced  by  fixing  the  rod  at 
any  part,  and  rubbing  it  in  the  direction  of  its  length  with  a  piece  of  cloth 
sprinkled  with  resin.  But  in  the  latter  case  the  sound  is  only  produced  when 
the  point  of  the  rod  at  which  it  has 
been  fixed  is  some  aliquot  part  of 
its  length,  as  a  half,  a  third,  or  a 
quarter. 

It  is  shown  by  calculation  that 
the  number  of  transverse  vibrations 
made  in  a  given  time  by  rods  and 
thin  plates  of  the  same  kind  is 
directly  as  their  thickness,  and  in- 
versely as  the  square  of  their  length. 
The  width  of  the  plate  does  not 
affect  the  number  of  vibrations.  A 
wide  plate,  however,  requires  a 
greater  force  to  set  it  in  motion  than 
a  narrow  one.  It  is,  of  course,  under- 
stood that  one  end  of  the  vibrating 
plate  is  held  firmly. 

The  laws  of  the  longitudinal  vi- 
brations of  strings,  are  expressed  in 

the  formula  ;/  =    T    »     ^  in  which  n, 


T    »  / 

2/-/V  TT< 


r,  /,  d,  and  g  have  all  the  same  mean- 
ing as  in  the  formula  for  the  trans- 
verse vibrations,  while  p.  is  the 
1  modulus  of  elasticity  of  the  string, 
the  number  which  expresses  the 


Stretched  in  order  to  eIonSa^  by  its  own 

K  ni  invented  b>'  Marloye,  and  known  as 

harp,  based  on  the  longitudinal  vibration  of  rods.     It  consists  of 
I   wooden-  pedestal  in  which  are  fixed  twenty  thin  deal  rods    some 


232 


Acoustics. 


[281- 


coloured  and  others  white.  They  are  of  such  a  length  that  the  white  rods 
give  the  diatonic  scale,  while  the  coloured  ones  give  the  semitones,  and 
complete  the  chromatic  scale.  The  instrument  is  played  by  rubbing  the 
rods  in  the  direction  of  their  length  between  the  finger  and  thumb,  which 
have  been  previously  covered  with  powdered  resin.  The  notes  produced 
resemble  those  of  a  pandsean  pipe. 

The  tuning-fork^  the  triangle,  and  musical  boxes  are  examples  of  the 
transverse  vibrations  of  rods.  In  musical  boxes  small  plates  of  steel  of 
different  dimensions  are  fixed  on  a  rod,  like  the  teeth  of  a  comb.  A  cylinder 
whose  axis  is  parallel  to  this  rod,  and  whose  surface  is  studded  with  steel 
teeth,  arranged  in  a  certain  order,  is  placed  near  the  plates.  By  means  of 
a  clockwork  motion,  the  cylinder  rotates,  and  the  teeth  striking  the  steel 
plate  set  them  in  vibration,  producing  a  tune,  which  depends  on  the  arrange- 
ment of  the  teeth  on  the  cylinder. 

If  a  given  rod  be  clamped  either  in  the  middle,  or  at  both  ends,  the 
wave-length  of  the  note  produced  by  making  it  vibrate  longitudinally,  is 
double  its  own  length,  and  if  it  be  clamped  at  one  end  only,  and  made  to 
vibrate  longitudinally,  the  wave-length  of  the  sound  is  four  times  its  own  length. 

Thus  the  former  case  is  analogous  to  an  open  pipe,  and  the  latter  to  a 
stopped  pipe,  in  respect  of  the  sounds  produced. 

Stefan  has  determined  the  velocity  of  sound  in  soft  bodies  by  attaching 
them,  in  the  form  of  rods,  to  long  glass  or  wooden  rods.  The  compound  rod 
was  made  to  vibrate  and  the  number  of  vibrations  of  the  note  wras  determined. 
Knowing  this  and  also  the  velocity  of  sound  in  the  longer  rod,  the  velocity  in 
the  shorter  rod  was  at  once  obtained.  By  this  method  some  of  the  numbers 
in  the  table  in  article  234  were  obtained. 

282.  Vibrations  of  plates. — In  order  to  make  a  plate  vibrate,  it  is  fixed 
in  the  centre  (fig.  237),  and  a  bow  rapidly  drawn  across  one  of  the  edges  ; 


Fig.  237. 


Fig.  238. 


or  else  it  is  fixed  at  any  point  of  its  surface,  and  caused  to  vibrate  by 
rapidly  drawing  a  string  covered  with  resin  against  the  edges  of  a  central 
hole  (fig.  238). 


-283]  Vibrations  of  Membranes.  233 

Vibrating  plates  contain  nodal  lines  (269),  which  vary  in  number  and 
position  according  to  the  form  of  the  plates,  their  elasticity,  the  mode  of 
excitation,  and  the  number  of  vibrations.  These  nodal  lines  may  be  made 
visible  by  covering  the  plate  with  fine  sand  before  it  is  made  to  vibrate. 
As  soon  as  the  vibrations  commence,  the  sand  leaves  the  vibrating  parts, 
and  accumulates  on  the  nodal  lines,  as  seen  in  figs.  237  and  238. 

The  position  of  the  nodal  lines  may  be  determined  by  touching  the 
points  at  which  it  is  desired  to  produce  them.  Their  number  increases  with 
the  number  of  vibrations ;  that  is,  as  the  note  given  by  the  plates  is  higher. 
The  nodal  lines  always  possess  great  symmetry  of  form,  and  the  same  form 
is  always  produced  on  the  same  plate  under  the  same  conditions.  They 
were  discovered  by  Chladni. 

The  vibrations  of  plates  are  governed  by  the  following  law  : — In  plates 
of  the  same  kind  and  shape,  and  giving  the  same  system  of  nodal  lines,  the 
number  of  vibrations  in  a  second  is  directly  as  the  thickness  of  'the plate 's,  and 
inversely  as  their  area. 

Gongs  and  cymbals  are  examples  of  instruments  in  which  sounds  are 
produced  by  the  vibration  of  metal  plates.  The  glass  and  the  steel  harmo- 
nicon  depend  on  the  vibrations  of  glass  and  of  steel  plates  respectively. 

283.  Vibrations  of  membranes. — In  consequence  of  their  flexibility, 
membranes  cannot  vibrate  unless  they  are  stretched,  like  the  skin  of  a  drum. 
The  sound  they  give  is  more  acute  in  proportion  as  they  are  smaller  and 
more  tightly  stretched.  To  obtain  vibrating  membranes,  Savart  fastened 
gold-beater's  skin  on  wooden  frames. 

In  the  drum,  the  skins  are  stretched  on  the  ends  of  a  cylindrical  box. 
When  one  end  is  struck,  it  communicates  its  vibrations  to  the  internal 
column  of  air,  and  the  sound  is  thus  considerably  strengthened.  The  cords 
stretched  against  the  lower  skin  strike  against  it  when  it  vibrates,  and  pro- 
duce the  sound  characteristic  of  the  drum. 

Membranes  either  vibrate  by  direct  percussion,  as  in  the  drum,  or  they 
may  be  set  in  vibration  by  the  vibrations  of  the  air,  as  Savart  has  observed, 
provided  these  vibrations  are  sufficiently  intense.  Fig.  239  shows  a  mem- 


Fig.  239- 

brane  vibrating  under  the  influence  of  the  vibrations  in  the  air  caused  by 
a  sounding  bell.  Fine  sand  strewn  on  the  membrane  shows  the  formation 
of  nodal  lines  just  as  upon  plates. 

There  are  numerous  instances  in  which  solid  bodies  are  set  in  vibration 


234  Acoustics.  [283- 

by  the  vibrations  of  the  air.  The  condition  most  favourable  for  the  produc- 
tion of  this  phenomenon  is,  that  the  body  to  be  set  in  vibration  is  under 
such  conditions  that  it  can  readily  produce  vibrations  of  the  same  duration 
as  those  transmitted  to  it  by  the  air.  The  following  are  some  of  these 
phenomena : 

If  two  violoncello  strings  tuned  in  unison  are  stretched  on  the  same 
sound-box,  as  soon  as  one  of  them  is  sounded,  the  other  is  set  in  vibration. 
This  is  also  the  case  if  the  interval  of  the  strings  is  an  octave,  or  a  perfect 
fifth.  A  violin  string  may  also  be  made  to  vibrate  by  sounding  a  tuning- 
fork. 

Two  large  glasses  are  taken  of  the  same  shape,  and  as  nearly  as  possible 
of  the  same  dimensions  and  weight,  and  are  brought  in  unison  by  pouring 
into  them  proper  quantities  of  water.  If  now  one  of  them  is  sounded,  the 
other  begins  to  vibrate,  even  if  it  is  at  some  distance  ;  but  if  water  be  added 
to  the  latter,  it  ceases  to  vibrate. 

Breguet  found  that  if  two  clocks,  whose  time  was  not  very  different, 
were  fixed  on  the  same  metallic  support,  they  soon  attained  exactly  the  same 
time. 

Membranes  are  eminently  fitted  for  taking  up  the  vibrations  of  the  air, 
on  account  of  their  small  mass,  their  large  surface,  and  the  readiness  with 
which  they  subdivide.  With  a  pretty  strong  whistle,  nodal  lines  may  be 
produced  in  a  membrane  stretched  on  a  frame,  even  at  the  distant  end  of  a 
large  room. 

The  phenomenon  so  easily  produced  in  easily-moved  bodies  is  also  found 
in  larger  and  less  elastic  masses  ;  all  the  pillars  and  walls  of  a  church  vibrate 
more  or  less  while  the  bells  are  being  rung. 


-284] 


Methods  of  Studying  Vibratory  Motions. 


235 


CHAPTER   VI. 

GRAPHICAL   METHOD   OF   STUDYING   MOTIONS. 

284.  Xiissajous'  method  of  making  vibrations  apparent. — The  method 
bf  Lissajous  exhibits  the  vibratory  motion  of  bodies  either  directly  or  by 
projection  on  a  screen.  It  has  also  the  great  advantage  that  the  vibratory 
motions  of  two  sounding  bodies  may  be  compared  without  the  aid  of  the  ear, 
so  as  to  obtain  the  exact  relation  between  them. 

This  method,  which  depends  on  the  persistence  of  visual  sensations  on 
the  retina,  consists  in  fixing  a  small  mirror  on  the  vibrating  body,  so  as  to 
vibrate  with  it,  and  impart  to  a  luminous  ray  a  vibratory  motion  similar  to 
its  own. 

Lissajous  uses  tuning-forks,  and  fixes  to  one  of  the  prongs  a  small 
metallic  mirror,  m  (fig.  240),  and  to  the  other  a  counterpoise,  n,  which  is 


Fig.  240. 

necessary  to  make  the  tuning-fork  vibrate  regularly  for  a  long  time.  At  a 
few  yards'  distance  from  the  mirror  there  is  a  lamp  surrounded  by  a  dark 
chimney,  in  which  is  a  small  hole,  giving  a  single  luminous  point.  The 
tuning-fork  being  at  rest,  the  eye  is  placed  so  that  the  luminous  point  is  seen 
at  o.  The  tuning-fork  is  then  made  to  vibrate,  and  the  image  elongates  so 


Acoustics. 


[284- 


as  to  form  a  persistent  Image,  m\  which  diminishes  in  proportion  as  the 
amplitude  of  the  oscillation  decreases.  If,  during  the  oscillation  of  the  mirror, 
it  is  made  to  rotate  by  rotating  the  tuning-fork  on  its  axis,  a  sinuous  line,  oix, 
is  produced  instead  of  the  straight  line  oi.  These  different  effects  are  ex- 
plained by  the  successive  displacements  of  the  luminous  pencil,  and  by  the 
duration  of  these  luminous  impressions  on  the  eye  after  the  cause  has 
ceased — a  phenomenon  to  which  we  shall  revert  in  treating  of  vision. 

If  instead  of  viewing  these  effects  directly,  they  are  projected  on  the 
screen,  the  experiment  is  arranged  as  shown  in  fig.  241,  the  pencil  reflected 


Fig.  241. 

from  the  vibrating  mirror  is  reflected  a  second  time  from  a  fixed  mirror,  mt 
which  sends  it  towards  an  achromatic  lens,  /,  placed  so  as  to  project  the: 
images  on  the  screen. 

285.  Combination  of  two  vibratory  motions  in  the  same  direction. — 
Lissajous  resolved  the  problem  of  the  optical  combination  of  two  vibratory 
motions — vibrating  at  first  in  the  same  direction,  and  then  at  right  angles  to 
each  other. 

Fig.  242  represents  the  experiment  as  arranged  for  combining  two 
parallel  motions.  Two  tuning-forks  provided  with  mirrors  are  so  arranged 
that  the  light  reflected  from  one  of  them  reaches  the  other,  which  is  almost 
parallel  to  it,  and  is  then  sent  towards  a  screen  after  having  passed  through 
a  lens. 

If  now  the  first  tuning-fork  alone  vibrates,  the  image  on  the  screen  is  the 
same  as  in  figure  242  ;  but  if  they  both  vibrate,  supposing  they  are  in  unison, 
the  elongation  increases  or  diminishes  according  as  the  simultaneous 
motions  imparted  to  the  image  by  the  vibrations  of  the  mirrors  do  or  do  not 
coincide. 


-286] 


Optical  Combination  of  Vibratory  Motions. 


237 


If  the  tuning-forks  pass  their  position  of  equilibrium  in  the  same  time 
and  in  the  same  direction,  the  image  attains  its  maximum  ;  and  the  image 
is  at  its  minimum  when  they  pass  at  the  same  time  but  in  opposite  direc- 
tions. Between  these  two  extreme  cases,  the  amplitude  of  the  image  varies 
according  to  the  time  which  elapses  between  the  exact  instant  at  which  the 
tuning-forks  pass  through  their  position  of  rest  respectively.  The  ratio  of 


Fig.  242. 

this  time  to  the  time  of  a  double  vibration  is  called  a  difference  of  phase  of 
the  vibration. 

If  the  tuning-forks  are  exactly  in  unison,  the  luminous  appearance  on  the 
screen  experiences  a  gradual  diminution  of  length  in  proportion  as  the  ampli- 
tude of  the  vibration  diminishes  ;  but  if  the  pitch  of  one  is  very  little  alte.ed, 


Fig.  ?43. 

the  magnitude  of  the  image  varies  periodically,  and,  while  the  beats  resulting 
from  the  imperfect  harmony  are  distinctly  heard,  the  eye  sees  the  concomi- 
tant pulsations  of  the  image. 

286.  Optical  combination  of  two  vibratory  motions  at  right  angles 
to  each  other. — The  optical  combination  of  two  rectangular  vibratory 
motions  is  effected  as  shown  in  the  figure  243  ;  that  is,  by  means  of  two 
tuning-forks,  one  of  \\hich  is  horizontal  and  the  other  vertical,  and  both 


Acoustics. 


[286- 


provided  with  mirrors.  If  the  horizontal  fork  first  vibrates  alone,  a  hori- 
zontal luminous  outline  is  seen  on  the  screen,  while  the  vibration  of  the 
other  produces  a  vertical  image.  If  both  tuning-forks  vibrate  simultaneously 
the  two  motions  combine,  and  the  reflected  pencil  describes  a  more  or  less 
complex  curve,  the  form  of  which  depends  on  the  number  of  vibrations  of 
the  two  tuning-forks  in  a  given  time.  This  curve  gives  a  valuable  means  of 
comparing  the  number  of  vibrations  of  two  sounding  bodies. 


Fig.  244. 


Fig.  244  shows  the  luminous  image  on  the  screen  when  the  tuning-forks 
are  in  unison  ;  that  is,  when  the  number  of  vibrations  is  equal. 

The  fractions  below  each  curve  indicate  the  differences  of  phase  between 
them.  The  initial  form  of  the  curve  is  determined  by  the  difference  of  phase. 
The  curve  retains  exactly  the  same  form  when  the  tuning-forks  are  in  unison, 
provided  that  the  amplitudes  of  the  two  rectangular  vibrations  decrease  in 
the  same  ratio. 


Fig.  245. 


If  the  tuning-forks  are  not  quite  in  unison,  the  initial  difference  of  phase 
is  not  preserved,  and  the  curve  passes  through  all  its  variations. 

Fig.  245  represents  the  different  appearances  of  the  luminous  image  when 
the  difference  between  the  tuning-forks  is  an  octave ;  that  is,  when  the 


-287]  The  Phonautograph.  239 

numbers  of  their  vibrations  are  as  1:2;   and  fig.  246  gives  the  series  of 
mrves  when  the  numbers  of  the  vibrations  are  as  3  :  4. 

It  will  be  seen  that  the  curves  are  more  complex  when  the  ratios  of  the 


numbers  of  vibrations  are  less  simple.  M.  Lissajous  has  examined  these 
curves  theoretically  and  has  calculated  their  general  equations. 

\Yhen  these  experiments  are  made  with  a  Duboscq's  photo-electrical 
apparatus  instead  of  an  ordinary  lamp,  the  phenomena  are  remarkably 
brilliant. 

287.  Leon  Scott's  Phonauto  graph. — This  apparatus  registers  not  only 
the  vibrations  produced  by  solid  bodies  but  also  those  produced  by  wind 


Fig.  247. 

instruments,  by  the  voice  in  singing,  and  even  by  any  noise  whatsoever ;  for 
instance,  that  of  thunder,  or  the  report  of  a  cannon.     It  consists  of  an  ellip- 


240  Acoustics.  [287- 

soidal  barrel,  AB,  about  a  foot  and  a  half  long  and  a  foot  in  its  greatest 
diameter,  made  of  plaster  of  Paris.  The  end  A  is  open,  but  the  end  B  is 
closed  by  a  solid  bottom,  to  the  middle  of  which  is  fixed  a  brass  tube,  a,  bent 
at  an  elbow  and  terminated  by  a  ring  on  which  is  fixed  a  flexible  membrane 
which  by  means  of  a  second  ring  can  be  stretched  to  the  required  amount. 
Near  the  centre  of  the  membrane,  fixed  by  ceiling-wax,  is  a  hog's  bristle 
which  acts  as  a  style,  and,  of  course,  shares  the  movements  of  the  membrane. 
In  order  that  the  style  might  not  be  at  a  node,  M.  Scott  fitted  the  stretching 
ring  with  a  movable  piece,  z,  which  he  calls  a  subdivide^  and  which,  being 
made  to  touch  the  membrane  first  at  one  point  and  then  at  another,  enables 
the  experimenter  to  alter  the  arrangements  of  the  nodal  lines  at  will.  By 
means  of  a  subdivider  the  point  is  made  to  coincide  with  a  loop  ;  that  is,  a 
point  where  the  vibrations  of  the  membrane  are  at  a  maximum. 

When  a  sound  is  produced  near  the  apparatus,  the  air  in  the  ellipsoid, 
the  membrane,  and  the  style  will  vibrate  in  unison  with  it,  and  it  only  re- 
mains to  trace  on  a  sensitive  surface  the  vibrations  of  the  style,  and  to  fix 
them.  For  this  purpose  there  is  placed  in  front  of  the  membrane  a  brass 
cylinder,  C,  turning  round  a  horizontal  axis  by  means  of  a  handle,  m.  On 


Fig.  248. 


Fig.  249. 


Fig.  251. 

the  prolonged  axis  of  the  cylinder  a  screw  is  cut  which  works  in  a  nut  ;  con- 
sequently, when  the  handle  is  turned,  the  cylinder  gradually  advances  in  the 
direction  of  its  axis.  Round  the  cylinder  is  wrapped  a  sheet  of  paper 
covered  with  a  thin  layer  of  lampblack. 

The  apparatus  is  used  by  bringing  the  prepared  paper  into  contact  with 
the  point  of  the  style,  and  then  setting  the  cylinder  in  motion  round  its  axis. 
So  long  as  no  sound  is  heard  the  style  remains  at  rest,  and  merely  removes 


-288] 


Konigs  Manometric  Flames. 


241 

the  lampblack  along  a  line  which  is  a  helix  on  the  cylinder,  but  which  becomes 
straight  when  the  paper  is  unwrapped.  But  when  a  sound  is  heard,  the 
membrane  and  the  style  vibrate  in  unison,  and  the  line  traced  out  is  no 
longer  straight,  but  undulates ;  each  undulation  corresponding  to  a  double 
vibration  of  the  style.  Consequently  the  figures  thus  obtained  faithfully 
denote  the  number,  amplitude,  and  isochronism  of  the  vibrations. 

Fig.  248  shows  the  trace  produced -when  a  simple  note  is -sung,  and 
strengthened  by  means  of  its  upper  octave.  The  latter  note  is  represented 
by  the  curve  of  lesser  amplitude.  Fig.  249  represents  the  sound  produced 
jointly  by  two  pipes  whose  notes  differ  by  an  octave.  Fig.  250  in  its  lower 
line  represents  the  rolling  sound  of  the  letter  R  when  pronounced  with  a 
ring ;  and  fig.  251  on  its  lower  line  represents  the  sound  produced  by  a  tin 
plate  when  struck  with  the  finger. 

The  upper  lines  of  figs.  250  and  251  are  the  same,  and  represent  the 
perfectly  isochronous  vibrations  of  a  tuning-fork  placed  near  the  ellipsoid. 
These  lines  were  traced  by  a  fine  point  on  one  branch  of  the  fork,  which  was 
thus  found  to  make  exactly  500  vibrations  per  second.  In  consequence, 
each  undulation  of  the  upper  line  corresponds  to  the  -~~  part  of  a  second  ; 
and  thus  these  lines  become  very  exact  means  of  measuring  short  intervals 
of  time.  For  example,  in  fig.  250,  each  of  the  separate  shocks  producing 
the  rolling  sound  of  the  letter  R  corresponds  to  about  18  double  vibra- 


Fig.  252. 

tions  of  the  tuning-fork,  and  consequently  lasts  about  ™  or  about  ^  °f  a 
second. 

288.  Xonig's  manometric  flames. — Konig's  method  consists  in  trans- 
mitting the   motion   of  the  sonorous   waves   which  constitute  a  sound  to 

M 


242  Acoustics.  [288- 

gas  flames,  which,  by  their  pulsations,  indicate  the  nature  of  the  sounds. 
For  this  purpose  a  metal  capsule,  represented  in  section  at  A,  fig.  252,  is 
divided  into  two  compartments  by  a  thin  membrane  of  caoutchouc  ;  on  the 
right  of  the  figure  is  a  gas  jet,  and  below  it  a  tube  conveying  coal  gas  ;  on 

Fig   253. 


Fig   254. 

the  left  is  a  tubulure,  to  which  may  be  attached  a  caoutchouc  tube.  The 
other  end  of  this  may  be  placed  at  the  node  of  an  organ-pipe  (274)  or  it 
terminates  in  a  mouthpiece,  in  front  of  which  a  given  note  may  be  sung ; 
this  is  the  arrangement  represented  in  fig.  252. 

Fig.  255. 


Fig.  256. 

When  the  sound  waves  enter  the  capsule  by  the  mouthpiece  and  the 
tube,  the  membrane  yielding  to  the  condensation  and  rarefaction  of  the 
waves,  the  coal  gas  in  the  compartment  on  the  right  is  alternately  contracted 


-289]  Determination  of  the^ Intensity  of  Sounds.  243 

and  expanded,  and  hence  are  produced  alternations  in  the  length  of  the 
flame,  which  are,  however,  scarcely  perceptible  when  the  flame  is  observed 
directly.  But  to  render  them  distinct  they  are  received  on  a  mirror  with 
four  faces,  M,  which  may  be  turned  by  two  cog-wheels  and  a  handle.  As 
long  as  the  flame  burns  steadily  there  appears  in  the  mirror,  when  turned,  a 
continuous  band  of  light.  But  if  the  capsule  is  connected  with  a  sounding 
tube  yielding  the  fundamental  note,  the  image  of  the  flame  takes  the  form 

Fig  257 


Fig.  258 

represented  in  fig.  253,  and  that  of  the  figure  254  if  the  sound  yields  the 
octave.  If  the  two  sounds  reach  the  capsule  simultaneously  the  flame  has 
the  appearance  of  fig.  255  ;  in  that  case,  however,  the  tube  leading  to  the 
capsule  must  be  connected  by  a  T-pipe  with  two  sounding  tubes,  one  giving 
the  fundamental  note,  and  the  other  the  octave.  If  one  gives  the  funda- 
mental note  and  the  other  the  third,  the  flame  has  the  appearance  of 
figure  256. 

If  the  vowel  E  be  sung  in  front  of  the  mouth-piece  first  upon  c,  and 
then  upon  c',  the  turning  mirror  gives  the  flames  represented  in  figs.  257 
and  258. 

289.  Determination  of  the  intensity  of  sounds. — Meyer  has  devised 
a  plan  by  which  the  intensities  of  two  sounds  of  the  same  pitch  may  be 
directly  compared.  The  two  sounds  are  separated  from  each  other  by  a 
medium  impervious  to  sound,  and  in  front  of  each  of  them  is  a  resonance 
globe  '255)  accurately  tuned  to  the  sound.  Each  of  these  resonance  globes 
is  attached  by  means  of  caoutchouc  tubes  of  equal  length  to  the  two  ends  of 
a  U  tube,  in  the  middle  of  the  bend  of  which  is  a  third  tube  provided  with  ,1 
manometric  capsule. 

If  the  resonance  globes  are  each  at  the  same  distance  from  the  sounding 
bodies,  and  if  the  note  of  only  one  01  them  is  produced,  the  flame  vibrates. 
If  both  sounds  are  produced,  and  they  are  of  the  same  intensity,  and  in  the 
same  phase,  they  interfere  completely  in  the  tube,  so  that  the  flame  of  the 

M   2 


244  Acoustics.  [289- 

manometric  capsule  is  quite  stationary,  and  appears  in  the  turning  mirror  as 
a  straight  luminous  band. 

If,  however,  the  sounds  are  not  of  the  same  intensity  the  interference 
will  be  incomplete,  and  the  luminous  band  will  be  jagged  at  the  edge.  The 
distance  of  one  of  the  sounds  from  the  resonance  globes  is  altered  until  the 
flame  is  stationary.  The  intensities  of  the  two  sounds  are  thus  directly  as 
the  squares  of  their  distances  from  the  resonators. 

290.  Acoustic  attraction  and  repulsion. — It  was  observed  by  Guyot, 
and  afterwards  independently  by  Guthrie  and  by  Schellbach,  that  a  sound- 
ing body,  one  in  a  state  of  vibration  therefore,  exercises  an  action  on  a 
body  in  its  neighbourhood  which  is  sometimes  one  of  attraction  and  some- 
times of  repulsion.  The  vibrations  of  an  elastic  medium  attract  bodies 
which  are  specifically  heavier  than  itself,  and  repel  those  which  are  specific- 
ally lighter.  Thus  a  balloon  of  goldbeater's  skin  filled  with  carbonic  acid, 
is  attracted  towards  the  opening  of  a  resonance  box  on  which  is  a  vibrating 
tuning-fork  ;  while  a  similar  balloon  filled  with  hydrogen  and  tied  down  by 
a  thread  is  repelled.  This  result  always  follows,  even  when  the  hydrogen 
balloon  is  made  heavier  than  air  by  loading  it  with  wax. 

A  light  piece  of  cardboard  suspended  and  held  near  a  tuning-fork  moves 
towards  it  when  the  fork  is  made  to  vibrate.  If  the  tuning-fork  is  suspended 
and  is  then  made  to  vibrate,  it  moves  towards  the  card  if  the  latter  is  fixed. 
Two  suspended  tuning-forks  in  a  state  of  vibration  move  towards  each  other. 
The  flame  of  a  candle  placed  near  the  end  of  a  sounding  tuning-fork  was 
repelled  if  held  near  it  ;  if  held  underneath  it  was  flattened  out  to  a  disc. 
A  gas  flame  near  the  end  of  the  tuning-fork  was  divided  into  two  arms. 

Guthrie  finds  that  when  one  prong  of  a  tuning-fork  is  enclosed  in  a  tube 
provided  with  a  capillary  tube  dipping  into  a  liquid  and  is  set  in  vibration 
by  bowing  the  free  prong,  the  air  around  the  enclosed  prong  is  expanded, 
and  he  thence  concludes  that  the  approach,  above  described,  of  a  suspended 
body  to  the  sounding-fork,  is  due  to  the  diminution  of  the  pressure  of  the 
air  between  the  fork  and  the  body  below  that  on  the  other  side  of  the 
body. 

Light  resonators  of  glass  or  metal  are  repelled  when  brought  near  the 
sounding-box  of  a  tuning-fork,  vibrating  in  unison  with  the  resonators. 
When  a  small  mill  with  four  arms,  each  provided  with  a  small  resonator,  is 
placed  near  the  open  end  of  the  sounding-box,  the  repulsion  is  so  strong  as 
to  produce  a  uniform  rotation. 

These  phenomena  do  not  seem  to  be  due  to  the  aspirating  action  of  cur- 
rents of  air,  nor  are  they  caused  by  any  heating  effect ;  and  it  must  be  con- 
fessed that  the  phenomena  require  further  elucidation  ;  they  are  of  special 
interest  as  furnishing  a  possible  clue  to  the  solution  of  the  problem  of  attrac- 
tion in  general. 

291.  Edison's  phonograph. — Edison  has  devised  an  apparatus  for  re- 
producing sound,  which  is  equally  remarkable  for  the  simplicity  of  its  con- 
struction, and  for  the  striking  character  of  the  results  which  it  produces. 

Fig.  259  represents  a  mouthpiece  E,  which  is  closed  by  a  thin  elastic 
metal  disc.  By  means  of  a  spring  a  small  steel  point,  rounded  at  the  end,  is 
fixed,  at  the  back  of  the  disc  ;  this  point  gently  presses  against  the  surface 
of  tinfoil,  to  which  it  transfers  the  vibrations  of  the  disc  by  the  intervention 


-291] 


Edison's  Phonograph. 


24$ 


of  small  pieces  of  india-rubber  tubing.  Another  small  piece  of  tubing  helps 
to  deaden  the  vibrations  of  the  spring  itself.  This  arrangement  is  repre- 
sented on  a  larger  scale  in  fig.  260. 


Fig.  260. 


Fig-  259- 

The  tinfoil  is  placed  on  the  circumference  of  a  long  cylinder  C,  on  the 
surface  of  which  is  a  very  accurately  constructed  spiral  groove,  the  threads 
being  about  ~  of  an  inch  apart.  The  cylinder  works 
on  a  screw  AA',  the  thread  of  which  is  the  same  as  that 
on  the  cylinder  ;  it  is  turned  by  a  handle  M,  the  motion 
being  regulated  by  a  large  fly-wheel.  There  is  also 
an  arrangement  \^vm  by  which  the  position  of  the 
mouthpiece,  and  its  pressure  against  the  tinfoil,  may  be 
adjusted. 

When  the  disc  is  made  to  vibrate,  by  speaking  or 
singing  into  the  mouthpiece,  while,  at  the  same  time,  the 
cylinder  is  turned  with  a  uniform  motion,  a  series  of  dots 
or  indentations  are  produced  upon  the  tinfoil,  which, 
being  a  non-elastic  substance,  retains  them. 

If  now  the  part  which  the  mouthpiece  plays  be  reversed,  the  indented 
tinfoil  can  be  used  to  reproduce  the  sound.  This  is  best  effected  by  having 
a  special  mouthpiece  of  larger  size,  with  a  diaphragm  of  similar  construction. 
This  is  so  adjusted  that  the  point  is  made  to  work  along  the  indentations  in 
the  groove,  this  sets  the  diaphragm  in  vibrations,  and  these  being  communi- 
cated to  the  air  by  the  mouthpiece  reproduce  the  sound.  For  loudness,  a 
thin  elastic  membrane  is  best,  while  for  distinctness,  a  stouter  rigid  plate  is 
preferable. 

In  this  way  sound  has  been  reproduced  so  as  to  be  audible  to  a  large 
audience ;  the  articulation  is  distinct  though  feeble ;  it  reproduces  the 
quality  of  the  person's  voice  who  speaks  into  it,  but  with  a  nasal  intonation. 
Speech  may  thus  be  treasured  up  on  a  sheet  of  tinfoil  and  kept  for  an  indefi- 
nite period  ;  the  sound  may  be  reproduced  more  than  once  by  means  of  its 
tinfoil  register,  but  after  the  second  reproduction  the  strength  is  greatly 
diminished. 

If  the  velocity  of  rotation  is  greater  than  before,  the  pitch  of  the  speech 
is  altered  ;  and  if  it  is  not  uniform,  then,  in  the  case  of  a  song,  the  reproduc- 
tion is  incorrect.  In  order  to  produce  a  uniform  velocity,  clockwork  may  be 
used. 

There  is  great  difference  in  the  distinctness  with  which  the  various  con- 
sonants and  vowels  are  reproduced ;  the  s,  for  instance,  is  very  difficult 


246  Acoustics.  [291- 

If  the  phonograph  be  rotated  in  the  reverse  direction,  the  individual  letters 
retain  their  character,  but  the  words  as  well  as  the  letters  are  reproduced  in 
the  reverse  order. 

If  the  instrument  be  reset  to  the  starting-point  of  the  phonographic 
record  of  a  song,  and  be  again  sung  into,  it  will  reproduce  both  series  of 
sounds,  as  if  two  persons  were  singing  at  the  same  time  ;  and  by  repeating 
the  same  process,  a  third  or  fourth  part  may  be  added,  or  one  or  more  in- 
strumental parts. 

The  impressions  on  the  tinfoil  appear  at  first  sight  as  a  series  of  successive 
points  or  dots,  but  when  examined  under  a  microscope  they  are  seen  to  have 
a  distinct  form  of  their  own.  When  a  cast  is  taken  by  means  of  fusible 
metal,  and  a  longitudinal  section  made,  the  outline  closely  resembles  the 
jagged  edge  of  a  Konig's  flame.  According  to  Edison's  statement,  as 
many  as  40,000  words  can  be  registered  on  a  space  not  exceeding  10  square 
inches. 

The  phonograph  has  been  used  by  Jenkins  and  King  for  the  analysis  of 
vocal  sounds,  for  which  purpose  it  is  better  suited  than  Konig's  flames. 


-292]  Heat.  247 


BOOK   VI. 

ON   HEAT. 


CHAPTER    I. 

PRELIMINARY   IDEAS.      THERMOMETERS. 

292.  Heat.  Hypothesis  as  to  its  nature. — In  ordinary  language  the 
term  heat  is  used  not  only  to  express  a  particular  sensation,  but  also  to  de- 
scribe that  particular  state  or  condition  of  matter  which  produces  this  sensa- 
tion. Besides  producing  this  sensation,  heat  acts  variously  upon  bodies  ;  it 
melts  ice,  boils  water,  makes  metals  red-hot,  produces  electrical  currents, 
decomposes  compound  bodies,  and  so  forth. 

Two  theories  as  to  the  cause  of  heat  have  been  propounded ;  these  are 
the  theory  of  emission  and  the  theory  of  undulation. 

On  the  first  theory,  heat  is  caused  by  a  subtle  imponderable  fluid,  which 
surrounds  the  molecules  of  bodies,  and  which  can  pass  from  one  body  to 
another.  These  heat  atmospheres,  which  thus  surrcund  the  molecules,  exert 
a  repelling  influence  on  each  other,  in  consequence  of  which  heat  acts  in 
opposition  to  the  force  of  cohesion.  The  entrance  of  this  substance  into  our 
bodies  produces  the  sensation  of  warmth,  its  egress  the  sensation  of  cold. 

On  the  second  hypothesis  the  heat  of  a  body  is  caused  by  an  extremely 
rapid  oscillating  or  vibratory  motion  of  its  molecules  ;  and  the  hottest  bodies 
are  those  in  which  the  vibrations  have  the  greatest  velocity  and  the  greatest 
amplitude.  At  any  given  time  the  whole  of  the  molecules  of  a  body  possess 
a  sum  of  vis  viva  which  is  the  heat  they  contain.  To  increase  their  tempera- 
.ture  is  to  increase  their  vis  viva  ;  to  lower  their  temperature  is  to  decrease 
their  vis  viva.  Hence,  on  this  view,  heat  is  not  a  substance  but  a  condition 
of  matter,  and  a  condition  which  can  be  transferred  from  one  body  to  another. 
When  a  heated  body  is  placed  in  contact  with  a  cooler  one  the  former  cedes 
more  molecular  motion  than  it  receives  ;  but  the  loss  of  the  former  is  the 
equivalent  of  the  gain  of  the  latter. 

It  is  also  assumed  that  there  is  an  imponderable  elastic  ether,  which  per- 
vades all  matter  and  infinite  space.  A  hot  body  sets  this  in  rapid  vibration, 
and  the  vibrations  of  this  ether  being  communicated  to  material  objects  set 
them  in  more  rapid  vibration  ;  that  is,  increase  their  temperature.  Here  we 
have  an  analogy  with  sound ;  a  sounding  body  is  in  a  state  of  vibration,  and 
its  vibrations  are  transmitted  by  atmospheric  air  to  the  auditory  apparatus 
in  which  is  produced  the  sensation  of  sound. 


248  On  Heat.  [292- 

This  hypothesis  as  to  the  nature  of  heat  is  now  admitted  by  the  most 
distinguished  physicists.  It  affords  a  better  explanation  of  all  the  phenomena 
of  heat  than  any  other  theory,  and  it  reveals  an  intimate  connection  between 
heat  and  light.  It  will  be  subsequently  seen  that  by  the  friction  of  bodies 
against  each  other  an  'indefinite  quantity  of  heat  is  produced.  Experiment 
has  shown  that  there  is  an  exact  equivalence  between  the  motion  thus  de- 
stroyed and  the  heat  produced.  These  and  many  other  facts  are  utterly  in- 
explicable on  the  assumption  that  heat  is  a  substance,  and  not  a  form  of  motion. 

In  what  follows,  however,  the  phenomena  of  heat  will  be  considered,  as 
far  as  possible,  independently  of  either  hypothesis  ;  but  we  shall  subsequently 
return  to  the  reasons  for  the  adoption  of  the  latter  hypothesis. 

Assuming  that  the  heat  of  bodies  is  due  to  the  motion  of  their  particles, 
we  may  admit  the  following  explanation  as  to  the  nature  of  this  motion  in 
the  various  forms  of  matter  : — 

In  solids  the  molecules  have  a  kind  of  vibratory  motion  about  certain 
fixed  positions.  This  motion  is  probably  very  complex  ;  the  constituents  of 
the  molecule  may  oscillate  about  each  other,  besides  the  oscillation  of  the 
molecule  as  a  whole  ;  and  this  latter  again  may  be  a  to-and-fro  motion,  or  it 
may  be  a  rotatory  motion  about  the  centre. 

In  the  liquid  state  the  molecules  have  no  fixed  positions.  They  can 
rotate  about  their  centres  of  gravity,  and  the  centre  of  gravity  itself  may 
move.  But  the  repellent  action  of  the  motion,  compared  with  the  mutual 
attraction  of  the  molecules,  is  not  sufficient  to  separate  the  molecules  from 
each  other.  A  molecule  no  longer  adheres  to  particular  adjacent  ones  ;  but 
it  does  not  spontaneously  leave  them  except  to  come  into  the  same  relation 
to  fresh  ones  as  to  its  previous  adjacent  ones.  Thus  in  a  liquid  there  is  a 
vibratory,  rotatory,  and  progressive  motion. 

In  the  gaseous  state  the  molecules  are  entirely  without  the  sphere  of  their 
mutual  attraction.  They  fly  forward  in  straight  lines  according  to  the  ordi- 
nary laws  of  motion,  until  they  impinge  against  other  molecules,  or  against 
a  fixed  envelope  which  they  cannot  penetrate,  and  then  return  in  an  opposite 
direction,  with,  in  the  main,  their  original  velocity.  If  the  molecules  were  in 
space  where  no  external  force  could  act  upon  them,  they  would  fly  apart, 
and  disappear  in  infinity.  But  if  contained  in  any  vessel,  the  molecules 
continually  impinge  in  all  directions  against  the  sides,  and  thus  arises  the 
pressure  which  a  gas  exerts  on  its  vessel. 

The  perfection  of  the  gaseous  state  implies  that  the  space  actually 
occupied  by  the  molecules  of  the  gas  be  infinitely  small  compared  with  the 
entire  volume  of  the  gas  ;  that  the  time  occupied  by  the  impact  of  a  mole- 
cule either  against  another  molecule,  or  against  the  sides  of  the  vessel,  be 
infinitely  small  in  comparison  with  the  interval  between  any  two  impacts  ; 
and  that  the  influence  of  molecular  attraction  be  infinitely  small.  When 
these  conditions  are  not  fulfilled  the  gas  partakes  more  or  less  of  the  nature 
of  a  liquid,  and  exhibits  certain  deviations  from  Boyle's  law.  This  is  the 
case  with  all  gases  ;  to  a  very  slight  extent  with  the  less  easily  condensable 
gases,  but  to  a  far  greater  extent  with  vapours  and  the  more  condensable 
gases,  especially  near  their  points  of  liquefaction. 

293.  Dynamical  theory  of  gases. — We  have  seen,  that  in  the  gaseous 
condition,  the  particles  are  assumed  to  fly  about  in  right  lines  in  all  possible 


-294]  Molecular  Velocity.  249 

directions.  A  rough  illustration  of  this  condition  of  matter  is  afforded  by 
imagining  the  case  of  a  number  of  bees  enclosed  in  a  box. 

Let  us  suppose  a  cubical  vessel  to  be  filled  with  air  under  standard  con- 
ditions of  temperature  and  pressure.  Let  the  length  of  the  sides  be  a.  We 
will  for  the  present  suppose  that  each  particle  moves  freely  in  the  space 
without  striking  against  another  particle.  All  possible  motions  may  be  con- 
ceived to  be  resolved  into  motions  in  three  directions  which  are  parallel  to 
the  faces  of  the  cube.  Conceive  any  single  particle,  of  mass  m  ;  it  will  strike 
against  one  face  with  such  a  velocity  as  not  only  to  annul  its  own  motion, 
but  to  cause  it  to  rebound  in  the  opposite  direction  with  the  same  velocity  ; 
hence  the  measure  of  the  momentum  with  which  it  strikes  against  the  side 
will  be  imn.  Now  by  their  rapid  succession  and  their  uniform  distribu- 
tion the  total  action  of  these  separate  impacts  is  to  produce  a  pressure 
against  the  sides  of  the  vessel  which  is  the  elastic  force  of  the  gas  ;  and  to 
measure  the  pressure  on  the  side,  we  must  multiply  the  momentum  of  each 
individual  impact  by  the  total  number  of  such  impacts. 

Since  the  length  of  the  side  is  #,  if  there  are  n  molecules  in  the  unit  of 

space,  there  will  be  net"  in  the  volume  of  the  cube,  of  which    —  will  be 

moving  in  a  direction  parallel  to  each  one  of  the  sides.  To  get  the  number  of 
impacts  on  one  face,  we  must  remember  that  they  succeed  each  other,  after  the 
interval  of  time  required  for  a  particle  to  fly  to  the  opposite  side  and  back  again. 
Hence,  u  being  the  velocity,  the  number  of  impacts  which  each  particle  makes 

in  the  unit  of  time,  a  second,  will  be  —  ,  and  the  number  of  all  such  which 


20. 


strike  against  one  side  will  be  ^na~— 

Now,  since  each  one  exerts  a  pressure  represented  by  2mu,  we  shall  have 
for  the  total  pressure^  on  the  surface  a2 


and  therefore  the  pressure  on  the  unit  of  surface  will  be 

p  =  \nmiP. 

Now,  if  N  is  the  number  of  molecules  in  the  volume  z/,  N  =  nv,  and 
therefore 

p  =  $i  mu1*  ;  that  is,  pv  =  \Xmir. 

But,  for  any  given  mass  of  gas,  N,  m,  and  u  are  constant  quantities,  and  the 
product  pv  must  therefore  also  be  constant  ;  this,  however,  is  Boyle's  law  (174). 

294.  Molecular  velocity.  —  In  the  formula  p  =  \nmu*,  nm  represents  the 
mass  in  the  unit  of  volume  which  we  may  designate  as  the  density  p  of  the 
gas,  referred  to  that  of  water  ;  as  the  pressure  p  is  also  capable  of  direct 
measurement,  we  can  calculate  the  third  magnitude  u  in  absolute  measure. 

The  pressure  p  on  a  gas  is  equal  to  the  action  of  gravity  on  a  column  of 
mercury  of  given  height  h  ;  so  that  if  d  is  the  density  of  mercury  =  I3'596, 
and  g  the  acceleration  of  gravity,  p  =  §gh  and 


M3 


250  On  Heat.  [294- 

Now,  if  o-  be  the  specific  gravity  of  the  gas  as  compared  with  air,  which  is 
—  lighter  than  water,  p  x  773*3  =  o-,  or  p  =  -  —  , 

ui  =  3*  13-596  x  076x9-81  15x773-3 
cr 

'which  gives  u  =  —  L.;  that  is,  that  for  atmospheric  air  the  mean  velocity  of  the 

-v/o- 

particles  is  485  metres  in  a  second.     For  other  gases  we  have,  expressed  in 
the  same  units, 

0=461 

N  -  492 


In  a  gas  the  velocities  of  the  particles  are  unequal  ;  for,  even  supposing  that 
they  were  all  originally  the  same,  it  is  not  difficult  to  see  that  they  would 
soon  alter.  For  imagine  a  particle  to  be  moving  parallel  to  one  side,  and  to 
be  struck  centrically  by  another  moving  at  right  angles  to  the  direction  of 
its  motion,  the  particle  struck  would  proceed  on  its  new  path  with  increased 
velocity,  while  the  striking  particle  would  rebound  in  a  different  direction 
with  a  smaller  velocity. 

Notwithstanding  the  accidental  character  of  the  velocity  of  any  individual 
particle  in  such  a  mass  of  gas  as  we  have  been  considering,  there  will,  at  any 
one  given  time,  be  a  certain  average  distribution  of  velocities.  Now,  from 
considerations  based  on  the  theory  of  probabilities,  it  follows  that  some 
velocities  will  be  more  probable  than  others  —  that  there  will,  indeed,  be  one 
velocity  which  is  more  probable  than  any  other.  This  is  called  the  most 
probable  velocity.  The  mean  velocity  of  the  particle,  as  found  above,  is 
not  this,  nor  is  it  the  same  as  the  arithmetical  mean  of  all  the  velocities  ;  it 
may  be  defined  to  be  that  velocity  which,  if  all  the  molecules  possessed  it, 
the  mean  energy  of  the  molecular  impacts  against  the  side  would  be  the 
same  as  that  which  actually  exists.  This  mean  velocity  is  about  ~  greater 
than  the  arithmetical  mean  velocity,  and  is  i|  that  of  the  most  probable 
single  velocity. 

295.  General  effects  of  beat.  —  The  general  effects  of  heat  upon  bodies 
may  be  classed  under  three  heads.  One  portion  is  expended  in  raising  the 
temperature  of  the  body  ;  that  is,  in  increasing  the  vis  viva  of  its  molecules. 
In  the  second  place,  the  molecules  of  bodies  have  a  certain  attraction  for 
each  other,  to  which  is  due  their  relative  position  ;  hence  a  second  por- 
tion of  heat  is  consumed  in  augmenting  the  amplitude  of  the  oscillations, 
by  which  an  increase  of  volume  is  produced,  or  in  completely  altering  the 
relative  positions  of  the  molecules,  by  which  a  change  of  state  is  effected. 
These  two  effects  are  classed  as  internal  work.  Thirdly,  since  bodies  are 
surrounded  by  atmospheric  air  which  exerts  a  certain  pressure  on  their  sur- 
face, this  has  to  be  overcome  or  lifted  through  a  certain  distance.  The  heat 
or  work  required  for  this  is  called  the  external  work. 

If  Q  units  of  heat  are  imparted  to  a  body,  and  if  A  be  the  quantity  of 
heat  which  is  equivalent  to  the  unit  of  work;  then  if  W  is  the  amount  of 
heat  which  serves  to  increase  the  temperature,  I  that  required  to  alter  the 


-29  6]  Expansion. 

position  of  the  molecules,  and  if  L  be  the  equivalent  of  the  external  work, 
then 


296.  Expansion.  —  All  bodies  expand  by  the  action  of  heat.  As  a  general 
rule,  gases  are  the  most  expansible,  then  liquids,  and  lastly  solids. 

In  solids  which  have  definite  figures,  we  can  either  consider  the  expan- 
sion in  one  dimension,  or  the  linear  expansion  ;  in  two  dimensions,  the 
superficial  expansion  ;  or  in  three  dimensions,  the  cubical  expansion  or  the 
expansion  of  volume,  although  one  of  these  never  takes  place  without  the 
other.  As  liquids  and  gases  have  no  definite  figures,  the  expansions  of 
volume  have  in  them  alone  to  be  considered. 

To  show  the  linear  expansion  of  solids,  the  apparatus  represented  in  fig. 
261  may  be  used.  A  metal  rod,  A,  is  fixed  at  one  end  by  a  screw  B,  while 


Fig.  261. 

the  other  end  presses  against  the  short  arm  of  an  index,  K,  which  moves  on 
a  scale.  Below  the  rod  there  is  a  sort  of  cylindrical  lamp  in  which  alcohol 
is  burned.  The  needle  K  is  at  first  at  the  zero  point,  but  as  the  rod  becomes 
heated,  it  expands,  and  moves  the  needle  along  the  scale. 

The  cubical  expansion  of  solids  is  shown  by  a  Gravesande1  s  ring.  It  con- 
sists of  a  brass  ball  a  (fig.  262),  which  at  the  ordinary  temperature  passes 
freely  through  a  ring,  m,  almost  of  the  same  diameter.  But  when  the  ball 
has  been  heated,  it  expands  and  no  longer  passes  through  the  ring. 

In  order  to  show  the  expansion  of  liquids,  a  large  glass  bulb  provided 
with  a  capillary  stem  is  used  (fig.  263).  If  the  bulb  and  a  part  of  the  stem 
contain  some  coloured  liquid,  the  liquid  rapidly  rises  in  the  stem  when  heat 
is  applied,  and  the  expansion  thus  observed  is  far  greater  than  in  the  case 
of  solids. 

The  same  apparatus  may  be  used  for  showing  the  expansion  of  gases. 
Being  filled  with  air,  a  small  thread  of  mercury  is  introduced  into  the  capillary 
tube  to  serve  as  index  (fig.  264).  When  the  globe  is  heated  in  the  slightest 
degree,  even  by  approaching  the  hand,  the  expansion  is  so  great  that  the 
index  is  driven  to  the  end  of  the  tube,  and  is  finally  expelled.  Hence,  even 
for  a  very  small  degree  of  heat,  gases  are  highly  expansible. 

In  these  different  experiments  the  bodies  contract  on  cooling,  and  when 
they  have  attained  their  former  temperature  they  resume  their  original 
volume.  Certain  metals,  however,  especially  zinc,  form  an  exception  to  this 
rule,  and  it  appears  to  be  also  the  case  with  some  kinds  of  glass. 


252 


On  Heat. 


[297- 


MEASUREMENT  OF  TEMPERATURE.      THERMOMETRY. 

297.  Temperattire. — The  temperature  or  hotness  of  a  body,  indepen- 
dently of  any  hypothesis  as  to  the  nature  of  heat,  may  be  defined  as  being 


Fig.  262. 


Fig.  263.  Fig.  264. 


the  greater  or  less  extent  to  which  it  tends  to  impart  sensible  heat  to  other 
bodies.  The  temperature  of  a  body  must  not  be  confounded  with  the  quan- 
tity of  heat  it  possesses  :  a  body  may  have  a  high  temperature  and  yet  have 
a  very  small  quantity  of  heat,  and  conversely  a  low  temperature  and  yet 
possess  a  large  amount  of  heat.  If  a  cup  of  water  be  taken  from  a  bucketful, 
both  will  indicate  the  same  temperature,  yet  the  quantities  they  possess  will 
be  different.  This  subject  of  the  quantity  of  heat  will  be  afterwards  more 
fully  explained  in  the  chapter  on  Specific  Heat. 

298.  Thermometers. —  Thermometers  are  instruments  for  measuring 
temperatures.  Owing  to  the  imperfections  of  our  senses  we  are  unable  to 
measure  temperatures  by  the  sensation  of  heat  or  cold  which  they  produce 
in  us,  and  for  this  purpose  recourse  must  be  had  to  the  physical  actions  of 
heat  on  bodies.  These  actions  are  of  various  kinds,  but  the  expansion  of 
bodies  has  been  selected  as  the  easiest  to  observe.  But  heat  also  produces 
electrical  phenomena  in  bodies  ;  and  on  these  the  most  delicate  methods 
of  observing  temperatures  have  been  based,  as  we  shall  see  in  a  subsequent 
chapter. 

Liquids  are  best  suited  for  the  construction  of  thermometers — the  ex- 
pansion of  solids  being  too  small,  and  that  of  gases  too  great.  Mercury  and 
alcohol  are  the  only  liquids  used — the  former  because  it  only  boils  at  a  very 
high  temperature,  and  the  latter  because  it  does  not  solidify  at  the  greatest 
known  cold. 

The  mercurial  thermometer  is  the  most  extensively  used.     It  consists  of  a 


-301] 


Graduation  of  tke  TJiermometer. 


253 


capillary  glass  tube,  at  the  end  of  which  is  blown  the  bulb,  a  cylindrical  or 
spherical  reservoir.  Both  the  bulb  and  a  part  of  the  stem  are  filled  with 
mercury,  and  the  expansion  is  measured  by  a  scale  graduated  either  on  the 
stem  itself,  or  on  a  frame  to  which  it  is  attached. 

Besides  the  manufacture  of  the  bulb,  the  construction  of  the  thermometer 
comprises  three  operations  :  the  calibration  of  the  tube,  or  its  division  into 
pans  of  equal  capacity,  the  introduction  of  the  mercury  into  the  reservoir, 
and  the  graduation, 

299.  Division  of  the  tube  into  parts  of  equal  capacity. — As  the  in- 
dications of  the  thermometer  are  only  correct  when  the  divisions  of  the  scale 
correspond  to  equal  expansions  of  the  mercury  in  the  reservoir,  the  scale 
must  be  graduated,  so  as  to  indicate  parts  of  equal  capacity  in  the  tube.     If 
the  tube  were  quite  cylindrical,  and  of  the  same  diameter  throughout,  it 
would  only  be  necessary  to  divide  it  into  equal  lengths.     But  as  the  diameter 
of  glass  tubes  is  usually  greater  at  one  end  than  another,  parts  of  equal 
capacity  in  the  tube  are  represented  by  unequal  lengths  of  the  scale. 

In  order,  therefore,  to  select  a  tube  of  uniform  calibre,  a  thread  of  mercury 
about  an  inch  long  is  introduced  into  the  capillary  tube,  and  moved  in 
different  positions  in  the  tube,  care  being  taken  to  keep  it  at  the  same  tem- 
perature. If  the  thread  is  of  the  same  length  in  every  part  of  the  tube,  it 
shows  that  the  capacity  is  everywhere  the  same ; 
but  if  the  thread  occupies  different  lengths  the 
tube  is  rejected,  and  another  one  sought 

300.  rilling   the   thermometer. — In  order  to 
fill  the  thermometer  with  mercury,  a  small  funnel, 
C    fig.  265),  is  blown  on  at  the  top,  and  is  filled 
with  mercury ;  the  tube  is  then  slightly  inclined, 
and  the  air  in  the  bulb  expanded  by  heating  it 
with  a  spirit  lamp.     The  expanded  air  partially 
escapes  by  the  funnel,  and  on  cooling,  the  air  which 
remains  contracts,  and  a  portion  of  the  mercury 
passes  into  the  bulb  D.     The  bulb  is  then  again 
warmed,  and  allowed  to  cool,  a  fresh  quantity  of 
mercury  enters,  and  so  on,  until  the  bulb  and  part 
of  the  tube  are  full  of  mercury.     The  mercury  is 
then  heated  to  boiling ;  the  mercurial  vapours  in 
escaping  carry  with    them  the  air  and  moisture 
which  remain  in  the  tube.     The  tube,  being  full  of 
the  expanded  mercury  and  of  mercurial  vapour,  is 
hermetically  sealed  at  one  end.     When  the  ther- 
mometer is  cold,  the  mercury  ought  to  fill  the  bulb 
and  a  portion  of  the  stem. 

301.  Graduation  of  the  thermometer. — The 
thermometer  being  filled,  it  requires  to  be  gradu- 
ated ;  that  is,  to  be  provided  with  a  scale  to  which 
variations  of  temperature  can  be  referred.     And, 

first  of  all,  two  points  must  be  fixed  which  represent  identical  temperatures 
and  which  can  always  be  easily  reproduced. 

Experiment  has  shown  that  ice  always  melts  at  the  same  temperature 


Fig.  265. 


254  On  Heat.  [301- 

whatever  be  the  degree  of  heat,  and  that  distilled  water  under  the  same 
pressure,  and  in  a  vessel  of  the  same  kind,  always  boils  at  the  same  tem- 
perature. Consequently,  for  the  first  fixed  point,  or  zero,  the  temperature  of 
melting  ice  has  been  taken  :  and  for  a  second  fixed  point,  the  temperature 
of  boiling  water  in  a  metal  vessel  under  the  normal  atmospheric  pressure 
of  760  millimetres. 

This  interval  of  temperature — that  is,  the  range  from  zero  to  the  boiling 
point — is  taken  as  the  unit  for  comparing  temperatures  ;  just  as  a  certain 
length,  a  foot  or  a  metre  for  instance,  is  used  as  a  basis  for  comparing 
lengths. 

302.  Determination  of  the  fixed  points. — To  obtain  zero,  snow  or 
pounded  ice  is  placed  in  a  vessel  in  the  bottom  of  which  is  an  aperture  by 
which  water  escapes  (fig.  266).  The  bulb  and  a 
part  of  the  stem  of  the  thermometer  are  immersed 
in  this  for  about  a  quarter  of  an  hour,  and  a  mark 
made  at  the  level  of  the  mercury  which  represents 
zero. 

The  second  fixed  point  is  determined  by  means 
of  the  apparatus  represented  in  the  figures  267  and 
268,  of  which  268  represents  a  vertical  section.  In 
both,  the  same  letters  designate  the  same  parts. 
The  whole  of  the  apparatus  is  of  metal.  A  central 
tube,  A,  open  at  both  ends,  is  fixed  on  a  cylindrical 
vessel  containing  water  ;  a  second  tube,  B,  con- 
centric with  the  first,  and  surrounding  it,  is  fixed 
on  the  same  vessel,  M.  In  this  second  cylinder, 
which  is  closed  at  both  ends,  there  are  three 
tubulures,  #,  E,  D.  A  cork,  in  which  is  the  ther- 
mometer /,  fits  in  a.  To  E,  a  glass  tube,  containing 
mercury,  is  attached,  which  serves  as  a  manometer 
for  measuring  the  pressure  of  the  vapour  in  the 
apparatus.  D  is  an  escape  tube  for  the  vapour  and  condensed  water. 

The  apparatus  is  placed  on  a  furnace  and  heated  till  the  water  boils  ; 
the  vapour  produced  in  M  rises  in  the  tube  A,  and,  passing  through  the  two 
tubes  in  the  direction  of  the  arrows,  escapes  by  the  tubulure  D.  The 
thermometer  /  being  thus  surrounded  with  vapour,  the  mercury  expands,  and 
when  it  has  become  stationary,  the  point  at  which  it  stops  is  marked.  This 
is  the  point  sought  for.  The  object,  of  the  second  case  B,  is  to  avoid  the 
cooling  of  the  central  tubulure  by  its  contact  with  the  air. 

The  determination  of  the  point  100  (see  next  article)  would  seem  to 
require  that  the  height  of  the  barometer  during  the  experiment  should  be 
760  millimetres,  for  when  the  barometric  height  is  greater  or  less  than  this 
quantity,  water  boils  either  above  or  below  100  degrees.  But  the  point  100 
may  always  be  exactly  obtained,  by  making  a  suitable  correction.  For 
every  27  millimetres  difference  in  height  of  the  barometer  there  is  a  differ- 
ence in  the  boiling  point  of  I  degree.  If,  for  example,  the  height  of  the 
barometer  is  778 — that  is,  18  millimetres,  or  two-thirds  of  27,  above  760 — 
water  would  boil  at  100  degrees  and  two-thirds.  Consequently  ioo|  would 
have  to  be  marked  at  the  point  at  which  the  mercury  stops. 


Fig.  266. 


-303] 


Construction  ef  tJie  Scale. 


255 


Gay-Lussac  observed  that  water  boils  at  a  somewhat  higher  temperature 
in  a  glass  than  in  a  metal  vessel :  and  as  the  boiling  point  is  raised  by  any 
isalts  which  are  dissolved,  it  has  been  assumed  that  it  was  necessary  to  use 
,a  metal  vessel  and  distilled  water  in  fixing  the  boiling  point.  Rudberg 
•showed,  however,  that  these  latter  precautions  are  superfluous.  The 
nature  of  the  vessel  and  salts  dissolved  in  ordinary  water  influence  the  tem- 
perature of  boiling  water,  but  not  that  of  the  vapour  which  is  formed.  That 
.is  to  say,  that  it  the  temperature  of  boiling  water  from  any  of  the  above 
causes  is  higher  than  100  degrees,  the  temperature  of  the  vapour  does  not 
exceed  100,  provided  the  pressure  is  not  more  than  760  millimetres.  Con- 
sequently, the  higher  point  may  be  determined  in  a  vessel  of  any  material 


Fig.  268. 


/provided  the  thermometer  is  quite  surrounded  by  vapour,  and  does  not  dip 
.in  the  water. 

Even  with  distilled  water,  the  bulb  of  the  thermometer  must  not  dip  in 
I   the  liquid ;  for  it  is  only  the  upper  layer  that  really  has  the  temperature  of 
.100  degrees,  since  the  temperature  increases  from  layer  to  layer  towards  the 
i    bottom  in  consequence  of  the  increased  pressure. 

303.  Construction  of  the  scale. — Just  as  the  foot-rule  which  is  adopted 
as  the  unit  of  comparison  for  length  is  divided   into  a  number  of  equal 
i  divisions  called  inches  for  the  purpose  of  having  a  smaller  unit  of  comparison, 
j  so  likewise  the  unit  of  comparison  of  temperatures,  the  range  from  zero  to 
i  the  boiling  point,  must  be  divided  into  a  number  of  parts  of  equal  capacity 
-called  degrees.    On  the  Continent,  and  more  especially  in  France,  this  space 
I  js  divided  into  100  parts,  and  this  division  is  called  the  Centigrade  or  Celsius 
\   scale  ;  the  latter  being  the  name  of  the  inventor.     The  Centigrade  thermo- 
meter is  almost  exclusively  adopted  in  foreign  scientific  works,  and  as  its  use 


256  On  Heat.  [30.3- 


is  gradually  extending  in  this  country,  it  has  been  and  will  be  adopte 
this  book. 

The  degrees  are  designated  by  a  small  cipher  placed  a  little 
above  on  the  right  of  the  number  which  marks  the  temperature,  and 
to  indicate  temperatures  below  zero  the  minus  sign  is  placed  before 
them.  Thus,  —15°  signifies  15  degrees  below  zero. 

In  accurate  thermometers  the  scale  is  marked  on  the  stem  itself 
(fig.  269).  It  cannot  be  displaced,  and  its  length  remains  fixed, 
as  glass  has  very  little  expansibility.  The  graduation  is  effected 
by  covering  the  stem  with  a  thin  layer  of  wax,  and  then  marking 
the  divisions  of  the  scale,  as  well  .  as  the  corresponding  numbers, 
with  a  steel  point.  The  thermometer  is  then  exposed  for  about  ten 
minutes  to  the  vapours  of  hydrofluoric  acid,  which  attacks  the  glass 
where  the  wax  has  been  removed.  The  rest  of  the  wax  is  then  re- 
moved, and  the  stem  is  found  to  be  permanently  etched. 

Besides  the  Centigrade  scale  two  others  are  frequently  used  — 
Fahrenheit's  scale  and  Reaumur's  scale. 

In  Reaumur's  scale  the  fixed  points  are  the  same  as  on  the 
Centigrade  scale,  but  the  distance  between  them  is  divided  into 
80  degrees,  instead  of  into  100.  That  is  to  say,  80  degrees  Reaumur 
are  equal  to  100  degrees  Centigrade  ;  one  degree  Reaumur  is  equal 
to  "0°  or  |  of  a  degree  Centigrade,  and  one  degree  Centigrade 
equals  ~  or  |  degrees  Reaumur.  Consequently  to  convert  any 
number  of  Reaumur's  degrees  into  Centigrade  degrees  (20  for 
example),  it  is  merely  necessary  to  multiply  them  by  f  (which  gives 
25).  Similarly,  Centigrade  degrees  are  converted  into  Reaumur  by 
multiplying  them  by  f. 

The  thermometric  scale  invented  by  Fahrenheit  in  1714  is  still 
much  used  in  England,  and  also  in  Holland  and  North  America. 
The  higher  fixed  point  is,  like  that  of  the  other  scales,  the  tem- 
perature of  boiling  water  ;  but  the  null  point  or  zero  is  the  tem- 
perature obtained  by  mixing  equal  weights  of  sal-ammoniac  and 
snow,  and  the  interval  between  the  two  points  is  divided  into  212 
2&9'  degrees.  The  zero  was  selected  because  the  temperature  was  the 
lowest  then  known,  and  was  thought  to  represent  absolute  cold.  When 
Fahrenheit's  thermometer  is  placed  in  melting  ice  it  stands  at  32  degrees, 
and  therefore,  100  degrees  on  the  Centigrade  scale  are  equal  to  180  degrees 
on  the  Fahrenheit  scale,  and  thus  i  degree  Centigrade  is  equal  to  §  of  a 
degree  Fahrenheit,  and  inversely  I  degree  Fahrenheit  is  equal  to  f  of  a 
degree  Centigrade. 

If  it  be  required  to  convert  a  certain  number  of  Fahrenheit  degrees  (95, 
for  example)  into  Centigrade  degrees,  the  number  32  must  first  be  subtracted, 
in  order  that  the  degrees  may  count  from  the  same  part  of  the  scale.  The  re- 
mainder in  the  example  is  thus  63,  and  as  I  degree  Fahrenheit  is  equal  to  '  of 
a  degree  Centigrade,  63  degrees  are  equal  to  63  x  |  or  35  degrees  Centigrade. 
If  F  be  the  given  temperature  in  Fahrenheit  degrees  and  C  the  corre- 
sponding temperature  in  Centigrade  degrees,  the  former  may  be  converted 
into  the  latter  by  means  of  the  formula 

(F-32)S  =  C, 


-306]  Alcohol  Thermometers.  257 

and  conversely,  Centigrade  degrees  may  be  converted  into  Fahrenheit  by 
means  of  the  formula 

|C  +  32  =  F. 

These  formulas  are  applicable  to  all  temperatures  of  the  two  scales  pro- 
vided the  signs  are  taken  into  account.  Thus,  to  convert  the  temperature 
of  5  degrees  Fahrenheit  into  Centigrade  degrees,  we  have 


In  like  manner  we  have,  for  converting  Reaumur  into  Fahrenheit  degrees, 
the  formula 

!R  +  32  =  F> 

and  conversely,  for  changing  Fahrenheit  into  Reaumur  degrees,  the  formula 

(F-32)J  =  R. 

304.  Displacement   of  zero.  —  Thermometers,  even    when   constructed 
with  the  greatest  care,  are  subject  to  a  source  of  error  which  must  be  taken 
into  account  ;  that  is,  that  in  course  of  time  the  zero  tends  to  rise,  the  dis- 
placement sometimes  extending  to  as  much  as  two  degrees  ;  so  that  when 
the  thermometer  is  immersed  in  melting  ice  it  no  longer  sinks  to  zero. 

This  is  generally  attributed  to  a  diminution  of  the  volume  of  the  bulb  and 
also  of  the  stem,  occasioned  by  the  pressure  of  the  atmosphere.  It  is  usual 
with  very  accurate  thermometers  to  fill  them  two  or  three  years  before  they 
are  graduated. 

Besides  this  slow  displacement,  there  are  often  variations  in  the  position 
of  the  zero,  when  the  thermometer  has  been  exposed  to  high  temperatures, 
caused  by  the  fact  that  the  bulb  and  stem  do  not  contract  on  cooling  to  their 
original  volume  (294),  and  hence  it  is  necessary  to  verify  the  position  of  zero 
when  a  thermometer  is  used  for  delicate  determinations. 

Regnault  noticed  that  some  mercurial  thermometers,  which  agree  at 
o°  and  at  100°,  differ  between  these  points,  and  that  these  differences  fre- 
quently amount  to  several  degrees.  Regnault  ascribed  this  to  the  unequal 
expansion  of  different  kinds  of  glass. 

305.  Limits  to  the  employment  of  mercurial  thermometers.  —  Of  all 
thermometers  in  which  liquids  are  used,  the  one  with  mercury  is  the  most 
useful,  because  this  liquid  expands  most  regularly,  and  is  easily  obtained 
pure,  and  because  its  expansion  between  —  36°  and  100°  is  regular',  that  is, 
proportional  to  the  degree  of  heat.     It  also  has  the  advantage  of  having  a 
very  low  specific  heat.     But  for  temperatures  below  —36°  C.  the  alcohol 
thermometer  must  be  used,  since  mercury  solidifies  at  -40°  C.     Above  100 
degrees  the  coefficient  of  expansion  increases  and  the  indications  of  the 
mercurial  thermometers  are  only  approximate,  the  error  rising  sometimes 
to  several  degrees.     Mercury  thermometers  also  cannot  be  used  for  tem- 
peratures above  350°,  for  this  is  the  boiling  point  of  mercury. 

306.  Alcohol  thermometer.  —  The  alcohol  thermometer  differs  from  the 
mercury  thermometer  in   being  filled  with  coloured  alcohol.     But  as   the 
expansion  of  liquids  is  less  regular1  in  proportion  as  they  are  near  the  boiling 
point,   alcohol,  which   boils   at   78°  C.,  expands   very  irregularly.     Hence, 
alcohol   thermometers  are  usually  graduated  by  placing  them  in  baths  at 


258  On  Heat.  [306- 

different  temperatures  together  with  a  standard  mercurial  thermometer,  and 
marking  on  the  alcohol  thermometer  the  temperature  indicated  by  the 
mercury  thermometer.  In  this,  manner  the  alcohol  thermometer  is  com- 
parable with  the  mercury  one  ;  that  is  to  say,  it  indicates  the  same  tem- 
peratures under  the  same  conditions.  The  alcohol  thermometer  is  especially 
used  for  low  temperatures,  for  it  does  not  solidify  at  the  greatest  known  cold. 

307.  Conditions  of  the  delicacy  of  a  thermometer. — A  thermometer 
may  be  delicate  in  two  ways  : — I.  When  it  indicates  very  small  changes  of 
temperature.     2.  When  it  quickly  assumes  the  temperature  of  the  surround- 
ing medium. 

The  first  object  is  attained  by  having  a  very  narrow  capillary  tube  and 
a  very  large  bulb  ;  the  expansion  of  the  mercury  on  the  stem  is  then  limited 
to  a  small  number  of  degrees,  from  10  to  20  or  20  to  30  for  instance,  so  that 
each  degree  occupies  a  great  length  on  the  stem,  and  can  be  subdivided  into 
very  small  fractions.  The  second  kind  of  delicacy  is  obtained  by  making 
the  bulb  very  small,  for  then  it  rapidly  assumes  the  temperature  of  the  liquid 
in  which  it  is  placed. 

A  good  mercury  thermometer  should  answer  to  the  following  tests  : — 
When  its  bulb  and  stem,  to  the  top  of  the  column  of  mercury,  are  immersed 
in  melting  ice,  the  top  of  the  mercury  should  exactly  indicate  o°  C.  ;  and 
when  suspended  with  its  bulb  and  scale  immersed  in  the  steam  of  water 
boiling  in  a  metal  vessel  (as  in  fig.  267),  the  barometer  standing  at  760  mm., 
the  mercury  should  be  stationary  at  100°  C.  When  the  instrument  is  in- 
verted, the  mercury  should  fill  the  tube,  and  fall  with  a  metallic  click,  thus 
showing  the  complete  exclusion  of  air.  The  value  of  the  degrees  should  be 
uniform  :  to  ascertain  this,  a  little  cylinder  of  mercury  may  be  detached  from 
the  column  by  a  slight  jerk,  and  on  inclining  the  tube  it  may  be  made  to  pass 
from  one  portion  of  the  bore  to  another.  If  the  scale  be  properly  graduated, 
the  column  will  occupy  an  equal  number  of  degrees  in  all  parts  of  the  tube. 

308.  Differential  thermometer. — Sir   John    Leslie    constructed  a  ther- 
mometer for  showing  the  difference  of  temperature   of  two  neighbouring 
places,  from  which  it  has  received  the  name  differential  thermometer. 

A  modified  form  of  it  is  that  devised  by  Matthiessen  (fig.  270),  which  has 
the  advantage  of  being  available  for  indicating  the  temperature  of  liquids. 
It  consists  of  a  bent  glass  tube,  each  end  of  which  is  bent  twice,  and  ter- 
minates in  a  bulb  ;  the  bulbs  being  pendent  can  be  readily  immersed  in  a 
liquid.  The  bend  contains  some  coloured  liquid,  and  in  a  tube  which  con- 
nects the  two  limbs  is  a  stopcock,  by  which  the  liquid  in  each  limb  is  easily 
brought  to  the  same  level.  The  whole  is  supported  by  a  frame. 

When  one  of  the  bulbs  is  at  a  higher  temperature  than  the  other,  the 
liquid  in  the  stem  is  depressed,  and  rises  in  the  other  stem. 

The  instrument  is  now  only  used  as  a  thermoscope  ;  that  is,  to  indicate  a 
difference  of  temperature  between  the  two  bulbs,  and  not  to  measure  its 
amount. 

309.  Breguet's   metallic    thermometer. — Breguet    invented    a    ther- 
mometer of  considerable  delicacy,  which  depends  on  the  unequal  expansion 
of  metals.     It  consists  of  three  strips  of  platinum,  gold,  and  silver,  which  are 
passed  through  a  rolling  mill  so  as  to  form  a  very  thin  metallic  ribbon.     This 
is  then  coiled  in  a  spiral  form,  as  seen  in  fig.  271,  and  one  end  being  fixed  to 


-310] 


Rutherford 's  Thermometers. 


259 


-a  support,  a  light  needle  is  fixed  to  the  other,  which  is  free  to  move  round  a 
.graduated  scale. 

Silver,  which  is  the  most  expansible  of  the  metals,  forms  the  internal  face 
.of  the  spiral,  and  platinum  the  external.  When  the  temperature  rises,  the 
silver  expands  more  than  the  gold  or  platinum,  the  spiral  unwinds  itself,  and 


Fig.  270. 


Fig.  271. 


"the  needle  moves  from  left  to  right  of  the  above  figure.  The  contrary  effect 
'is  produced  when  the  temperature  sinks.  The  gold  is  placed  between  the 
other  two  metals  because  its  expansibility  is  intermediate  between  that  of  the 
silver  and  the  platinum.  Were  these  two  metals  employed  alone,  their  rapid 
unequal  expansion  might  cause  a  fracture.  Breguet's  thermometer  is  em- 
'pirically  graduated  in  Centigrade  degrees,  by  comparing  its  indications  with 
those  of  a  standard  mercury  thermometer. 

On  this  principle  depend  several  forms  of  pocket  thermometers,  and  it  is 
also  applied  in  some  registering  thermometers. 

310.  Rutherford's  maximum  and  minimum  thermometers. — It  is 
necessary,  in  meteorological  observations,  to  know  the  highest  temperature 
of  the  day  and  the  lowest  temperature  of  the  night.  Ordinary  thermometers 
could  only  give  these  indications  by  a  continuous  observation,  which  would  be 
impracticable.  Several  instruments  have  accordingly  been  invented  for  this 
purpose,  the  simplest  of  which  is  Rutherford's.  On  a  rectangular  piece  of 
plate-glass  (fig.  272)  two  thermometers  are  fixed,  whose  stems  are  bent 
horizontally.  The  one,  A,  is  a  mercury,  and  the  other,  B,  an  alcohol 
thermometer.  In  A  there  is  a  minute  piece  of  iron  wire,  A,  moving  freely  in 
the  tube,  which  serves  as  an  index.  The  thermometer  being  placed  hori- 
zontally, when  the  temperature  rises  the  mercury  pushes  the  index  before  it. 
But  as  soon  as  the  mercury  contracts,  the  index  remains  in  that  part  of  the 
tube  to  which  it  has  been  moved,  for  there  is  no  adhesion  between  the  iron 
and  the  mercury.  In  this  way  the  index  registers  the  highest  temperature 


26o 


On  Heat. 


[310- 


which  has  been  attained  ;  in  the  figure  this  is  31°.  In  the  minimum  ther- 
mometer there  is  a  small  hollow  glass  tube  which  serves  as  index.  -When  it 
is  at  the  end  of  the  column  of  liquid,  and  the  temperature  falls,  the  column 
contracts,  and  carries  the  index  with  it,  in  consequence  of  adhesion,  until  it 
has  reached  the  greatest  contraction.  When  the  temperature  rises  the 
alcohol  expands,  and,  passing  between  the  sides  of  the  tube  and  the  index, 


,n..,2P. 


Fig.  272. 

does  not  displace  B.     The  position  of  the  index  gives  therefore  the  lowest 
temperature  which  has  been  reached ;  in  the  figure  this  is  9-  degrees  below  zero. 

311.  Pyrometers. — The   name  Pyrometers  is  given  to  instruments   for 
measuring   temperatures  so  high  that  mercurial   thermometers   could   not 
be  used.     The  older  contrivances  for  this  purpose — Wedgwood's,  Daniell's 
(which  in  principle  resembled  the  apparatus  in  fig.  261),  Brongiart's,  &c. — 
are  gone  entirely  out  of  use.     None  of  them  give  an  exact  measure  of  tem- 
perature.    The  arrangements  now  used  for  the  purpose  are  either  based  on 
the  expansion  of  gases  and  vapours,  or  on  the  electrical  properties  of  bodies, 
and  will  be  subsequently  described. 

312.  Different  remarkable  temperatures. — The  following  table  gives 
some  of  the  most  remarkable  points  of  temperature.     It  maybe  observed  that 
it  is  easier  to  produce  very  high  temperatures  than  very  low  degrees  of  cold. 

Greatest  artificial  cold  produced  by  a  bath  of  bisulphide  of 

carbon  and  liquid  nitrous  acid —  I4O°C 

Greatest  cold  produced  by  ether  and  liquid  carbonic  acid     —  1 10 
Greatest  natural  cold  recorded  in  Arctic  expeditions    .         .  —   587 
Mercury  freezes     .         .         .         .         .         .         .         .         .  —    39^4 

Mixture  of  snow  and  salt       .         . —    20 

Ice  melts o 

Greatest  density  of  water      .         .         .         .         .         .  +  4 

Mean  temperature  of  London 9-9 

Blood  heat •  .         .         .       36-6 

Water  boils 100 

Mercury  boils 350 

Sulphur  boils .  44° 

Red  heat  (just  visible)         (Daniell) 526 

Silver  melts  „  .....   1000 

Zinc  boils  „  1040 

Cast  iron  melts  .         .       „  .....   153° 

Highest  heat  of  wind  furnace    „  .  1800 


-314] 


Expansion  of  Solids. 


261 


CHAPTER    II. 

EXPANSION   OF   SOLIDS. 

313.  Linear  expansion  and  cubical  expansion.  Coefficients  of  ex- 
pansion.— It  has  been  already  explained  that  in  solid  bodies  the  ex- 
pansion may  be  according  to  three  dimensions — linear,  superficial,  and 
cubical. 

The  coefficient  of  linear  expansion  is  the  elongation  of  the  unit  of  length 
of  a  body  when  its  temperature  rises  from  zero  to  i  degree  ;  the  coefficient  of 
superficial  expansion  is  the  increase  of  the  surface  in  being  heated  from  zero 
to  i  degree,  and  the  coefficient  of  cubical  expansion  is  the  increase  of  the  unit 
of  volume  under  the  same  circumstances. 

These  coefficients  vary  with  different  bodies,  but  for  the  same  body  the 
coefficient  of  cubical  expansion  is  three  times  that  of  the  linear  expansion,  as 
is  seen  from  the  following  considerations: — Suppose  a  cube,  the  length  of 
whose  side  is  i  at  zero.  Let  k  be  the  elongation  of  this  side  in  passing  from 
zero  to  i  degree,  its  length  at  i  degree  will  be  I  +  k,  and  the  volume  of  the 
cube,  which  was  i  at  zero,  will  be  (i  +  >£)3,  or  i  +3&  +  3&~  +  £3.  But  as  the 
elongation  k  is  always  a  very  small  fraction  (see  table,  Art.  314),  its  square  k*, 
and  still  more  its  cube  #*,  are  so  small  that  they  may  be  neglected,  and  the 
value  at  i  degree  becomes  very  nearly  i  +  3^.  Consequently,  the  increase  of 
volume  is  3^,  or  thrice  the  coefficient  of  linear  expansion. 

In  the  same  manner  it  may  be  shown  that  the  coefficient  of  superficial 
expansion  is  double  the  coefficient  of  linear  expansion. 

314.  Measurement  of  the  coefficient  of  linear  expansion.  Lavoisier 
and  Laplace's  method. — The  apparatus  used  by  Lavoisier  and  Laplace  for 
determining  the  coefficients  of  linear  expansion  (fig.  273)  consists  of  a  brass 


Fig.  273. 

trough,  placed  on  a  furnace  between  four  stone  supports.     On  the  two  sup- 
ports on  the  right  hand  there  is  a  horizontal  axis,  at  the  end  of  which  is  a 


262  On  Heat.  [314- 

telescope  ;  on  the  middle  of  this  axis,  and  at  right  angles  to  it,  is  fixed  a 
glass  rod,  turning  with  it,  as  does  also  the  telescope.  The  other  two  supports 
are  joined  by  a  cross  piece  of  iron,  to  which  another  glass  rod  is  fixed,  also 
at  right  angles.  The  trough,  which  contains  oil  or  water,  is  heated  by  a 
furnace  not  represented  in  the  figure,  and  the  bar  whose  expansion  is  to  be 
determined  is  placed  in  it. 

Fig.  274  represents  a  section  of  the  apparatus  ;  G  is  the  telescope,  KH 
the  bar,  whose  ends  press  against  the  two  glass  rods  F  and  D.     As  the  rod 


Fig.  274. 

F  is  fixed,  the  bar  can  only  expand  in  the  direction  KH,  and  in  order  to 
eliminate  the  effects  of  friction,  it  rests  on  two  glass  rollers.  Lastly,  the 
telescope  has  a  cross-wire  in  the  eyepiece,  which,  when  the  telescope  moves, 
indicates  the  depression  by  the  corresponding  number  of  divisions  on  a 
vertical  scale  AB\  at  a  distance  of  220  yards. 

The  trough  is  first  filled  with  ice,  and  the  bar  being  at  zero,  the  division 
on  the  scale  AB,  corresponding  to  the  wire  of  the  telescope,  is  read  off. 
The  ice  having  been  removed,  the  trough  is  filled  with  oil  or  water,  which  is 
heated  to  a  given  temperature.  The  bar  then  expands,  and  when  its  tempe- 
rature has  become  stationary,  which  is  determined  by  means  of  thermometers, 
the  division  of  the  scale,  seen  through  the  telescope,  is  read  off. 

From  these  data  the  elongation  of  the  bar  is  determined  ;  for  since  it  has 
become  longer  by  a  quantity,  CH,  and  the  optical  axis  of  the  telescope  has 
become  inclined  in  the  direction  GB,  the  two  triangles,  GHC  and  ABG, 
are  similar,  for  they  have  the  sides  at  right  angles  each  to  each,  so  that 

T-T  r*      C*  1-F° 

.-       =        .     In  the  same  way,  if  HC'  were  another  elongation,  and  AB'  a 

AB      AG 

TT/-'/          /"•  TT 

corresponding  deviation,  there  would  still  be  -.-^  =  -.-~  ;  from  which  it  fol- 

AB       AG 

lows  that  the  ratio  between  the  elongation  of  the  bar  and  the  deflection  of 

/—  TT 

the  telescope  is  constant,  for  it  is   always  equal  to-A~.      A   preliminary 

AG 

TT  /"• 

measurement  had  shown  that  this  ratio  was  y^.     Consequently,  =  7J¥, 

J\LJ 

AB 
whence  HC  =   -  — ;  that  is,  the  total  elongation  of  the  bar  is  obtained  by 

744 

dividing  the  length  on  the  scale  traversed  by  the  cross-wire  by  744.  Divid- 
ing this  elongation  by  the  length  of  the  bar,  and  then  by  the  temperature  of 
the  bath,  the  quotient  is  the  dilatation  for  the  unit  of  length  and  for  a  single 
degree — in  other  words,  the  coefficient  of  linear  dilatation. 

315.  Roy  and  Ramsden  s  method. — Lavoisier  and  Laplace's  method  is 
founded  on  an  artifice  which  is  frequently  adopted  in  physical  determinations, 


-315]  Expansion  of  Solids.  263 

and  which  consists  in  amplifying  by  a  known  amount  dimensions  which,  in 
themselves,  are  too  small  to  be  easily  measured.  Unfortunately  this  plan  is 
otten  more  fallacious  than  profitable,  for  it  is  first  necessary  to  determine  the 
ratio  of  the  motion  measured  to  that  on  which  it  depends.  In  the  present 
case  it  is  necessary  to  know  the  lengths  of  the  arms  of  the  lever  in  the 
apparatus.  But  this  preliminary  operation  may  introduce  errors  of  such  im- 
portance as  partially  to  counterbalance  the  advantage  of  great  delicacy. 
The  following  method,  which  was  used  by  General  Roy  in  1787,  and  which 
was  devised  by  Ramsden,  depends  on  another  principle.  Jt  measures  the 
elongations  directly,  and  without  amplifying  them  ;  but  it  measures  them  by 
means  of  a  micrometer,  which  indicates  very  small  displacements. 

The  apparatus  (fig.  275)  consists  of  three  parallel  metal  troughs  about  6 
feet  long.     In  the  middle  one  there  is  a  bar  of  the  body  whose  expansion  is 


Fig.  275. 

to  be  determined,  and  in  the  two  others  are  cast-iron  bars  of  exactly  the 
same  length  as  this  bar.  Rods  are  fixed  vertically  on  both  ends  of  these 
three  bars.  On  the  rods  in  the  troughs  A  and  B  there  are  rings  with  cross- 
wires  like  those  of  a  telescope.  On  the  rods  in  the  trough  C  are  small  tele- 
scopes also  provided  with  cross-wires. 

The  troughs  being  filled  with  ice,  and  all  three  bars  at  zero,  the  points  of 
intersectipn  of  the  wires  in  the  disc,  and  of  the  wires  in  the  telescope,  are  all 
in  a  line  at  each  end  of  the  bar.  The  temperature  in  the  middle  trough  is 
then  raised  to  100°  C.  by  means  of  spirit  lamps  placed  beneath  the  trough  ; 
the  bar  expands,  but  as  it  is  in  contact  with  the  end  of  a  screw,  «,  fixed  on 
the  side,  all  the  elongation  takes  place  in  the  direction  //;//,  and,  as  the  cross- 
wire  n  remains  in  position,  the  cross-wire  m  is  moved  towards  B  by  a  quantity 
equal  to  the  elongation.  But  since  the  screw  a  is  attached  to  the  bar,  by 
turning  it  slowly  from  right  to  left,  the  bar  is  moved  in  the  direction  ?nn. 


264  On  Heat.  [315- 

and  the  cross-wire  ;;/  regains  its  original  position.  To  effect  this,  the  screw- 
has  been  turned  by  a  quantity  exactly  equal  to  the  elongation  of  the  bar, 
and,  as  this  advance  of  the  screw  is  readily  deduced  from  the  number  of 
turns  of  its  thread  (n),  the  total  expansion  of  the  bar  is  obtained,  which, 
divided  by  the  temperature  of  the  bath,  and  this  quotient  by  the  length  of 
the  bar  at  zero,  gives  the  coefficient  of  linear  expansion. 

316.  Coefficients  of  linear  expansion. — By  one  or  the  other  method 
the  following  results  have  been  obtained  : — 

Coefficients  of  linear  expansion  for  i°  between  o°  and  100°  C. 

Pine 0-000003000  Gold      .     v    .     .     .     .  0-000014660 

Graphite 0-000007860  Copper 0-000017182 

Marble 0-000008490  Bronze 0-000018167 

White  glass     ....  0*000008613  Brass 0-000018782 

Platinum 0-000008842  Silver 0-000019097 

Untempered  steel    .     .  0-000010788  Tin 0-000^21730 

Cast  iron 0-000011250  Lead 0-000028575 

Sandstone 0-000011740  Zinc 0-000029417 

Wrought  iron      .     .     .  0*000012204  Sulphur 0-000064130 

Tempered  steel  .     .     .  0-000012395  Paraffine 0-000278540 

From  what  has  been  said  about  the  linear  expansion  (311),  the  coefficients 
of  cubical  expansion  of  solids  are  obtained  by  multiplying  those  of  linear 
expansion  by  three. 

The  coefficients  of  the  expansion  of  the  metals  vary  with  their  physical 
condition,  being  different  for  the  same  metal  according  as  it  has  been  cast 
or  hammered  and  rolled,  hardened  or  annealed.  As  a  general  rule,  opera- 
tions which  increase  the  density  increase  also  the  rate  of  expansion.  But 
even  for  substances  in  apparently  the  same  condition,  different  observers 
have  found  very  unequal  amounts  of  expansions  ;  this  may  arise  in  the  case 
of  compound  substances,  such  as  glass,  brass,  or  steel,  from  a  want  of  uniformity 
in  chemical  composition,  and  in  simple  bodies  from  slight  differences  of 
physical  state. 

The  expansion  of  amorphous  solids,  and  of  those  which  crystallise  in  the 
regular  system,  is  the  same  for  all  dimensions,  unless  they  are  subject  to  a 
strain  in  some  particular  direction.  A  fragment  of  such  a  substance  varies 
in  bulk,  but  retains  the  same  shape.  Crystals  not  belonging  to  the  regular 
system  exhibit,  when  heated,  an  unequal  expansion  in  the  direction  of  their 
different  axes,  in  consequence  of  which  the  magnitude  of  their  angles,  and 
therefore  their  form,  is  altered.  In  the  dimetric  system  the  expansion  is  the 
same  in  the  direction  of  the  two  equal  axes,  but  different  in  the  third.  In 
crystals  belonging  to  the  hexagonal  system  the  expansion  is  the  same  in  the 
direction  of  the  three  secondary  axes,  but  different  from  that  according  to 
the  principal  one.  In  the  trimetric  system  it  is  different  in  all  three  direc- 
tions. 

To  the  general  law  that  all  bodies  expand  by  heat  there  is  an  important 
exception  in  the  case  of  iodide  of  silver,  which  contracts  somewhat  when 
heated.  It  has  a  negative  coefficient  of  expansion,  the  value  of  which  is 
0-00000139  for  i°  C. 


-318]  Expansion  of  Solids.  265 

Flzeau  has  determined  the  expansion  of  a  great  number  of  crystallised 
bodies  by  an  optical  method.  He  placed  thin  plates  of  the  substance  on  a 
glass  plate  and  let  yellow  light  pass  through  them.  He  thus  obtained  alter- 
nately yellow  and  dark  Newton's  rings  (?.-z>.).  On  heating,  the  plate  of  the 
substance  expanded,  the  thin  layer  of  air  became  thinner,  and  the  position  of 
the  rings  was  altered.  From  the  alteration  in  their  position  the  amount  of 
the  expansion  could  be  deduced.  Among  the  results  he  has  obtained  is  the 
curious  one,  that  certain  crystallised  bodies,  such  as  diamond,  emerald,  and 
cupric  oxide,  contract  on  being  cooled  to  a  certain  temperature,  but  as  the 
cooling  is  continued  below  this  temperature  they  expand.  They  have  thus 
a  temperature  of  maximum  density,  as  is  the  case  with  water  (329).  In  the 
case  of  emerald  and  cuprous  oxide  this  temperature  is  at  —  4-2  J,  in  the  case 
of  diamond  at  —42-3°. 

317.  The  coefficients  of  expansion  increase  with  tlie  temperature.  — 
According  to  Dr.  Matthiessen,  who  determined  the  expansion  of  the  metals 
and  alloys  by  weighing  them  in  water  at  different  temperatures,  the  coeffi- 
cients of  expansion  are  not  quite  regular  between  o°  and  100°.     He  found 
the  following  values  for  the  linear  expansion  between  o°  and  100  :  — 

Zinc     .....  Lt  =  L0  (i  +0.00002741  /  +  o-ooopoop235  t*) 

Lead    .....  Lt  =  L0  (i  +0-00002726  /  +  0*0000000074  t) 

Silver       ....  Lt  =  L0  (i  +  0-0000  1809  /-PO'OOOOOOO  135  /2) 

Copper     ....  Lt  =  L0  (i  +0-0000  1408  /  +  0-0000000264  /2) 

Gold    .....  Lt  =  L0  (i  +  -000001358  /  +  0-0000000  112  /-) 

The  same  authority  found  that  alloys  expand  very  nearly  according  to  the 
following  law  :  —  '  The  coefficients  of  expansion  of  an  alloy  are  equal  to  the 
mean  of  the  coefficients  of  expansion  of  the  volumes  of  the  metals  compos- 
ing it.' 

318.  Formulae  relative  to  the  expansion  of  solids.  —  Let  /  be  the  length 
of  a  bar  at  zero,  /'  its  length  at  the  temperature  /°  C.,  and  a  its  coefficient  of 
linear  expansion.     The  tables  usually  give  the  expansion  for  i°  between  o° 
and  100°  as  in  Art.  316,  or  for  100°  ;  in  this  latter  case  a  is  obtained  by 
dividing  the  number  by  100. 

The  relation  existing  between  the  above  quantities  is  expressed  by  a  few 
simple  formulae. 

The  elongation  corresponding  to  t°  is  /  times  a  or  at  for  a  single  unit  of 
length,  or  at  I  for  /units.  The  length  of  the  bar  which  is  /at  zero  is  l+atl 
at  /,  consequently, 


This  formula  gives  the  length  of  a  body  /'  at  /°,  knowing  its  length  /  at 
zero,  and  the  coefficient  of  expansion  a  ;  and  by  simple  algebraical  transforma- 
tions we  can  obtain  from  it  formulae  for  the  length  at  zero,  knowing  the 
length  /'  at  /°,  and  also  for  finding  a  the  coefficient  of  linear  expansion, 
knowing  the  lengths  I'  and  /  at  f°  and  zero  respectively. 

It  is  obvious  that  the  formulae  for  cubical  expansion  are  entirely  analo- 
gous to  the  preceding. 

The  following  are  examples  of  the  application  of  these  formulae  :  — 

(i.)  A  metal  bar  has  a  length  I'  at  f°  ;  what  will  be  its  length  /  at  /°? 

N 


266  On  Heat.  [318- 

From  the  above  formula  we  first  .get  the  length  of  the  given  bar  at  zero, 

// 

which  is  --    :  by  means  of  the  same  formula  we  pass  from  zero  to  t'°  in 
I  +  a/' 

multiplying  by  I  +  a/,  which  gives  for  the  desired  length  the  formula 


I  +  «/' 

(ii.)  The  density  of  a  body  being  d  at  zero,  required  its  density  d'  at  /°. 

If  i  be  the  volume  of  the  body  at  zero,  and  D  its  coefficient  of  cubical 
expansion,  the  volume  at  /  will  be  I  +  D/  ;  and  as  the  density  of  a  body  is  in 
inverse  ratio  of  the  volume  which  the  body  assumes  in  expanding,  we  get 
the  inverse  proportion, 

d'  :  d=  i    :    i  +  D/ 

d  ~  F+~D/  '  ~  T+D7 

Consequently,  when  a  body  is  heated  from  o  to  /°,  its  density,  and  there- 
fore its  weight  for  an  equal  volume,  is  inversely  as  the  binomial  expression, 
i  +D/. 

319.  Application  of  the  expansion  of  solids.  —  In  the  arts  we  meet 
with  numerous  examples  of  the  influence  of  expansion,  (i.)  The  bars  of 
furnaces  must  not  be  fitted  tightly  at  their  extremities,  but  must,  at  least,  be 
free  at  one  end,  otherwise  in  expanding  they  would  split  the  masonry,  (ii.) 
In  making  railways  a  small  space  is  left  between  the  successive  rails,  for  if 
they  touched,  the  force  of  expansion  would  cause  them  to  curve  or  would 
break  the  chairs,  (iii.)  Water-pipes  are  fitted  to  one  another  by  means  of 
telescope  joints,  which  allow  room  for  expansion,  (iv.)  If  a  glass  is  heated 
or  cooled  too  rapidly  it  cracks  ;  this  arises  from  the  fact  that  glass  is  a  bad 
conductor  of  heat,  the  sides  become  unequally  heated,  and  consequently  un- 
equally expanded,  which  causes  a  fracture. 

When  bodies  have  been  heated  to  a  high  temperature,  the  force  pro- 
duced by  their  contraction  on  cooling  is  very  considerable  ;  it  is  equal  to 
the  force  which  is  needed  to  compress  or  expand  the  material  to  the  same 
extent  by  mechanical  means.  According  to  Barlow,  a  bar  of  malleable  iron 
a  square  inch  in  section  is  stretched  To^ootn  °f  'lts  length  by  a  weight  of  a 
ton  ;  the  same  increase  is  experienced  by  about  9°  C.  A  difference  of  45 
C.  between  the  cold  of  winter  and  the  heat  of  summer  is  not  unfrequently 
experienced  in  this  country.  In  that  range,  a  wrought-iron  bar  ten  inches 
long  will  vary  in  length  by  ^th  of  an  inch  and  will  exert  a  strain,  if  its  ends 
are  securely  fastened,  of  fifty  tons.  It  has  been  calculated  from  Joule's  data 
that  the  force  exerted  by  heat  in  expanding  a  pound  of  iron  between  o°  and 
1  00°,  during  which  it  increases  about  —^  of  its  bulk,  is  equal  to  16,000 
foot-pounds  ;  that  is,  it  could  raise  a  weight  of  7  tons  through  a  height  of  one 
foot. 

(i.)  An  application  of  this  contractile  force  is  seen  in  the  mode  of  secur- 
ing tires  on  wheels.  The  tire  being  made  red  hot,  and  thus  considerably 
expanded,  is  placed  on  the  circumference  of  the  wheel  and  then  cooled. 
The  tire,  when  cold,  embraces  the  wheel  with  such  force  as  not  only  to 
secure  itself  on  the  rim,  but  also  to  press  home  the  joints  of  the  spokes  into 


-320] 


Compensation*  Pendulum. 


267 


the  felloes  and  nave,  (ii.)  Another  interesting  application  was  made  in  the 
case  of  a  gallery  at  the  Conservatoire  des  Arts  et  Metiers  in  Paris,  the  walls 
of  which  had  begun  to  bulge  outwards.  Iron 
bars  were  passed  across  the  building  and 
screwed  into  plates  on  the  outside  of  the  walls. 
Each  alternate  bar  was  then  heated  by  means 
of  lamps,  and  when  the  bar  had  expanded  it 
was  screwed  up.  The  bars  being  then  allowed 
to  cool  contracted,  and  in  so  doing  drew  the 
walls  together.  The  same  operation  was  per- 
formed on  the  other  bars. 

320.  Compensation  pendulum. — An  im- 
portant application  of  the  expansion  of  metals 
has  been  made  in  the  compensation  pendulum. 
This  is  a  pendulum  in  which  the  elongation, 
when  the  temperature  rises,  is  so  compensated 
that  the  distance  between  the  centre  of  sus- 
pension and  the  centre  of  oscillation  (80)  re- 
mains constant,  which,  from  the  laws  of  the 
pendulum  (81),  is  necessary  for  isochronous 
oscillations,  and  in  order  that  the  pendulum 
may  be  used  as  a  regulator  of  clocks. 

In  fig.  276,  which  represents  the  gridiron 
pendulum,  one  of  the  commonest  forms  of 
compensation  pendulum,  the  ball,  L,  instead 
of  being  supported  by  a  single  rod,  is  sup- 
ported by  a  framework,  consisting  of  alternate 
rods  of  steel  and  brass.  In  the  figure,  the 
shaded  rods  represents  steel ;  including  a 
small  steel  rod,  b,  which  supports  the  whole  of 
the  apparatus,  there  are  six  of  them.  The 
rest  of  the  rods,  four  in  number,  are  of  brass. 
The  rod  /,  which  supports  the  ball,  is  fixed  at  its  upper  end  to  a  horizontal 
cross-piece ;  at  its  lower  end  it  is  free,  and  passes  through  the  two  circular 
holes  in  the  lower  horizontal  cross-pieces. 

Now  it  is  easy  to  see  from  the  manner  in  which  the  vertical  rods  are 
fixed  to  the  cross-pieces,  that  the  elongation  of  the  steel  rods  can  only  take 
place  in  a  downward  direction,  and  that  of  the  brass  rods  in  an  upward 
direction.  Consequently,  in  order  that  the  pendulum  may  remain  of  the 
same  length,  it  is  necessary  that  the  elongation  of  the  brass  rods  shall  tend 
to  make  the  ball  rise,  by  exactly  the  same  quantity  that  the  elongation  of  the 
steel  rod  tends  to  lower  it  :  a  result  which  is  attained  when  the  sum  of  the 
lengths  of  the  steel  rods  A  is  to  the  sum  of  the  lengths  of  the  brass  rods  B  in 
the  inverse  ratio  of  the  coefficients  of  expansion  of  steel  and  brass,  a  and  b ; 
that  is,  in  the  proportion  A  :  B  =  b  :  a. 

The  elongation  of  the  rod  may  also  be  compensated  for  by  means  of 
compensating  strips.  These  consist  of  two  blades  of  copper  and  iron 
soldered  together  and  fixed  to  the  pendulum  rod,  as  represented  in  fig.  277. 
The  copper  blade,  which  is  more  expansible,  is  below  the  iron.  When  the 

N  2 


THK 


268  On  Heat.  [320- 

temperature  sinks,  the  pendulum  rod  becomes  shorter,  and  the  ball  rises. 

But  at  the  same  time  the  compensating  strips  become  curved,  as  seen  in 

fig.  278,  in  con- 
sequence of  the 
copper  contract- 
ing more  than 
the  iron,  and  two 
metallic  balls  at 
their  extremities 
become  lower.  If 
they  have  the 

Fig.277.  Fig.278.  Fig.279.  Pr°Per     size     in 

reference  to   the 

pendulum  ball,  the  parts  which  tend  to  approach  the  centre  of  suspen- 
sion compensate  those  which  tend  to  remove  from  it,  and  the  centre  of 
oscillation  is  not  displaced.  If  the  temperature  rises,  the  pendulum  ball 
descends  ;  but  at  the  same  time  the  small  balls  ascend,  as  shown  in  fig.  279, 
so  that  there  is  always  compensation. 

One  of  the  most  simple  compensating  pendulums  is  the  mercury  pen- 
dulum, invented  by  an  English  watchmaker,  Graham.  The  ball  of  the  pen- 
dulum, instead  of  being  solid,  consists  of  a  glass  cylinder,  containing  pure 
mercury,  which  is  placed  in  a  sort  of  stirrup,  supported  by  a  steel  rod. 
When  the  temperature  rises  the  rod  and  stirrup  become  longer,  and  thus 
lower  the  centre  of  gravity  ;  but  at  the  same  time  the  mercury  expands,  and, 
rising  in  the  cylinder,  produces  an  inverse  effect,  and  as  mercury  is  much 
more  expansible  than  steel,  a  compensation  may  be  effected  without  making 
the  mercurial  vessel  of  undue  dimensions. 

The  same  principle  is  applied  in  the  compensating  balances  of  chronometers 
(fig.  280).  The  motion  here  is  regulated  by  a  balance  or  wheel,  furnished  with 
a  spiral  spring  not  represented  in  the  figure,  and  the  time 
of  the  chronometer  depends  on  the  force  of  the  spring,  the 
mass  of  the  balance,  and  on  its  circumference.  Now 
when  the  temperature  rises  the  circumference  increases, 
j[B  and  the  chronometer  goes  slower ;  and  to  prevent  this, 
part  of  the  mass  must  be  brought  nearer  the  axis.  The 
circumference  of  the  balance  consists  of  compensating 
strips  BC,  of  which  the  more  expansible  metal  is  on  the 
outside,  and  towards  the  end  of  these  are  small  masses 
of  metal  D,  which  play  the  same  part  as  the  balls  in  the  above  case.  When 
the  radius  is  expanded  by  heat,  the  small  masses  are  brought  nearer  the 
centre  in  consequence  of  the  curvature  of  the  strips  ;  and  as  they  can  be 
fixed  in  any  position,  they  are  easily  arranged  so  as  to  compensate  for  the 
expansion  of  the  balance. 


-322] 


Expansion  of  Liquids. 


269 


CHAPTER    III. 

EXPANSION   OF   LIQUIDS. 

321.  Apparent  and  real  expansion. — If  a  flask  of  thin  glass,  provided 
with  a  narrow  stem,  the  flask  and  part  of  the  stem  being  filled  with  some 
coloured  liquid,  be  immersed  in  hot   water 

(fig.  281),  the  column  of  liquid  in  the  stem  at 
first  sinks  from  b  to  a,  but  then  immediately 
after  rises,  and  continues  to  do  so  until  the 
liquid  inside  has  the  same  temperature  as  the 
hot  water.  This  first  sinking  of  the  liquid  is 
not  due  to  its  contraction  ;  it  arises  from  the 
expansion  of  the  glass,  \vhich  becomes  heated 
before  the  heat  can  reach  the  liquid  ;  but  the 
expansion  of  the  liquid  soon  exceeds  that  of 
the  glass,  and  the  liquid  ascends. 

Hence  in  the  case  of  liquids  we  must  dis- 
tinguish between  the  apparent  and  the  real 
or  absolute  expansion.  The  apparent  expan- 
sion is  that  which  is  actually  observed  when 
liquids  contained  in  vessels  are  heated  ;  the 
absolute  expansion  is  that  which  \vould  be 
observed  if  the  vessel  did  not  expand  ;  or,  as 
this  is  never  the  case,  it  is  the  apparent  ex- 
pansion corrected  for  the  simultaneous  expansion  of  the  containing  vessel. 

As  has  been  already  stated,  the  cubical  expansion  of  liquids  is  alone 
considered  ;  and  as  in  the  case  of  solids,  the  coefficient  of  expansion  of  a 
liquid  is  the  increase  of  the  unit  of  volume  for  a  single  degree  ;  but  a 
distinction  is  here  made  between  the  coefficient  of  absolute  expansion  and  the 
coefficient  of  apparent  expansion.  Of  the  many  methods  which  have  been 
employed  for  determining  these  two  coefficients,  we  shall  describe  that  of 
Dulong  and  Petit. 

322.  Coefficient  of  tbe  absolute  expansion  of  mercury. — In  order  to 
determine  the  coefficient  of  the  absolute  expansion  of  mercury,  the  influence 
of  the  envelope  must  be  eliminated.     Dulong  and  Petit's  method  depends  on 
the  hydrostatical  principle  that,  in  two  communicating  vessels,  the  heights 
of  two  columns  of  liquid  in  equilibrium  are  inversely  as  their  densities  (108), 
a  principle  independent  of  the  diameters  of  the  vessels,  and  therefore  of 
their  expansions. 

The  apparatus  consists  of  two  glass  tubes,  A  and  B  (fig.  282),  joined  by  a 
capillary  tube,  and  kept  vertical  on  an  iron  support,  KM,  the  horizontality 


270  On  Heat.  [322- 

of  which  is  adjusted  by  means  of  two  levelling  screws  and  two  spirit  levels, 
m  and  n.  Each  of  the  tubes  is  surrounded  by  a  metal  case,  of  which  the 
smaller,  D,  is  filled  with  ice  ;  the  other,  E,  containing  oil,  can  be  heated  by 
the  furnace,  which  is  represented  in  section  so  as  to  show  the  case.  Mercury 
is  poured  into  the  tubes  A  and  B  ;  it  remains  at  the  same  level  in  both,  as 


Fig  282. 

long  as  they  are  at  the  same  temperature,  but  rises  in  B  in  proportion  as  it 
is  heated,  and  expands. 

Let  h  and  d  be  the  height  and  density  of  the  mercury  in  the  leg  A,  at  the 
temperature  zero,  and  h'  and  d'  the  same  quantities  in  the  leg  B.  From  the 
hydrostatical  principle  previously  cited  we  have  had  hd=h'  d'.  Now  from 

the  problem  in  Art.  311,  d '= ,  D   being  the  coefficient  of  absolute 

i  +  D/ 

expansion  of  mercury ;    substituting  this  value  of  (T  in  the  equation,  we 


have 


h'd 


,  from  which  we  get  D 


i  +  D/  ht 

The  coefficient  of  absolute  expansion  of  mercury  is  obtained  from  this 
formula,  knowing  the  heights  //'  and  //,  and  the  temperature  /  of  the  bath  in 
which  the  tube  B  is  immersed.  In  Dulong  and  Petit's  experiment  this 
temperature  was  measured  by  a  weight  thermometer,  P  (323),  the  mercury  of 
which  overflowed  into  the  basin,  C,  and  by  means  of  an  air  thermometer,  T 
(331).;  the  heights  h'  and  //  were  measured  by  a  cathetometer,  K  (89). 

Dulong  and  Petit  found  by  this  method  that  the  coefficient  of  absolute 
expansion  of  mercury  between  o°  and  100°  C.  is  j^~.  But  they  found  that 
the  coefficient  increased  with  the  temperature.  Between  100°  and  200° 
it  is  5/25,  and  between  200°  and  300°  it  is  5^.  The  same  observation 
has  been  made  in  reference  to  other  liquids,  showing  that  their  expansion 
is  not  regular.  It  has  been  found  that  this  expansion  is  less  regular  in 
proportion  as  liquids  are  near  a  change  in  their  state  of  aggregation  ;  that 


^frBiiS^?Bii&  ______ 

^ 


^\^        ~/x  *= 

J    ^Jf^'^L  ..     *^  * 


-325]  U'cight  Thermometer.  271 

is,  approach  their  freezing  or  boiling  points.  Dulong  and  Petit  found  that 
the  expansion  of  mercury  between  —36°  and  100°  is  practically  quite  uniform. 

Regnault,  who  has  determined  this  important  physical  constant,  has  found 
that  the  mean  coefficient  between  o°  and  100°  is  5.^,  between  ioo°and  200°, 
^Yi?  and  between  200°  and  300°,  v^. 

323.  Coefficient    of  the   apparent  expansion   of  mercury.  —  The   co- 
efficient of  apparent  expansion  of  a  liquid  varies  with  the  nature  of  the 
envelope.    That  of  mercury  in  glass 
was  determined  by  means  of  the 
qpp|ratus  represented  in  fig.  283. 
It  consists  of  a  glass  cylinder  to 
which  is  joined   a   bent   capillary 
glass  tube,  open  at  the  end. 

The  apparatus  is  weighed  first 

empty,  and  then  when  filled  with  Fig.  283. 

mercury   at    zero  ;    the    difference 

gives  the  weight  of  the  mercury,  P.  It  is  then  raised  to  a  known  temperature, 
/  ;  the  mercury  expands,  a  certain  quantity  passes  out,  which  is  received  in 
the  capsule  and  weighed.  If  the  weight  of  this  mercury  be  /,  that  of  the 
mercury  remaining  in  the  apparatus  will  be  P  —  p. 

When  the  temperature  is  again  zero,  the  mercury  in  cooling  produces  an 
empty  space  in  the  vessel,  which  represents  the  contraction  of  the  weight  of 
mercury  P  —  /,  from  /°  to  zero,  or,  what  is  the  same  thing,  the  expansion 
of  the  same  weight  from  o  to  /°  ;  that  is,  the  weight  p  represents  the  ex- 
pansion of  the  weight  P  —  /,  for  /°.  If  this  weight  expands  in  glass  by  a 


quantity  p  for  /°,  a  single  unit  of  weight  would  expand       *    ,  for  P   and 
JL2-        for  a  smgfe  degree;  consequently,  for  D',  the  coefficient  of  ap- 


parent expansion  of  mercury  in  glass,  we  have  D'  =  Dulong 

and  Petit  found  the  coefficient  of  apparent  expansion  of  mercury  in  glass  to 

berfi* 

324.  Weight  thermometer.  —  The  apparatus  represented  in  fig.  283  is 
called  the  weight  thermometer,  because  the  temperature  can  be  deduced  from 
the  weight  of  mercury  which  overflows. 

The  above  experiments  have  placed  the  coefficient  of  apparent  expansion 

:  we  have  therefore  the  equation  ,p      »    =  g^,  from  which  we  get 

f  _    >  °°P  ^  a  formula  which  gives  the  temperature  /  when  the  weights  P  and 

p  are  known. 

325.  Coefficient  of  the  expansion  of  glass.  —  As  the  absolute  expansion 
of  a  liquid  is  the  apparent  expansion,  plus  the  expansion  due  to  the  envelope, 
the  coefficient  of  the  cubical  expansion  of  glass  has  been  obtained  by  taking 
the  difference  between  the  coefficient  of  absolute  expansion  of  mercury  in 
glass  and  that  of  its  apparent  expansion.     That  is,  the  coefficient  of  cubical 
expansion  of  glass  is 

•  sVi  -  eiio  =  IsToo  =  °'°°2  584 


272  On  Heat.  [325- 

Regnault  has  found  that  the  coefficient  of  expansion  varies  with  different 
kinds  of  glass,  and  further  with  the  sha.pe  of  the  vessel.  For  ordinary 
chemical  glass  tubes,  the  coefficient  is  0-0000254. 

326.  Coefficients  of  expansion  of  various  liquids. — The  apparent  ex- 
pansion of  liquids  may  be  determined  by  means  of  the  weight  thermometer, 
and  the  absolute  expansion  is  obtained  by  adding  to  this  coefficient  the  ex- 
pansion of  the  glass. 

Total  apparent  expansions  of  liquids  between  o  and  100°  C. 

Mercury      ....  o-oi|43  Ether o> 

Distilled  water    .         .         .  0-0406  Fixed  oils       ....  0-08 

Water  saturated  with  salt  .0-05  Nitric  acid      .         .         .         .OTI 

Sulphuric  acid     .         .         .  0-06  Alcohol.         .         .        ,         .0-116 

Hydrochloric  acid        .         .  0*06  Bisulphide  of  carbon     .         .0-128 

Oil  of  turpentine         .         .  0-07  Chloroform    .         .         .         .  0-157 

The  coefficient  of  apparent  expansion  for  i°  C.  is  obtained  by  dividing  these 
numbers  by  100  ;  but  the  number  thus  obtained  does  not  represent  the  mean 
coefficient  of  expansion  of  liquids,  for  the  expansion  of  these  bodies  increases 
gradually  from  zero.  The  expansion  of  mercury  is  practically  constant 
between  —36°  and  ico°  C,  while  water  contracts  from  zero  to  4°,  and  then 
expands. 

For  many  physical  experiments  a  knowledge  of  the  exact  expansion  of 
water  is  of  great  importance.  This  physical  constant  was  determined  with 
great  care  by  Matthiessen,  who  found  that  between  4°  and  30°  it  may  be 
expressed  by  the  formula 

V/=  i —0-00000253  (/  —  4)  +  0-0000008389  (/  — 4)2 +  o-ooqpoop7i73  (/  —  4)3; 
and  between  30°  and  100°  by 

V/  =  0-999695  +o-ooooo54724/2 +  0-000^00^)1 1 26/3. 

Many  liquids,  with  low  boiling  points,  especially  condensed  gases,  have  very 
high  coefficients  of  expansion.  Thilorier  found  that  liquid  carbonic  acid 
expands  four  times  as  much  as  air.  Drion  confirmed  this  observation,  and 
has  obtained  analogous  results  with  chloride  of  ethyle,  liquid  sulphurous 
acid,  and  liquid  hyponitrous  acid. 

327.  Correction  of  tne  barometric  height. — It  has  been  already  ex- 
plained under  the  Barometer  (164),  that,  in  order  to  make  the  indications  of 
this  instrument  comparable  in  different  places  and  at  different  times,  they 
must  be  reduced  to  a  uniform  temperature,  which  is  that  of  melting  ice. 
The  correction  is  made  in  the  following  manner  : — 

Let  H  be  the  barometric  height  at  /°,  and  //  its  height  at  zero,  d  the 
density  of  mercury  at  zero,  and  d'  its  density  at  /°.  The  heights  H  and  h 

are  inversely  as  the  densities  dfand  d' ;  that  is,  —  =  -.    If  we  call  i  the  volume 

H     d 

of  mercury  at  zero,  its  volume  at  t°  will  be  i  +  D/,  D  being  the  coefficient 
of  absolute  expansion  of  mercury.  But  these  volumes,  i  +  D/  and  i, 

7/ 

are  inversely  as  the  densities  d  and  d' ;  that  is,      = —  .      Consequently, 


-330]  Maximum  Density  of  Water.  273 

H  =  i  +~D?  whence  ^=  7~T)7'     Replacing   D   by  its  value  -^^   we   have 
*  ' 


i+_L        5508  +  /' 
5508 

In  this  calculation,  the  coefficient  of  absolute  expansion  of  mercury  is 
taken,  and  not  that  of  apparent  expansion  ;  for  the  value  H  is  the  same  as 
if  the  glass  did  not  expand,  the  barometric  height  being  independent  of  the 
diameter  of  the  tube,  and  therefore  of  its  expansion. 

328.  Correction  of  thermometric  readings.  —  If  the  whole  mercury  of  a 
thermometer  is  noi  immersed  in  the  space  whose  temperature  is  to  be  deter- 
mined, it  is  necessary  to  make  a  correction,  which  in  the  accurate  deter- 
mination of  boiling  points,  for  instance,  is  of  great  importance,  in  order  to 
arrive  at  the  true  temperature  which  the  thermometer  should  show.     That 
part  of  the  stem  which  projects  will  have  a  temperature  which  must  be 
estimated,  and  which  may  roughly  be  taken  as  something  over  that  of  the 
surrounding  air. 

Supposing,  for  instance,  the  reading  is  160°  and  that  the  whole  of  the 
part  over  80  is  outside  the  vessel,  while  the  temperature  of  the  surrounding 
air  is  15°.  We  will  assume  that  the  mean  temperature  of  the  stem  is  25° 
and  that  a  length  of  160°  —  80°  is  to  be  heated  through  160  —  25  =  135°  ;  this 

gives  80  x    !  35  =  i  -66  (taking  the  coefficient  of  apparent  expansion  of  mer- 
6480 

cury)  ;  so  that  the  true  reading  is  i6r66. 

329.  Force  exerted  by  liquids  in  expanding-.  —  The  force  which  liquids 
exert  in  expanding  is  very  great,  and  equal  to  that  which  would  be  required 
in  order  to  bring  the  expanded  liquid  back  to  its  original  volume.     Now  we 
know  what  an  enormous  force  is  required  to  compress  a  liquid  to  even  a  very 
small  extent  (98).     Thus  between  o°  and  10°,  mercury  expands  by  0*0015790 
of  its  volume  at  o°  ;  its  compressibility  is  O'ooooo295  of  its  volume  for  one 
atmosphere  ;  hence  a  pressure  of  more   than  600  atmospheres  would  be 
requisite  to  prevent  mercury  expanding  when  it  is  heated  from  o°  to  10°. 

330.  Maximum    density    of  water.  —  Water   presents  the    remarkable 
phenomenon  that  when  its  temperature  sinks  it  contracts  up  to  4°  ;  but  from 
that  point,  although  the  cooling  continues,  it  expands  up  to  the  freezing  point, 
so  that  4°  represent  the  point  of  greatest  contraction  of  water. 

Many  methods  have  been  used  to  determine  the  maximum  density  of 
water.  Hope  made  the  following  experiment  :  —  He  took  a  deep  vessel  per- 
forated by  two  lateral  apertures,  in  which  he  fixed  thermometers,  and  having 
filled  the  vessel  with  water  at  o°,  he  placed  it  in  a  room  at  a  temperature  of 
15°.  As  the  layers  of  liquid  at  the  sides  of  the  vessel  became  heated  they 
sank  to  the  bottom,  and  the  lower  thermometer  marked  4°  while  the  upper 
one  was  still  at  zero.  Hope  then  made  the  inverse  experiment  :  having 
filled  the  vessel  with  water  at  15°,  he  placed  it  in  a  room  at  zero.  The 
lower  thermometer  having  sunk  to  4°  remained  stationary  for  some  time, 
while  the  upper  one  cooled  down  until  it  reached  zero.  Both  these  experi- 
ments prove  that  water  is  heavier  at  4°  than  at  o°,  for  in  both  cases  it  sinks 
to  the  lower  part  of  the  vessel. 

This  last  experiment  may  be  adapted  for  lecture  illustration  by  using  a 

N3 


274  On  Heat.  [330- 

cylinder  containing  water  at   15°  C.,  partially  surrounded  by  a  jacket  con- 
taining bruised  ice  (fig.  284). 

Hallstrom  made  a  determination  of  the  maximum  density  of  water  in  the 
following  manner  : — He  took  a  glass  bulb,  loaded  with  sand,  and  weighed  it 

'  in  water  of  different  temperatures.  Allow- 
ing for  the  expansion  of  glass,  he  found 
that  4"i°  was  the  temperature  at  which  it 
lost  most  weight,  and  consequently  this 
was  the  temperature  of  the  maximum 
density  of  water. 

Uespretz  arrived  at  the  temperature 
4°  by  another  method.  He  took  a  water 
thermometer — that  is  to  say,  a  bulbed  tube 
containing  water — and,  placing  it  in  a 
bath,  the  temperature  of  which  was  indi- 
cated by  an  ordinary  mercury  thermo- 
meter, found  that  the  water  contracted  to 
the  greatest  extent  at  4°,  and  that  this  is 
therefore  the  point  of  greatest  density. 

This  phenomenon  is  of  great  import- 
ance in  the  economy  of  nature.  In  winter 
the  temperature  of  lakes  and  rivers  falls 
from  being  in  contact  with  the  cold  air 
and  from  other  causes,  such  as  radia- 
tion. The  colder  water  sinks  to  the  bot- 
tom, and  a  continual  series  of  currents  goes  on  until  the  whole  has  a 
temperature  of  4°.  The  cooling  on  the  surface  still  continues,  but  the  cooled 
layers  being  lighter  remain  on  the  surface,  and  ultimately  freeze.  The  ice 
formed  thus  protects  the  water  below,  which  remains  at  a  temperature  of  4°, 
even  in  the  most  severe  winters,  a  temperature  at  which  fish  and  other 
inhabitants  of  the  water  are  not  destroyed. 

The  following  table  of  the  density  of  water  at  various  temperatures  is 
based  on  several  sets  of  observations  : — 

Density  of  water  between  o°  and  30°. 


Fig.  284. 


Tempe- 
ratures. 

Densities. 

Tempe- 
ratures. 

Densities. 

Tempe- 
ratures. 

Densities. 

0 

0-99988 

II 

0-99965 

22 

0-99785 

I 

0-99993 

12 

0-99955 

23 

0-99762 

•    2 

0-99997 

13 

0-99943 

24 

0-99738 

3 

0-99999 

H 

0-99930 

25 

0-99704 

4 

I  -00000 

15 

0-99915 

26 

0-99089 

5 

0-99999 

16 

0-99900 

27 

0-99662 

6 

0-99997 

I? 

0-99884 

28 

0-99635 

7 

0-99994 

18 

0-99800 

29 

0-99607 

8 

0-99988 

19 

0-99847 

30 

0-99579 

9 

0-99982 

20 

0-99807 

10 

0-99974 

21 

0-99806 

-331]  Expansion  and  Density  of  Gases.  275 


CHAPTER   IV. 

EXPANSION   AND   DENSITY   OF   GASES. 

331.  Gay-Lussacs  method. — Gases  are  the  most  expansible  of  all 
bodies,  and  at  the  same  time  the  most  regular  in  their  expansion.  The 
coefficients  of  expansion,  too,  of  the  several  gases  differ  only  by  very  small 
quantities.  The  cubical  expansion  of  gases  need  alone  be  considered. 

Gay-Lussac  first  determined  the  coefficient  of  the  expansion  of  gases  by 
means  of  the  apparatus  represented  in  fig.  285. 


Fig.  285. 

In  a  rectangular  metal  bath,  about  16  inches  long,  was  fitted  an  air  ther- 
mometer, which  consisted  of  a  capillary  tube,  AB,  with  a  bulb,  A,  at  one  end. 
The  tube  was  divided  into  parts  of  equal  capacity,  and  the  contents  of  the 
bulb  ascertained  in  terms  of  these  parts.  This  was  effected  by  weighing 
the  bulb  and  tube  full  of  mercury  at  zero,  and  then  heating  slightly  to  expel 
a  small  quantity  of  mercury,  which  was  weighed.  The  apparatus  being 
again  cooled  down  to  zero,  the  vacant  space  in  the  tube  corresponded  to 
the  weight  of  mercury  which  had  overflowed  ;  the  volume  of  mercury 
remaining  in  the  apparatus,  and  consequently  the  volume  of  the  bulb,  \ras 
determined  by  calculations  analogous  to  those  made  for  the  piezometer  (98). 

In  order  to  fill  the  thermometer  with  dry  air  it  was  first  filled  with 
mercury,  which  was  boiled  in  the  bulb  itself.  A  tube,  C,  filled  with  chloride 
of  calcium,  was  then  fixed  on  to  its  end  by  means  of  a  cork.  A  fine  platinum 
wire  having  then  been  introduced  into  the  stem  AB,  through  the  tube  C,  and 
the  apparatus  being  slightly  inclined  and  agitated  from  time  to  time,  air 
entered,  having  been  previously  well  dried  by  passing  through  the  chloride 


276  On  Heat.  [331- 

of  calcium  tube.  The  whole  of  the  mercury  was  displaced,  with  the  ex- 
ception of  a  small  thread,  which  remained  in  the  tube  AB  as  an  index. 

The  air  thermometer  was  then  placed  in  the  box  filled  with  melting  ice, 
the  index  moved  towards  A,  and  the  point  was  noted  at  which  it  became 
stationary.  This  gave  the  volume  of  air  at  zero  ;  for  the  capacity  of  the 
bulb  was  known.  Water  or  oil  was  then  substituted  for  the  ice,  and  the 
bath  successively  heated  to  different  temperatures.  The  air  expanded  and 
moved  the  index  from  A  towards  B.  The  position  of  the  index  in  each  case 
was  noted,  and  the  corresponding  temperature  was  indicated  by  means  of 
the  thermometers  D  and  E. 

Assuming  that  the  atmospheric  pressure  did  not  vary  during  the  experi- 
ment, and  neglecting  the  expansion  of  the  glass  as  being  small  in  comparison 
with  that  of  the  air,  the  total  expansion  of  the  air  is  obtained  by  subtracting 
from  its  volume  at  a  given  temperature,  its  volume  at  zero.  Dividing  this  by 
a  given  temperature,  and  then  by  the  number  of  units  contained  in  the 
volume  at  zero,  the  quotient  is  the  coefficient  of  expansion  for  a  single  unit 
of  volume  and  a  single  degree  ;  that  is,  the  coefficient  of  expansion.  It  will 
be  seen,  further  on,  how  corrections  for  pressure  and  temperature  may  be 
introduced. 

By  this  method  Gay-Lussac  found  that  the  coefficient  of  expansion  of  air 
was  0*00375  ;  the  two  following  laws  hold  in  reference  to  the  expansion  of 
gases : — 

I.  All  gases  have  the  same  coefficient  of  expansion  as  air. 

II.  This  coefficient  is  the  same  whatever  be  the  pressure  supported  by  the 
gas. 

These  simple  laws  are  not,  however,  rigorously  exact  (333)  ;  they  only 
express  the  expansion  of  gases  in  an  approximate  manner.  These  laws 
were  discovered  independently  by  Dalton  and  by  Gay-Lussac,  and  are 
usually  ascribed  to  them.  The  first  discoverer  of  the  former  law  was, 
however,  Charles. 

332.  Problems  on  the  expansion  of  gases. — Many  of  the  problems 
relative  to  the  expansion  of  gases  are  similar  to  those  on  the  expansion  of 
liquids.  With  obvious  modifications,  they  are  solved  in  a  similar  manner. 
In  most  cases  the  pressure  of  the  atmosphere  must  be  taken  into  account  in 
considering  the  expansion  of  gases.  The  following  is  an  example  of  the 
manner  in  which  this  correction  is  made  : — 

i.  The  volume  of  a  gas  at  /°,  and  under  the  pressure  H,  is  V ;  what  will 
be  the  volume  V  of  the  same  gas  at  zero,  and  under  the  normal  pressure 
760  millimetres  ? 

Here  there  are  two  corrections  to  be  made  ;  one  relative  to  the  tempera- 
ture, and  the  other  to  the  pressure.  It  is  quite  immaterial  which  is  taken 
first.  If  a  be  the  coefficient  of  cubical  expansion  for  a  single  degree,  by 
reasoning  similar  to  that  in  the  case  of  linear  expansion  (318),  the  volume  of 

y/ 

the  gas  at  zero,  but  still  under  the  pressure  H,  will  be .     This  pressure 

i  -i-  at 

is  reduced  to  the  pressure  760  in  accordance  with  Boyle's  law  (174),  by  put- 
ting V  x  760  =  V/  x  H  ;  whence  V  V/t 


I  +at  760(1  +af) 

ii.  A  volume  of  gas  weighs  P'  at  /° ;  what  will  be  its  weight  at  zero  ? 


-333] 


Regnaulfs  Method. 


277 

Let  P'  be  the  desired  weight,  a  the  coefficient  of  expansion  of  the  gas, 
<?  its  density  at  /°,  and  d  its   density  at  zero.     As   the  weights  of  equal 

P'     d' 
volumes  are  proportional  to  the  densities,  we  have  —  =  —      If  i    be   the 

volume  of  a  gas  at  zero,  its  volume  at  /  will  be  I  +  a/  ;  but  as  the  densities 

are  inversely  as  the  volumes  -  --^  —  ?—  , 

d     i  r  u/ 


and  therefore 


;  whence  P  =  P'  (I+Q/). 


From  this  equation  we  get  P' 


I  -rat 


which  gives  the  weight  at  /,  know- 


ing the  weight  at  zero,  and  which  further  shows  that  the  weight  P'  is  in- 
versely as  the  binomial  of  expansion  i  +  at. 

333.  Re^nault  s   method. — Regnault   used   successively    four   different 
methods   for   determining  the  expansion  of  gases.     In  some  of  them  the 


Fig.  286. 

pressure  was  constant  and  the  volume  variable,  as  in  Gay-Lussac's  method ; 
in  others  the  volume  remained  the  same  while  the  pressure  varied.  The 
first  method  will  be  described.  It  is  the  same  as  that  used  by  Rudberg 
and  Dulong,  but  is  distinguished  by  the  care  with  which  all  sources  of  error 
are  avoided. 

The  apparatus  consisted  of  a  pretty  large  cylindrical  reservoir,  B  (fig. 
286),  terminating  in  a  bent  capillary  tube.  In  order  to  fill  the  reservoir  with 
dry  air,  it  was  placed  in  a  hot-water  bath,  and  the  capillary  tube  connected 
by  a  caoutchouc  tube  with  a  series  of  drying  tubes.  These  tubes  were 
joined  to  a  small  air-pump,  P,  by  which  a  vacuum  could  be  produced  in  the 
reservoir  while  at  a  temperature  of  100°.  The  reservoir  was  first  exhausted, 
and  air  afterwards  admitted  slowly ;  this  operation  was  repeated  a  great 
many  times,  so  that  the  air  in  the  reservoir  became  quite  dry,  for  the  mois- 
ture adhering  to  the  sides  passed  off  in  vapour  at  1 00°,  and  the  air  which 
entered  became  dry  in  its  passage  through  the  U  tubes. 


278 


On  Heat. 


[333- 


The  reservoir  was  then  kept  for  half  an   hour  at  the  temperature  of 
boiling  water ;  the  air-pump  having  been  detached,  the  drying  tubes  were 
then  disconnected,  and  the  end  of  the  tube  her- 
metically sealed,  the  height  H  of  the  barometer 
being  noted.     When  the  reservoir  B  was  cool,  it 
was  placed  in  the  apparatus  represented  in  fig. 
287.     It  was  there  quite  surrounded  with  ice,  and 
the  end  of  the  tube  dipped  in  the  mercury  bath, 
C.     After  the  air  in  the  reservoir  B  had  sunk  to 
zero,  the  point  b  was  broken  off  by  means  of  a 
forceps ;    the   air   in  the  interior  became  con- 
densed  by  atmospheric   pressure,  the  mercury 
rising  to  a  height  oG.     In  order  to  measure  the 
height  of  this  column,  G0,  which  will  be  called 
h,  a  movable  rod,  go,  was  lowered  until  its  point, 
o ,  was  flush  with  the  surface  of  the  mercury  in 
the  bath  ;  the  distance  between  the  point  o  and 
the  level  of  the  mercury  G  was  measured   by 
means  of  the  cathetometer.     The  point  b  was 
finally  closed  with  wax  by  means  of  the  spoon  <2, 
and  the  barometric  pressure  noted  at  this  mo- 
ment.    If  this  pressure  be  H',  the  pressure  in 
the  reservoir  is  H'  —  h. 
The  reservoir  was  now  weighed  to  ascertain  P,  the  weight  of  the  mercury 
which  it  contained.     It  was  then  completely  filled  with  mercury  at  zero,  in 
order  to  have  the  weight  P'  of  the  mercury  in  the  reservoir  and  in  the  tube. 
If  8  be  the  coefficient  of  the  cubical  expansion  of  glass,  and  D  the  density 
of  mercury  at  zero,  the  coefficient  a  of  the  cubical  expansion  of  air  is  deter* 
mined  in  the  following  manner : — The  volume  of  the  reservoir  and  of  the 

P' 
tube  at  zero  is  —  ,from  the  formula  P  =  VD  (-126) ;  consequently  this  volume 


Fig   287. 


IS 


(O 


at  the  temperature  /°,  assuming,  as  is  the  case,  that  the  reservoir  and  tube 
expand  as  if  they  were  solid  glass.    But  from  the  formula  P  =  VD,  the  volume 

P'—  P 
of  air  in  the  reservoir  at  zero,  and  under  the  pressure  H'  —  /i,  is  --    At 


the  same  pressure,  but  at  /°,  its  volume  would  be 


and  by  Boyle's  law  (174),  at  the  pressure  H,  at  which  the  tube  was  sealed, 
this  volume  must  have  been 


DH 


Now  the  volumes  represented  by  these  formulae,  (i)  and  (2),  are  each 


-334]  Air  Thermometer.  279 

equal  to  the  volume  of  the  reservoir  and  the  tube  at  /° ;  they  are  therefore 
equal.     Removing  the  denominators,  we  have 

P'(i+8/)  H  =  (P'-P)  (i -fa/)  (H'-//)     , (3) 

from  which  the  value  of  a  is  deduced. 

The  means  of  a  great  number  of  experiments  between  zero  and  ioo°and 
for  pressure  between  300  millimetres  and  500  millimetres,  gave  the  following 
numbers  for  the  coefficients  of  expansion  for  a  single  degree  : 

Air 0-003667  Carbonic  acid    ....  0-003710 

Hydrogen 0-003661  Nitrous  oxide     ....  0-003719 

Nitrogen 0-003661  Cyanogen 0*003877 

Carbonic  oxide   ....  0-003667  Sulphurous  acid     .     .     .  0-003903 

These  numbers,  with  which  the  results  obtained  by  Magnus  closely  agree, 
show  that  the  coefficients  of  expansion  of  the  permanent  gases  differ  very 
little  ;  but  that  they  are  somewhat  greater  in  the  case  of  the  more  easily 
condensible  gases,  such  as  carbonic  and  sulphurous  acids.  Regnault  has 
further  found  that,  at  the  same  temperature,  the  coefficient  of  expansion  of 
any  gas  increases  with  the  pressure  which  it  supports.  Thus,  while  the  co- 
efficient of  expansion  of  air  under  a  pressure  of  i  iomm<  is  0-003648,  under  a 
pressure  of  365 5™"",  or  nearly  five  atmospheres,  it  is  0-003709. 

The  number  found  by  Regnault  for  the  coefficient  of  the  expansion  of  air, 
0-003667,  is  equal  to  ~  =  ^  nearly  ;  and  if  we  take  the  coefficient  of  ex- 
pansion at  0-0036666  .  .  .it  may  be  represented  by  the  fraction  §si_? 
which  is  convenient  for  purposes  of  calculation. 

The  difference  in  the  expansibility  of  various  gases  may  be  ascribed  to 
the  circumstance  that  when  a  gas  is  heated,  the  relative  positions  of  the 
atoms  in  the  molecules  is  thereby  altered  ;  and  a  certain  amount  of  internal 
work  is  required  for  this  which  is  different  for  different  gases. 

334.  Air  thermometer. — The  air  thermometer  is  based  on  the  expansion 
of  air.  When  it  is  used  to  measure  small  differences  of  temperature,  it  has 
the  same  form  as  the  tube  used  by  Gay-Lussac  in  determining  the  expansion 
of  air  (fig.  285),  that  is,  a  capillary  tube  with  a  bulb  at  the  end.  The  re- 
servoir being  filled  with  dry  air,  an  index  of  coloured  sulphuric  acid  is  passed 
into  the  tube  ;  the  apparatus  is  then  graduated  in  Centigrade  degrees  by 
comparing  the  positions  of  the  index  with  the  indications  of.  a  mercurial  ther- 
mometer. Of  course  the  end  of  the  tube  must  remain  open  ;  otherwise,  the 
air  above  the  index  condensing  or  expanding  at  the  same  time  as  that  in  the 
bulb,  the  index  would  remain  stationary.  A  correction  must  be  made  at 
each  observation  for  the  atmospheric  pressure. 

When  considerable  variations  of  temperature  are  to  be  measured,  the 
tube  has  a  form  like  that  used  in  Regnault's  experiments  (fig.  286  and  287). 
By  experiments  made  as  described  in  article  333,  P,  P',  H,  H',  and  h,  may 
be  found,  and  the  coefficients  a  and  d  being  known,  the  temperature  /  to 
which  the  tube  has  been  raised  is  readily  reduced  from  the  equation  (3). 

Regnault's  researches  show  that  the  air  and  the  mercurial  thermometer 
agree  up  to  260°,  but  above  that  point  mercury  expands  relatively  more  than 
air. 

In  cases  where  very  high  temperatures  are  to  be  measured,  the  reservoir 


2 So  On  Heat.  [334- 

is  made  of  platinum.  The  use  of  an  air  thermometer  is  seen  in  Dulong  and 
Petit's  experiment  (322)  ;  it  was  by  such  an  apparatus  that  Pouillet  measured 
the  temperature  corresponding  to  the  colours  which  metals  take  when  heated 
in  a  fire,  and  found  them  to  be  as  follows  : — 

Incipient  red    .         .         .     525°C.     Dark  orange   ....     iioo°C. 

Dull  red    ....     700          White 1300 

Cherry  red        .         .         .     900          Dazzling  white  .     1 500 

In  the  measurement  of  high  temperatures  Deville  and  Troost  have  used 
with  advantage  the  vapour  of  iodine  instead  of  air,  and  as  platinum  has  been 
found  to  be  permeable  to  gases  at  high  temperatures,  they  have  employed 
porcelain  instead  of  that  metal. 

335.  Density  of  gases. — The  relative  density  of  a  gas,  or  its  specific 
gravity,  is  the  ratio  of  the  weight  of  a  certain  volume  of  the  gas  to  that  of  the 
same  volume  of  air ;  both  the  gas  and  the  air  being  at  zero  and  under  a 
pressure  of  760  millimetres. 

In  order,  therefore,  to  find  the  specific  gravity  of  a  gas,  it  is  necessary  to 
determine  the  weight  of  a  certain  volume  of  this  gas  at  a  pressure  of  760 
millimetres,  and  a  temperature  of  zero,  and  then  the  weight  of  the  same 
volume  of  air  under  the  same  conditions.  For  this  purpose  a  large  globe  of 
about  two  gallons'  capacity  is  used,  the  neck  of  which  is  provided  with  a 
stopcock,  which  can  be  screwed  to  the  air-pump.  The  globe  is  first  weighed 
empty,  and  then  full  of  air,  and  afterwards  full  of  the  gas  in  question.  The 
weights  of  the  gas  and  of  the  air  are  obtained  by  subtracting  the  weight  of 
the  exhausted  globe  from  the  weight  of  the  globes  filled,  respectively,  with 
air  and  gas.  The  quotient,  obtained  by  dividing  the  latter  by  the  former, 
gives  the  specific  gravity  of  the  gas.  It  is  difficult  to  make  these  determina- 
tions at  the  same  temperature  and  pressure,  and  therefore  all  the  weights  are 
reduced  to  zero  and  the  normal  pressure  of  760  millimetres. 

The  gases  are  dried  by  causing  them  to  pass  through  drying  tubes  before 
they  enter  the  globe,  and  air  must  also  be  passed  over  potash  to  free  it  from 
carbonic  acid.  And  as  even  the  best  air-pumps  never  produce  a  perfect 
vacuum,  it  is  necessary  to  exhaust  the  globe  until  the  manometer  in  each 
case  marks  the  same  pressure. 

The  globe  having  been  exhausted,  dried  air  is  allowed  to  enter,  and  the 
process  is  repeated  several  times  until  the  globe  is  perfectly  dried.  It  is 
then  finally  exhausted  until  the  residual  pressure,  in  millimetres,  is  e.  The 
weight  of  the  exhausted  globe  is  p.  Air,  which  has  been  dried  and  purified 
by  passing  through  potash  and  chloride  of  calcium  tubes,  is  then  allowed  to 
enter  slowly.  The  weight  of  the  globe  full  of  air  is  P.  If  H  is  the  baro- 
metric height  in  millimetres,  and  /°  the  temperature  at  the  time  of  weighing, 
P  —  p  is  the  weight  of  the  air  in  the  globe  at  the  temperature  /,  and  the  pressure 
U-e. 

To  reduce  this  weight  to  the  pressure  760  millimetres  and  the  tempera- 
ture zero,  let  a  be  the  coefficient  of  the  expansion  of  air,  and  8  the  coefficient 
of  the  cubical  expansion  of  glass.  From  Boyle's  law  the  weight,  which  is 

P-/  at  /°  and  a  pressure  of  H-e,  would  be  '    ~^     -  under  the  pressure 
760  millimetres  and  at  the  same  temperature  /°.     If  the  temperature  is  o°, 


-336]    Regnaulfs  Method  of  determining  Density  of  Gases.     28 1 

the  capacity  of  the  globe  will  diminish  in  the  ratio  i  +  /to  i,  while  the 
weight  of  the  gas  increases  in  the  ratio  i  :  i  +  n/,  as  follows  from  the  pro- 
blems in  art.  332'.  Consequently,  the  weight  of  the  air  in  the  globe  at  o°  and 
at  the  pressure  760  millimetres  will  be 

/P_^      760(1+ a/)  ,. 


Further,  let  of  be  the  coefficient  of  expansion  of  the  gas  in  question  ;  let 
P'  be  the  weight  of  the  globe  full  of  gas  at  the  temperature  /'  and  the  pres- 
sure H',  and  let  p'  be  the  weight  of  the  globe  when  it  is  exhausted  to  the 
pressure  e  ;  the  weight  of  the  gas  in  the  globe  at  the  pressure  760  and  the 
temperature  zero  will  be 


760 


(2) 


Dividing  the  latter  formula  by  the  former  we  obtain  the  density 
D  _  (P'-^O  (H-g)  (i  +  a'O  (i  +  &Q 
(P-/)(H'-*)(i+a/)(n-*O 
If  the  temperature  and  the  pressure  do  not  vary  during  the  experiment, 

H  =  H'  and  /  =  /' ;  whence  D  =  ^p"^  (|  jffi  and  if  «  =  «'-  D  ,-  Pp^f' 

336.  Regnault's  method  of  determining-  the  density  of  gases. — 
Regnault  so  modified  the  above  method  that  many  of  the  corrections  may 
be  dispensed  with.  The  globe  in  which  the  gas  is  weighed  is  suspended 


Fig.  288. 

from  one  pan  of  a  balance,  and  is  counterpoised  by  means  of  a  second  globe 
of  the  same  dimensions,  and  hermetically  sealed,  suspended  from  the  other. 
These  two  globes,  expanding  at  the  same  time,  always  displace  the  same 


282  On  Heat.  [336- 

quantity  of  air,  and  consequently  variations  in  the  temperature  and  pressure 
of  the  atmosphere  do  not  influence  the  weighing.  The  globe,  too,  is  filled 
with  the  air  or  with  the  gas,  at  the  temperature  of  zero.  Thi's  is  effected  by 
placing  it  in  a  vessel  full  of  ice,  as  shown  in  fig.  287.  It  is  then  connected 
with  a  three-way  cock,  A,  by  which  it  may  be  connected  either  with  an  air- 
pump/  or  with  the  tubes  M  and  N,  which  are  connected  with  the  reservoir 
of  gas.  The  tubes  M  and  N  contain  substances  which  by  their  action  on 
the  gas  dry  and  also  purify  it. 

The  stopcock  A  being  so  turned  that  the  globe  is  only  connected  with 
the  air-pump,  a  vacuum  is  produced  ;  by  means  of  the  same  cock,  the  con- 
nection with  the  pump  being  cut  off,  but  established  between  M  and  N, 
the  gas  soon  fills  the  globe.  But  as  the  exhaustion  could  not  have  been 
complete,  and  some  air  must  have  been  left,  the  globe  is  again  exhausted 
and  the  gas  allowed  to  enter,  and  the  process  is  repeated  until  it  is  thought 
all  air  is  removed.  The  vacuum  being  once  more  produced,  a  differential 
barometer  (fig.  138),  connected  with  the  apparatus  by  the  tube  E,  indicates 
the  pressure  of  the  residual  rarefied  gas  e.  Closing  the  cock  B  and  detach- 
ing A,  the  globe  is  removed  from  the  ice,  and  after  being  cleaned  is  weighed. 
'  This  gives  the  weight  of  the  empty  globe  p  ;  it  is  again  replaced  in  the 
ice,  the  stopcock  A  adjusted,  and  the  gas  allowed  to  enter,  care  being  taken 
to  leave  the  stopcocks  open  long  enough  to  allow  the  gas  in  the  globe  to 
acquire  the  pressure  of  the  atmosphere,  H,  which  is  marked  by  the  baro- 
meter. The  stopcock  B  is  then  closed,  A  removed,  and  the  globe  weighed 
with  the  same  precautions  as  before.  This  gives  the  weight  P'  of  the  gas. 

The  same  operations  are  then  repeated  on  this  globe  with  air,  and  two 
corresponding  weights  p  and  P  are  obtained.  The  only  correction  necessary 
is  to  reduce  the  weights  in  the  two  cases  to  the  standard  pressure  by  the 
method  described  in  the  preceding  paragraph.  The  correction  for  tempera- 
ture is  not  needed,  as  the  gas  is  at  the  temperature  of  melting  ice.  The 
ratio  of  the  weight  of  the  gas  to  that  of  the  air  is  thus  obtained  by  the 
formula 

r>     P  -i> 


337.  Density  of  gases  which  attack  metals. — For  gases  which  attack 
the  ordinary  metals,  such  as  chlorine,  a  metal  stopcock  cannot  be  used,  and 
vessels  with  ground-glass  stoppers  are  substituted.  The  gas  is  introduced 
by  a  bent  glass  tube,  the  vessel  being  held  either  upright  or  inverted,  accord- 
ing as  the  gas  is  heavier  or  lighter  than  air  ;  when  the  vessel  is  supposed  to 
be  full,  the  tube  is  withdrawn,  the  stopper  inserted,  and  the  weight  taken. 
This  gives  the  weight  of  the  vessel  and  gas.  If  the  capacity  of  the  vessel 
be  measured  by  means  of  water,  the  weight  of  the  air  which  it  contains  is 
deduced,  for  the  density  of  air  at  o°  C.  and  760  millimetres  pressure  is  ^ 
that  of  distilled  water  under  the  same  circumstances.  The  weight  of  the 
vessel  full  of  air,  less  the  weight  of  the  contained  air,  gives  the  weight  of  the 
vessel  itself.  From  these  three  data — the  weight  of  the  vessel  full  of  the  gas, 
the  weight  of  the  air  which  it  contains,  and  the  weight  of  the  vessel  alone — 
the  specific  gravity  of  the  gas  is  readily  deduced,  the  necessary  corrections 
being  made  for  temperature  and  pressure. 


-337]  Density  of  Gases  which  attack  Metals.  283 

Density  of  gases  at  zero  and  at  a  pressure  of  760  millimetres,  that  of  air 
being  taken  as  unity. 

Air i-oooo  Sulphuretted  hydrogen         .  1-1912 

Hydrogen     ....  0-0693  Hydrochloric  acid         .         .  1-2540 

Ammoniacal  gas   .         .         .  0-5367  Protoxide  of  nitrogen  .         .  1-5270 

Marsh  gas     ....  9-5590  Carbonic  acid       .         .         .  i-529r 

Carbonic  oxide      .         .         .  0-9670  Cyanogen     ....  r86oo 

Nitrogen        .....  0-9714  Sulphurous  acid    .         .         .  2-2474 

Binoxide  of  nitrogen     .         .  I  -0360  Chlorine        ....  3'44°° 

Oxygen          ....  1-1057  Hydriodic  acid     .         .         .  4'443o 

Regnault  has  furnished  the  following  determinations  of  the  weight  of  a 
litre  of  the  most  important  gases  at  o°  C.  and  760  mm.  : — 

Air  ....     1-293187  grms.     Nitrogen          .         .     1-256157  grms,, 
Oxygen    .         .         .     1-429802       „       Carbonic  acid          .     1-977414      „ 
Hydrogen        .        .    0089578      „ 


284  On  Heat.  [338- 


CHAPTER  V. 

CHANGES   OF  CONDITION.      VAPOURS. 

338.  Fusion.  It«i  laws. — The  only  phenomena  of  heat  with  which  we 
have  hitherto  been  engaged  have  been  those  of  expansion.  In  the  case  of 
solids  it  is  easy  to  see  that  this  expansion  is  limited.  For  in  proportion  as 
a  body  absorbs  a  larger  quantity  of  heat,  the  repulsive  force  between  the 
molecules  is  increased,  and  ultimately  a  point  is  reached  at  which  the  mole- 
cular attraction  is  not  sufficient  to  retain  the  body  in  the  solid  state.  A  new 
phenomenon  is  then  produced  ;  fusion  takes  place  ;  that  is,  the  body  passes 
from  the  solid  into  the  liquid  state. 

Some  substances,  however,  such  as  paper,  wood,  wool,  and  certain  salts, 
do  not  fuse  at  a  high  temperature,  but  are  decomposed.  Many  bodies  have 
long  been  considered  refractory ;  that  is,  incapable  of  fusion  ;  but,  in  pro- 
portion as  it  has  been  possible  to  produce  higher  temperatures,  their  number 
has  diminished.  Gaudin  has  succeeded  in  fusing  rock  crystal  by  means  of  a 
lamp  fed  by  a  jet  of  oxygen  ;  and  Despretz,  by  combining  the  effects  of  the 
sun,  the  voltaic  battery,  and  the  oxy-hydrogen  blow-pipe,  melted  alumina 
and  magnesia,  and  softened  carbon  so  as  to  be  flexible,  which  is  a  condition 
near  that  of  fusion. 

It  has  been  found  experimentally  that  the  fusion  of  bodies  is  governed  by 
the  two  following  laws  : — 

I.  Every  substance  begins  to  fuse  at  a  certain  temperature,  which  is  in- 
variable for  each  substance,  if  the  pressure  be  constant. 

II.  Whatever  be  the  inte?isity  of  the  source  of  heat,  from  the  moment 
fusion  begins,  the  temperature  of  the  body  ceases  to  rise,  a?id  remains  con- 

stant  until  the  fusioji  is  complete. 

Fusing  points  of  certain  substances. 

Mercury          .         .         .         .-38-8°     Sodium 90° 

Oil  of  Turpentine  .         .         .  —  27  Rose's  fusible  metal        .         .  94 

Bromine          .         .         .         .  —  12-5      Sulphur 114 

Ice o         Tin 228 

Butter +  33         Bismuth 264 

Phosphorus    .         .         .         -44  Cadmium         .         .         .         .321 

Spermaceti     .         .         .         -49         Lead 335 

Potassium       .         .         .         .55         Zinc 422 

Margaric  acid         .         .         -57  Antimony         ....  450 

Stearine         .         .         .         .60         Silver 954 

White  wax     .         .         .         .65         Gold 1250 

Wood's  fusible  metal      .         .68         Iron 1500 

Stearic  acid    .         .         .         .70  Platinum          .         .         .         .1775 


-339]          Influence  of  Pressure  on  the  Melting  Point. 


285 


Some  substances  pass  from  the  solid  to  the  liquid  state  without  showing 
any  definite  melting  point ;  for  example,  glass  and  iron  become  gradually 
softer  and  softer  when  heated,  and  pass  by  imperceptible  stages  from  the 
solid  to  the  liquid  condition.  This  intermediate  condition  is  spoken  of  as 
the  state  of  vitreous  fusion.  Such  substances  may  be  said  to  melt  at  the 
lowest  temperature  at  which  perceptible  softening  occurs,  and  to  be  fully 
melted  when  the  further  elevation  of  temperature  does  not  make  them  more 
fluid  ;  but  no  precise  temperature  can  be  given  as  their  melting  points. 

The  determination  of  the  melting  point  of  a  body  is  a  matter  of  consider- 
able importance  in  fixing  the  identity  of  many  chemical  compounds,  and  is 
moreover  a  point  of  frequent  practical  application  in  determining  the  com- 
mercial value  of  tallow  and  other  fats. 

It  is  done  as  follows  : — A  portion  of  the  substance  is  melted  in  a  watch 
glass,  and  a  small  quantity  of  it  sucked  into  a  fine  capillary  tube,  the  end  of 
which  is  then  sealed.  This  tube  is  then  placed  in  a  bath  of  clear  water  in 
which  is  a  thermometer,  and  the  temperature  of  the  bath  is  gradually  raised 
until  the  substance  is  completely  melted,  which  from  its  small  mass  is  very 
easily  observed.  The  bath  is  then  allowed  to  cool,  and  the  solidifying  point 
noted  ;  and  the  mean  of  the  two  is  taken  as  the  true  melting  point. 

339.  Influence  of  pressure  on  the  melting  point. — Thomson  and 
Clausius  have  deduced  from  the  principles  of  the  mechanical  theory  of  heat 
that,  with  an  increase  of  pressure,  the  melting  point  of  a  body  must  w  ' 

be  raised.  All  bodies  which  expand  on  passing  from  the  solid  to 
the  liquid  state  have  to  perform  external  work — namely,  to  raise 
the  pressure  of  the  atmosphere  by  the  amount  of  this  expansion. 
Under  ordinary  circumstances,  the  amount  of  external  work  which 
solids  and  liquids  thus  perform  is  so  small  that  it  may  be  neglected. 
But  if  the  external  pressure  be  increased,  the  power  of  overcoming 
it  can  only  be  obtained  by  an  increase  of  vis  viva  of  the  molecules. 
This  increase  can  do  more  work  ;  the  temperature  effusion  as  well 
as  the  heat  of  fusion  are  both  increased.  Bunsen  examined  the 
influence  of  pressure  on  the  melting  point  by  means  of  the  ap- 
paratus represented  in  fig.  289,  in  which  acb  is  a  thick  tube  about 
the  thickness  of  a  straw  in  the  clear  in  the  parts  ca  and  the  bent 
part  b.  The  whole  tube  having  been  filled  with  mercury,  it  was 
sealed  at  #,  and  then  a  small  quantity  was  driven  out  at  b  and  some 
of  the  substance  introduced  ;  the  end  b  was  then  sealed  and  a 
opened,  and  the  whole  tube  gently  warmed  so  as  to  expel  some 
mercury,  upon  which  a  was  again  hermetically  sealed. 

When  the  tube  was  placed  in  a  bath  of  warm  water  a  little  above 
the  melting  point  of  the  body,  the  mercury  expanded  and  a  pres- 
sure resulted  which  could  be  accurately  measured  from  the  diminu- 
tion in  volume  of  the  air  in  ca,  which  was  carefully  calibrated  for 
this  purpose.  By  carefully  raising  or  lowering  the  instrument  in 
the  water,  the  pressure  could  be  increased  or  diminished  at  will, 
then  remained  to  observe  the  temperature  at  which  the  substance  solidi- 
fied and  the  corresponding  pressure  at  that  moment.  In  this  way  Bunsen 
found  that  spermaceti,  which  melts  at  48°  under  a  pressure  of  I  atmosphere, 
melts  at  51°  under  a  pressure  of  156  atmospheres.  Hopkins  found  that 


Fig.  289. 

It  only 


286  On  Heat.  [339^- 

spermaceti  melted  at  60°  under  a  pressure  of  519  atmospheres,  and  at  80° 
under  792  atmospheres  ;  the  melting  point  of  sulphur  under  these  pressures 
was  respectively  13  5°  and  141°. 

But  in  the  case  of  those  bodies  which  contract  on  passing  from  the  solid 
to  the  liquid  state,  and  of  which  water  is  the  best  example,  the  reverse  is 
the  case.  Melting  ice  has  no  external  work  to  perform,  since  it  has  no 
external  pressure  to  raise  ;  on  the  contrary,  in  melting,  it  assimilates  ex- 
ternal work,  which,  transformed  into  heat,  renders  a  smaller  quantity  of  heat 
necessary  ;  the  external  work  acts  in  the  same  direction  as  the  internal  heat 
— namely,  in  breaking  up  the  crystalline  aggregates.  Yet  these  differences 
of  temperature  must  be  but  small,  for  the  molecular  forces  in  solids  prepon- 
derate far  over  the  external  pressure  ;  the  internal  work  is  far  greater  than 
the  external. 

Sir  W.  Thomson  found  that  pressures  of  8*1  and  16*8  atmospheres 
lowered  the  melting  point  of  ice  by  0*059°  ano^  O'I26°  respectively.  These 
results  justify  the  theoretical  previsions  of  Prof.  J.  Thomson,  according  to 
which  an  increase  of  pressure  of  n  atmospheres  lowers  the  melting  point  of 
ice  by  o-oo74;z°  C. 

340.  Alloys.     Fluxes. — Alloys  are  generally  more  fusible  than  any  of 
the  metals  of  which  they  are  composed  ;  for  instance,  an  alloy  of  five  parts 
of  tin  and  one  of  lead  fuses  at   194°.     The  alloy  known  as  Rose's  fusible 
mental,  which  consists  of  4  parts  of  bismuth,  i  part  of  lead,  and  i  of  tin,  melts 
at  94°,  and  an  alloy  of  i  or  2  parts  of  cadmium  with  2  parts  of  tin,  4  parts  of 
lead,  and  7  or  8  parts  of  bismuth,  known  as    Wood's  fusible  metal,  melts 
between  66°  and  71°  C.     Fusible  alloys  are  of  extended  use  in  soldering  and 
in  taking  casts.     Steel  melts  at  a  lower  temperature  than  iron,  though  it 
contains  carbon,  which  is  almost  completely  infusible. 

Mixtures  of  the  fatty  acids  melt  at  lower  temperatures  than  the  pure  acids. 
A  mixture  of  the  chlorides  of  potassium  and  of  sodium  fuses  at  a  lower  tem- 
perature than  either  of  its  constituents  ;  the  same  is  the  case  with  a  mixture 
of  the  carbonates  of  potassium  and  sodium,  especially  when  they  are  mixed 
in  the  proportion  of  their  chemical  equivalents. 

An  application  of  this  property  is  met  with  in  the  case  of  fluxes,  which 
are  much  used  in  metallurgical  operations.  They  consist  of  substances 
which,  when  added  to  an  ore,  partly  by  their  chemical  action,  help  the  reduc- 
tion of  the  substance  to  the  metallic  state,  and,  partly,  by  presenting  a 
readily  fusible  medium,  promote  the  formation  of  a  regulus. 

341.  Latent  beat. — Since,  during  the  passage  of  a  body  from  the  solid 
to  the  liquid  state,  the  temperature  remains  constant  until  the  fusion  is  com- 
plete, whatever  be  the  intensity  of  the  source  of  heat,  it  must  be  concluded 
that,  in  changing  their  condition,  bodies  absorb   a  considerable  amount  of 
heat,  the  only  effect  of  which  is  to  maintain  them  in  the  liquid  state.     This 
heat,  which  is  not  indicated  by  the  thermometer,  is  called  latent  heat  or 
latent  heat  of  fusion,  an  expression  which,  though  not  in  strict  accordance 
with  modern  ideas,  is  convenient  from  the  fact  of  its  universal  recognition 
and  employment  (461). 

An  idea  of  what  is  meant  by  latent  heat  may  be  obtained  from  the  fol- 
lowing experiment  : — If  a  pound  of  water  at  80°  is  mixed  with  a  pound  of 
water  at  zero,  the  temperature  of  the  mixture  is  40°.  But  if  a  pound  of 


-345]  Solidification  and- Crystallisation.  287 

pounded  ice  at  zero  is  mixed  with  a  pound  of  water  at  80°,  the  ice  melts  and 
two  pounds  of  water  at  zero  are  obtained.  Consequently,  the  mere  change  of 
a  pound  of  ice  to  a  pound  of  water  at  the  same  temperature  requires  as 
much  heat  as  will  raise  a  pound  of  water  through  80°.  This  quantity  of  heat 
represents  the  latent  heat  of  the  fusion  of  ice,  or  the  latent  heat  of  water. 

Every  liquid  has  its  own  latent  heat,  and  in  the  chapter  on  Calorimetry 
\ve  shall  show  how  this  is  determined. 

342.  Solution. — A  body  is  said  to  dissolve  when  it  becomes  liquid  in  con- 
sequence of  an  affinity  between  its  molecules  and  those  of  a  liquid.     Gum 
arabic,  sugar,  and  most  salts  dissolve  in  water. 

During  solution,  as  well  as  during  fusion,  a  certain  quantity  of  heat  always 
becomes  latent,  and  hence  it  is  that  the  solution  01  a  substance  usually  pro- 
duces a  diminution  of  temperature.  In  certain  cases,  however,  instead  of 
the  temperature  being  lowered,  it  actually  rises,  as  when  caustic  potash  is 
dissolved  in  water.  This  depends  upon  the  fact  that  two  simultaneous  and 
contrary  phenomena  are  produced.  The  first  is  the  passage  from  the 
solid  to  the  liquid  condition,  which  always  lowers  the  temperature.  The 
second  is  the  chemical  combination  of  the  body  dissolved  with  the  liquid, 
and  which,  as  in  the  case  of  all  chemical  combinations,  produces  an  increase 
of  temperature.  Consequently,  as  the  one  or  the  other  of  these  effects  pre- 
dominates, or  as  they  are  equal,  the  temperature  either  rises  or  sinks,  or 
remains  constant. 

343.  Solidification. — Solidification   or   congelation  is  the  passage  of  a 
body  from  the  liquid  to  the  solid  state.     This  phenomenon  is  regulated  by 
the  two  following  laws  : — 

I.  Every  body,  under  the  same  pressure,  solidifies  at  a  fixed  temperature, 
•which  is  the  same  as  that  of  fusion. 

II.  From  t/u  commencement  to  the  end  of  the  solidification,  the  tempera- 
ture of  a  liquid  remains  constant. 

Certain  bodies,  more  especially  some  of  the  fats,  present  an  exception  to 
the  first  law,  in  so  far  that  by  repeated  fusions  they  seem  to  undergo  a 
molecular  change  which  alters  their  melting  point. 

The  second  law  is  the  consequence  of  the  fact  that  the  latent  heat  ab- 
sorbed during  fusion  becomes  free  at  the  moment  of  solidification. 

Many  liquids,  such  as  alcohol,  ether,  and  bisulphide  of  carbon,  do  not 
solidify  even  at  the  lowest  known  temperature.  Despretz,  by  the  cold  pro- 
duced by  a  mixture  of  liquid  protoxide  of  nitrogen,  solid  carbonic  acid,  and 
ether,  reduced  alcohol  to  such  a  consistence  that  the  vessel  containing  it 
could  be  inverted  without  losing  the  liquid. 

344.  Crystallisation. — Generally  speaking,  bodies    which    pass   slowly 
from  the  liquid  to  the  solid  state  assume  regular  geometrical  forms,  such  as 
the  cube,  prisms,  rhombohedra,  &c.  ;  these  are  called  crystals.     If  the  crys- 
tals are   formed   from  a  body  in   fusion,  such  as  sulphur  or  bismuth,  the 

•  crystallisation  is  said  to  take  place  by  the  dry  way.  But  if  the  crystallisa- 
tion takes  place  owing  to  the  slow  evaporation  of  a  solution  of  a  salt,  it  is 
said  to  be  by  the  moist  'way.  Snow,  ice,  and  many  salts  present  examples 
of  crystallisation. 

345.  Retardation  of  the  point  of  solidification. — The  freezing  point  of 
pure  water  can  be  diminished  by  several  degrees,  if  the  water  be  previously 


288  On  Heat.  [345- 

freed  from  air  by  boiling  and  be  then  kept  in  a  perfectly  still  place.  In  fact, 
it  may  be  cooled  to  -15°  C,  and  even  lower,  without  freezing.  But  when 
it  is  slightly  agitated,  the  liquid  at  once  solidifies.  This  may  be  conveniently 
shown  by  means  of  the  apparatus  represented  in  fig.  290,  which  consists  of 
a  delicate  thermometer  round  the  bulb  of  which  is  a  wider  one  con- 
taining some  water.  Before  melting  at  a  the  whole  outside  bulb 
was  filled  with  water,  which  was  then  boiled  out  and  sealed  so  that 
over  the  water  the  space  is  quite  empty. 

The  vessel  is  placed  in  snow  at  o°  and  then  in  alcohol  cooled 
to  -6°  or  —8°.    The  thermometer  sinks  a  few  degrees,  but  at  once 
rises  to  zero  when  the  water  in  the  bulb  solidifies.     The  smaller  the 
j>°     quantity  of  liquid  the  lower  the  temperature  to  which  it  can  be 
cooled,  and   the  greater  the  mechanical   disturbance  it  supports 
without  freezing.     Fournet  has  observed  the  frequent  occurrence  of 
20     mists  formed  of  particles  of  liquid  matter  suspended  in  an  atmo- 
sphere whose  temperature  was  io°or  even  15°  below  zero. 

A  very  rapid  agitation  also  prevents  the  formation  of  ice.  The 
same  is  the  case  with  all  actions  which,  hindering  the  molecules  in 
their  movements,  do  not  permit  them  to  arrange  themselves  in  the 
conditions  necessary  for  the  solid  state.  Despretz  was  able  to 
lower  the  temperature  of  water  contained  in  fine  capillary  tubes 
to  -  20°  without  their  solidifying.  This  experiment  shows  how  it  is 
that  plants  in  many  cases  do  not  become  frozen,  even  during  severe 
cold,  as  the  sap  is  contained  in  very  fine  capillary  vessels.  Finally, 
Mousson  found  that  a  powerful  pressure  not  only  retards  the 
freezing  of  water,  but  prevents  its  complete  solidification.  In  this 
case  the  pressure  opposes  the  tendency  of  the  water  to  expand 
on  freezing,  and  thus  virtually  lowers  the  point  of  solidification. 

If  water  contains  salts,  or   other   foreign   bodies,  its    freezing 
point  is  lowered.     Sea  water  freezes  at  -2-5°  to  —  3°  C.  ;  the  ice 
which  forms  is  quite  pure,  and  a  saturated  solution  remains.     In 
Finland,   advantage  is  taken  of  this  property  to  concentrate  sea 
Fig.  290.     water   for  the  purpose  of  extracting  salt  from  it.     If  water  con- 
tains alcohol,  precisely  analogous  phenomena  are  observed  ;  the  ice  formed 
is  pure,  and  practically  all  the  alcohol  is  contained  in  the  residue. 

Dufour  has  observed  some  very  curious  cases  of  liquids  cooled  out  of 
contact  with  solid  bodies.  His  mode  of  experimenting  was  to  place  the 
liquid  in  another  of  the  same  specific  gravity  but  of  lower  melting  point, 
and  in  which  it  is  insoluble.  Drops  of  water,  for  instance,  suspended  in  a 
mixture  of  chloroform  and  oil,  usually  solidified  between  —4°  and  -12°, 
while  still  smaller  globules  cooled  down  to  —  1 8°  or  —  20°.  Contact  with 
a  fragment  of  ice  immediately  set  up  congelation.  Globules  of  sulphur 
(which  solidifies  at  115°)  remained  liquid  at  40°  ;  and  globules  of  phosphorus 
(solidifying  point  42°)  at  20°. 

When  a  liquid  solidifies  after  being  cooled  below  its  normal   freezing 
point,  the  solidification  takes  place  very  rapidly,  and  is  accompanied  byaj 
disengagement  of  heat,  which  is  sufficient  to  raise  its  temperature  from  the 
point  at  which  solidification  begins  up  to  its  ordinary  freezing  point.     This 
is  well  seen  in  the  case  of  hyposulphite  of  sodium,  which  melts  in  its  own 


-346]    Change  of  Volume  on  'Solidification  and  Liquefaction.    289 

water  of  crystallisation  at  45°,  and  when  carefully  cooled  will  remain  liquid 
at  the  ordinary  temperature  of  the  atmosphere.  If  it  then  be  made  to 
solidify  by  agitation,  or  by  adding  a  small  fragment  of  the  solid  salt,  the  rise 
of  temperature  is  distinctly  felt  by  the  hand.  In  this  case  the  heat  which 
had  become  latent  in  the  process  of  liquefaction,  again  becomes  free,  and  a 
portion  of  the  substance  remains  melted  ;  for  it  is  kept  liquid  by  the  heat  of 
solidification  of  that  which  has  solidified. 

346.  Change  of  volume  on  solidification  and  liquefaction. — The  rate 
of  expansion  of  bodies  generally  increases  as  they  approach  their  melting 
points,  and  is  in  most  cases  followed  by  a  further  expansion  at  the  moment 
of  liquefaction,  so  that  the  liquid  occupies  a  greater  volume  than  the  solid 
from  which  it  is  formed.  The  apparatus  represented  in  fig.  291  is  well 
adapted  for  exhibiting  this  phenomenon.  It  consists  of  a  glass 
tube  ab  containing  water  or  some  other  suitable  liquid,  to  which  is 
carefully  fitted  a  cork  with  a  graduated  glass  tube  c.  This  forms,  in 
fact,  a  thermometer,  and  the  values  of  the  degrees  on  the  tube  c 
are  determined  in  terms  of  the  capacity  of  the  whole  apparatus.  A 
known  volume  of  the  substance  is  placed  in  the  tube  aa  and  the 
cork  inserted  ;  the  apparatus  is  then  placed  in  a  space  at  a  known 
temperature  very  little  below  the  melting  point  of  the  body  in 
question,  until  it  has  acquired  its  temperature,  and  the  position  of 
the  liquid  in  c  is  noted.  The  temperature  is  then  allowed  to  rise 
slowly,  and  the  position  noted  when  the  melting  is  complete. 
Knowing  then  the  difference  in  the  two  readings  and  the  volume  of 
the  substance  under  experiment,  and  making  a  correction  for  the 
expansion  of  the  liquid  and  of  the  glass,  it  is  easy  to  deduce  the 
increase  due  to  the  melting  alone.  Phosphorus,  for  instance, 
increases  about  3-4  per  cent,  on  liquefaction  ;  that  is,  100  volumes 
of  solid  phosphorus  at  44°  (the  melting  point)  become  103-4  a*  the 
same  temperature  when  melted.  Sulphur  expands  about  5  per 
cent,  on  liquefying,  and  stearic  acid  about  1 1  per  cent. 

Water  presents  a   remarkable   exception  ;    it   expands  at   the 
moment  of  solidifying,  or  contracts  on  melting,  by  about  10  per 
cent.     One  volume  of  ice  at  o°  gives  0-9178  of  water  at  o°,  or  I 
volume  of  water  at  o°  gives  1-102  of  ice  at  the  same  temperature.    Fi 
In  consequence  of  this  expansion,  ice  floats  on  the  surface  of  water. 
According  to  Dufour,  the  specific  gravity  of  ice  is  0-9178  ;  Bunsen  found  for 
ice  which  had  been   freed   from  water  by  boiling  the  somewhat  smaller 
number  0-91674. 

The  increase  of  volume  in  the  formation  of  ice  is  accompanied  by  an 
expansive  force  which  sometimes  produces  powerful  mechanical  effects,  of 
which  the  bursting  of  water-pipes  and  the  breaking  of  jugs  containing  water 
are  familiar  examples.  The  splitting  of  stones,  rocks,  and  the  swelling  up 
of  moist  ground  during  frost,  are  caused  by  the  fact  that  water  penetrates 
into  the  pores  and  there  becomes  frozen  ;  in  short,  the  great  expansion  of 
water  on  freezing  is  the  most  active  and  powerful  agent  of  disintegration  on 
the  earth's  surface. 

The  expansive  force  of  ice  was  strikingly  shown  by  some  experiments  of 
Major  Williams,  in  Canada.  Having  quite  filled  a  1 3-inch  iron  bomb-shell 

O 


290  On  Heat.  [346- 

with  water,  he  firmly  closed  the  touch-hole  with  an  iron  plug  weighing  three 
pounds,  and  exposed  it  in  this  state  to  the  frost.  After  some  time  the  iron 
plug  was  forced  out  with  a  loud  explosion,  and  thrown  to  a  distance  of  415 
feet,  and  a  cylinder  of  ice  8  inches  long  issued  from  the  opening.  In 
another  case  the  shell  burst  before  the  plug  was  driven  out,  and  in  this  case 
a  sheet  of  ice  spread  out  all  round  the  crack.  It  is  possible  that  under  the 
great  pressure  some  of  the  water  still  remained  liquid  up  to  the  time  at 
which  the  resistance  was  overcome  ;  that  it  then  issued  from  the  shell  in  a 
liquid  state,  but  at  a  temperature  below  o°,  and  therefore  instantly  began 
to  solidify  when  the  pressure  was  removed,  and  thus  retained  the  shape  of 
the  orifice  whence  it  issued. 

Cast-iron,  bismuth,  and  antimony  expand  on  solidifying  like  water,  and 
can  thus  be  used  for  casting  ;  but  gold,  silver,  and  copper  contract,  and 
hence  coins  of  these  metals  cannot  be  cast,  but  must  be  stamped  with  a 
die. 

347.  Freezing*  mixtures.  —  The  absorption  of  heat  in  the  passage  of 
bodies  from  the  solid  to  the  liquid  state  has  been  used  to  produce  artificial 
cold.  This  is  effected  by  mixing  together  bodies  which  have  an  affinity  for 
each  other,  and  of  which  one  at  least  is  solid,  such  as  water  and  a  salt,  ice 
and  a  salt,  or  an  acid  and  a  salt.  Chemical  affinity  accelerates  the  fusion  : 
the  portion  which  melts  robs  the  rest  of  the  mixture  of  a  large  quantity  of 
sensible  heat,  which  thus  becomes  latent.  In  many  cases  a  very  consider- 
able diminution  of  temperature  is  produced. 

The  following  table  gives  the  names  of  the  substances  mixed,  their  pro- 
portions, and  the  corresponding  diminutions  of  temperature  :  — 

Parts  Reduction  of 

Substances  by  weight  temperature 

Sulphate  of  sodium        .        .        .       8)  +io°t    —  17° 

Hydrochloric  acid          .        .  5  [ 

Pounded  ice  or  snow  2  )  T  0  .          00 

„  .  .     .     .      +  10  to  —  io 

Common  salt  .         .         .       I  ) 


Sulphate  of  sodium        ...       3)  +io°to-i90 

Dilute  nitric  acid  .         .         .  2  ) 

6\ 

5  1 
4) 


Sulphate  of  sodium  .  .  6 

Nitrate  of  ammonium  .  .  5  ...      +io°to—  26 

Dilute  nitric  acid  .  .  . 

Phosphate  of  sodium  .  .  .       9  )  +  10°  to  -  20° 

Dilute  nitric  acid  .  .  .  4  ) 

If  the  substances  taken  be  themselves  first  previously  cooled  down,  a  still 
more  considerable  diminution  of  temperature  is  occasioned. 

Freezing  mixtures  are  frequently  used  in  chemistry,  in  physics,  and  in 
domestic  economy.  One  form  of  the  portable  ice-making  machines  which 
have  come  into  use  during  the  last  few  years  consists  of  a  cylindrical 
metallic  vessel  divided  into  four  concentric  compartments.  In  the  central 
one  is  placed  the  water  to  be  frozen  ;  in  the  next  there  is  the  freezing 
mixture,  which  usually  consists  of  sulphate  of  sodium  and  hydrochloric  acid  ; 
6  pounds  of  the  former  and  5  of  the  latter  will  make  5  to  6  pounds  of  ice  in 
an  hour.  The  third  compartment  also  contains  water,  and  the  outside  one 


-349]  Outline's  Researches.  291 

contains  some  badly-conducting  substance,  such  as  cotton,  to  cut  off  the 
influence  of  the  external  temperature.  The  best  effect  is  obtained  when 
pretty  large  quantities  (2  or  3  pounds)  of  the  mixture  are  used,  and  when 
they  are  intimately  mixed.  It  is  also  advantageous  to  use  the  machines  for 
a  series  of  successive  operations. 

348.  Guthrie's  researches. — It  appears   from  recent   experiments   of 
Guthrie,  that  what  are  called   freezing  mixtures  may  be  divided  into  two 
classes,  namely  those  in  which  one  of  the  constituents  is  liquid  and  those  in 
which  both  are  solid.    The  temperature  indicated  by  the  thermometer  placed 
in  a  freezing  mixture  is,  of  course,  due  to  the  loss  of  heat  by  the  thermometer 
to  the  liquefying  freezing  mixture,  and  is  measured  by  the  rate  of  such  loss. 
The  quantity  of  heat  absorbed  by  the  freezing  mixture  is  obviously  the  heat 
required  to  melt  the  constituents,  together  with  ( + )  the  heat  of  combination 
of  the  constituents.     When  one  constituent  is  liquid,  as  when  hydrochloric 
acid  is  added  to  ice,  then  a  lower  temperature  is  got  by  previously  cooling  the 
hydrochloric  acid.     There  is  no  advantage  in  cooling  the  ice.     But  when 
both  constituents  are  solid,  as  in  the  case  of  the  ice  salt  freezing  mixture, 
there  is  no  advantage  to  be  gained  by  cooling  one  or  both  constituents. 
Within  very  wide  limits  it  is  also  in  the  latter  case  a  matter  of  indifference 
as  to  the  ratio  between  the  constituents.     Nor  does  it  matter  whether  the 
ice  be  finely  powdered  as  snow  or  in  pieces  as  large  as  a  pea. 

The  different  powers  of  various  salts  when  used  in  conjunction  with 
ice  as  freezing  mixtures,  appear  to  have  remained  unexplained  until  Guthrie 
showed  that,  with  each  salt,  there  is  always  a  minimum  temperature  below 
which  it  is  impossible  for  an  aqueous  solution  of  any  strength  of  that  salt  to 
exist  in  the  liquid  form  ;  that  there  is.  a  certain  strength  of  solution  for  each 
salt  which  resists  solidification  the  longest ;  that  is,  to  the  lowest  temperature. 
Weaker  solutions  give  up  ice  on  being  cooled,  stronger  solutions  give  up 
the  salt  either  in  the  anhydrous  state  or  in  combination  with  water.  That 
particular  strength  of  a  particular  salt,  which  resists  solidification  to  the 
lowest  temperature,  is  called  by  Guthrie  a  cryohydrate.  It  is  of  such  a 
strength  that  when  cooled  below  o°  C.  it  solidifies  as  a  whole  ;  that  is,  the  ice 
and  the  salt  solidify  together  and  form  crystals  of  constant  composition  and 
constant  melting  and  the  same  solidifying  temperatures.  The  liquid  portion 
of  a  freezing  mixture,  as  long  as  the  temperature  is  at  its  lowest,  is,  indeed, 
a  melted  cryohydrate.  The  slightest  depression  of  temperature  below  this 
causes  solidification  of  the  cryohydrate,  and  hence  the  temperature  can  never 
sink  below  the  solidifying  temperature  of  the  cryohydrate. 

Guthrie  has  also  shown  that  colloid  bodies,  such  as  gum  and  gelatine, 
neither  raise  the  boiling  point  of  water,  nor  depress  the  solidifying  point,  nor 
can  they  act  as  elements  in  freezing  mixtures. 

VAPOURS.      MEASUREMENT   OF  THEIR  TENSION. 

349.  Vapours. — We  have  already  seen  (146)  that  vapours  are  the  aeri- 
form fluids  into  which  volatile  substances,  such  as  ether,  alcohol,  water,  and 
mercury,  are  changed  by  the  absorption  of  heat.      Volatile  liquids  are  those 
which  thus  possess  the  property  of  passing  into  the  aeriform  state,  and  fixed 
liquids  those  which  do  not  form  vapours  at  any  temperature  without  under- 

o  2 


292 


On  Heat. 


[349^ 


going  chemical  decomposition,  such  as  the  fatty  oils.  There  are  some 
solids,  such  as  ice,  arsenic,  camphor,  and  in  general  all  odoriferous  solid 

substances,  which  can  directly  form  vapours  without 

first  becoming  liquid. 

Vapours  are  transparent  like  gases,  and  generally 

colourless  ;  there  are  only  a  few  coloured  liquids  which 

also  give  coloured  vapours. 

350.  Vaporisation. — The  passage  of  a  liquid  into 
the  gaseous  state  is  designated  by  the  general  term 
vaporisation ;   the   term   evaporation    especially  refers 
to  the  slow  production  of  vapour  at  the  free  surface  of 
a  liquid,  and  boiling  to   its   rapid    production  in  the 
mass  of  the  liquid  itself.     We  shall  presently  see  (356) 
that  at  the  ordinary  atmospheric  pressure,  ebullition, 
like  fusion,  takes  place  at  a  definite  temperature.     This 
is  not  the  case  with  evaporation,  which  takes  place  even 
with  the  same  liquid  at  very  different  temperatures, 
although  the  formation  of  a   vapour  seems   to   cease 
below  a  certain  point.     Mercury,  for  example,  gives  no 
vapour  below  —  10°,  nor  sulphuric  acid  below  30°. 

351.  Elastic  force   of  vapours. — Like    gases,  va- 
pours have   a   certain  elastic  force,  in  virtue  of  which 
they  exert  pressures  on  the  sides  of  vessels  in  which 
they  are  contained.     The  elastic  force  of  vapours  may 
be   demonstrated  by  the    following  experiment  :  —  A 
quantity  of  mercury  is  placed  in  a  bent  glass  tube  (fig. 

292),  the  shorter  leg  of  which  is  closed ;  a  few  drops  of  ether  are  then 
passed  into  the  closed  leg  and  the  tube  immersed  in  a  water  bath  at  a 
temperature  of  about  45°.  The  mercury  then  sinks  slowly  in  the  short 
branch,  and  the  space  ab  is  filled  with  a  gas  which  has  all  the  appearance 
of  air,  and  whose  elastic  force  counterbalances  the  pressure  of  the  column 
of  mercury  cd,  and  the  atmospheric  pressure  on  d.  This  gas  is  the  vapour 
of  ether.  If  the  water  be  cooled,  or  if  the  tube  be  removed  from  the  bath, 
the  vapour  which  fills  the  space  ab  disappears,  and  the  drop  of  ether  is 
reproduced.  If,  on  the  contrary,  the  bath  be  heated  still  higher,  the  level  of 
the  mercury  descends  below  £,  indicating  an  increase  in  the  elastic  force  of 
the  vapour, 

352.  Formation  of  vapours  in  a  vacuum. — In  the  previous  experiment 
the  liquid  changed  very  slowly  into  the  vaporous  condition ;  the  same  is  the 
case  when  a  liquid  is  freely  exposed  to  the  air.  In  both  cases  the  atmo- 
sphere is  an  obstacle  to  the  vaporisation.  In  a  vacuum  there  is  no  resist- 
ance, and  the  formation  of  vapours  is  instantaneous,  as  is  seen  in  the 
following  experiment : — Four  barometer  tubes,  filled  with  mercury,  are 
immersed  in  the  same  trough,  fig.  293.  One  of  them,  A,  serves  as  a  baro- 
meter, and  a  few  drops  of  water,  alcohol,  and  ether  are  respectively  intro- 
duced into  the  tubes,  B,  C,  D.  When  the  liquids  reach  the  vacuum,  a 
depression  of  the  mercury  is  at  once  produced.  And  as  this  depression 
cannot  be  produced  by  the  weight  of  the  liquid,  which  is  an  infinitely  small 
fraction  of  the  weight  of  the  displaced  mercury,  it  must  be  due  to  the 


Fig.  292. 


-353] 


Saturated  Vapours. 


293 


ABE  C  D 


formation  of  some  vapour  whose  elastic  force  has  depressed  the  mercurial 
column. 

The  experiment  also  shows  that  the  depression  is  not  the  same  in  all  the 
tubes  ;  it  is  greater  in  the  case  of  alcohol  than  of  water,  and  greater  with 
ether  than  with  alcohol.  We  consequently  obtain  the  two  following  laws  for 
the  formation  of  vapours  : — 

I.  In  a  vacuum  all  volatile  liquids  are  instantaneously  converted  into 
vapour. 

II.  A t  the  same  temperature  the  vapours  of  different  liquids  have  differ- 
ent elastic  forces. 

For  example,  at  20°  the  tension  of  ether  vapour  is  25  times  as  great  as 
that  of  aqueous  vapour. 

353.  Saturated  vapours.  Maximum  of  tension. — When  a  very  small 
quantity  of  a  volatile  liquid,  such  as '  ether,  is  introduced  into  a  barometer 
tube,  it  is  at  once  completely  vaporised,  and  the  mercurial  column  is  not 
depressed  to  its  full  extent ;  for  if  some  more  ether  be  introduced  the 
depression  increases.  By  continuing  the  addition  of  ether,  it  finally  ceases 
to  vaporise,  and  remains  in  the  liquid  state.  There  is,  therefore,  for  a 
certain  temperature,  a  limit  to  the  quantity  of  vapour  which  can  be  formed 
in  a  given  space.  This  space  is  accordingly  said  to  be  saturated.  Further, 
when  the  vaporisation  of  the  ether  ceases, 
the  depression  of  the  mercurial  column 
stops.  And  hence  there  is  a  limit  to  the 
tension  of  the  vapour,  a  limit  which,  as  we 
shall  presently  see  (354),  varies  with  the  tem- 
perature, but  which  for  a  given  temperature 
is  independent  of  the  pressure. 

To  show  that,  in  a  closed  space,  saturated 
with  vapour  and  containing  liquid  in  excess, 
the  temperature  remaining  constant,  there 
is  a  maximum  of  tension  which  the  vapour 
cannot  exceed,  a  barometric  tube  is  used 
which  dips  in  a  deep  bath  (fig.  293).  This 
tube  is  filled  with  mercury,  and  then  so 
much  ether  is  added  as  to  be  in  excess  after 
the  Torricellian  vacuum  is  saturated.  The 
height  of  the  mercurial  column  is  next  noted 
by  means  of  the  scale  graduated  on  the  tube 
itself.  Now,  whether  the  tube  be  depressed, 
which  tends  to  compress  the  vapour,  or 
whether  it  be  raised,  which  tends  to  expand 
it,  the  height  of  the  mercurial  column  is 
constant.  The  tension  of  the  vapour  remains 
constant  in  the  two  cases,  for  the  depression 
neither  increases  nor  diminishes  it.  Hence 
it  is  concluded  that  when  the  saturated 
vapour  is  compressed,  a  portion  returns  to 

the  liquid  state  ;  that  when,  on  the  other  hand,  the  pressure  is  diminished,  a 
portion  of  the  excess  of  liquid  vaporises,  and  the  space  occupied  by  the 


294 


On  Heat. 


[353- 


vapour  is  again  saturated  ;  but  in  both  cases  the  tension  and  the  density  of 
the  vapour  remain  constant. 

354.  iron-saturated  vapours. — From  what  has  been  said,  vapours  pre- 
sent two  very  different  states,  according  as  they  are  saturated  or  not.  In 
the  first  case,  where  they  are  saturated  and  in  contact  with  the  liquid,  they 
differ  completely  from  gases,  since  for  a  given  temperature  they  can  neither 
be  compressed  nor  expanded ;  their  elastic  force  and  their  density  remain 
constant. 

In  the  second  case,  on  the  contrary,  where  they  are  not  saturated,  they 
exactly  resemble  gases.  For  if  the  experiments  (fig.  294)  be  repeated,  only  a 
small  quantity  of  ether  being  introduced,  so  that  the  vapour  is  not  saturated, 
and  if  the  tube  be  then  slightly  raised,  the  level  of  the  mercury  is  seen  to 
rise,  which  shows  that  the  elastic  force  of  the  vapour  has  diminished. 
Similarly,  by  immersing  the  tube  still  more,  the  level  of  the  mercury  sinks. 
The  vapour  consequently  behaves  just  as  a  gas  would  do,  its  tension  dimin- 
ishes when  the  volume  increases,  and  vice  versa  ;  and  as  in  both  cases  the 

volume  of  the  vapour  is 
inversely  as  the  pressure, 
it  is  concluded  that  non- 
saturated  vapours  obey 
Boyle's  law. 

When  a  non-saturated 
vapour  is  heated,  its  vol- 
ume increases  like  that  of 
a  gas  ;  and  the  number 
0-00366,  which  is  the  co- 
efficient of  the  expansion 
of  air,  may  be  taken  for 
that  of  vapours. 

Hence  we  see  that  the 
physical  properties  of  un- 
saturated  vapours  are 
comparable  with  those  of 
permanent  gases,  and  that 
the  formulas  for  the  com- 
pressibility and  expan- 
sibility of  gases  (176  and 
332)  also  apply  to  unsatu- 
rated  vapours.  But  it 
must  not  be  forgotten  that 
there  is  always  a  limit  of 
pressure  or  of  cooling  at 
which  unsaturated  vapours 
pass  into  a  state  of  satura- 
tion, and  that  they  have 
then  a  maximum  of  ten- 
sion an<}  density  which 


Fig.  294. 


Fig.  295. 


can  only  be  exceeded  when  the  temperature  rises  while  they  are  in  contact 
with  the  liquid. 


356]  Tension  of  Aqueous  Vapour.  295 

355.  Tension  of  aqueous  vapour  below  zero.  —  In  order  to  measure  the 
elastic  force  of  aqueous  vapour  below  zero,  Gay-Lussac  used  two  barometer 
tubes  filled  with  mercury,  and  placed  in  the  same  bath  (fig.  295).  The 
straight  tube  A  serves  as  a  barometer  ;  the  other,  B,  is  bent,  so  that  part  of 
the  Torricellian  vacuum  can  be  surrounded  by  a  freezing  mixture  (347). 
When  a  little  water  is  admitted  into  the  bent  tube,  the  level  of  the  mercury 
sinks  below  that  in  the  tube  A  to  an  extent  which  varies  with  the  tempera- 
ture of  the  freezing  mixture. 

At      o°  the  depression  is      ...     4-54  millimetres. 


»    -3°        »        »        •        •        •        • 

5J         ~~  5  J)  V  •  •  *  *         3*1  *  5) 

„     -7°        „„....     2-67 
„  -10°        „„....    2-08 

„    -20°  „„....      0-84 

„    -30°      '    ,l  »      .....      0'36 

These  depressions,  which  must  be  due  to  the  tension  of  aqueous  vapour 
in  the  space  BC,  show  that  even  at  very  low  temperatures  there  is  always 
some  aqueous  vapour  in  the  atmosphere. 

Although  in  the  above  experiment  the  part  B  and  the  part  C  are  not 
both  immersed  in  the  freezing  mixture,  we  shall  presently  see  that  when 
two  communicating  vessels  are  at  different  temperatures,  the  tension  of  the 
vapour  is  the  same  in  both,  and  always  corresponds  to  that  of  the  lowest 
temperature. 

That  water  evaporates  even  below  zero  follows  from  the  fact  that  wet 
linen  exposed  to  the  air  during  frost  becomes  first  stiff  and  then  dry,  showing 
that  the  particles  of  water  evaporate  even  after  the  latter  has  been  converted 
into  ice. 

356.  Tension  of  aqueous  vapour  between  zero  and  one  hundred 
degrees.  —  i.  Daltoris  method.  Dalton  measured  the  elastic  force  of  aqueous 
vapour  between  o  and  100°  by  means  of  the  apparatus  represented  in  fig. 
296.  Two  barometer  tubes,  A  and  B,  are  filled  with  mercury,  and  inverted 
in  an  iron  bath  full  of  mercury,  and  placed  on  a  furnace.  The  tube  A  con- 
tains a  small  quantity  of  water.  The  tubes  are  supported  in  a  cylindrical 
vessel  full  of  water,  the  temperature  of  which  is  indicated  by  the  thermometer. 
The  bath  being  gradually  heated,  the  water  in  the  cylinder  becomes  heated 
too  ;  the  water  which  is  in  the  tube  A  vaporises,  and  in  proportion  as  the 
tension  of  its  vapour  increases,  the  mercury  sinks.  The  depressions  of  the 
mercury  corresponding  to  each  degree  of  the  thermometer  are  indicated  on 
the  scale  E,  and  in  this  manner  a  table  of  the  elastic  forces  between  zero  and 
100°  has  been  constructed. 

ii.  Regnaulfs  method.  —  Dalton's  method  is  wanting  in  precision,  for  the 
liquid  in  the  cylinder  has  not  everywhere  the  same  temperature,  and  con- 
sequently the  exact  temperature  of  the  aqueous  vapour  is  not  indicated. 
Regnault's  apparatus  is  a  modification  of  that  of  Dalton.  The  cylindrical 
vessel  is  replaced  by  a  large  cylindrical  zinc  drum,  MN  (fig.  297),  in  the  bottom 
of  which  are  two  tubulures.  The  tubes  A  and  B  pass  through  these  tubu- 
lures,  and  are  fixed  by  caoutchouc  collars.  The  tube  containing  vapour,  B, 


296 


On  Heat. 


[356- 


is  connected  with  a  flask,  a,  by  means  of  a  brass  three-way  tube,  O.  The 
third  limb  of  this  tube  is  connected  with  a  drying  tube,  D,  containing 
pumice  impregnated  with  sulphuric  acid,  which  is  connected  with  the  air- 
pump. 

When  the  flask  a  contains  some  water,  a  small  portion  is  distilled  into  B 
by  gently  heating  the  flask.  Exhausting,  then,  by  means  of  the  air-pump, 
the  water  distils  continuously  from  the  flask  and  from  the  barometric  tube 
towards  D,  which  condenses  the  vapours.  After  having  vaporised  some 


Fig.  296. 


Fig.  297. 


quantity  of  water,  and  when  it  is  thought  that  the  air  in  the  tube  is  withdrawn, 
the  capillary  tube  which  connects  B  with  the  three-way  tube  is  sealed.  The 
tube  B  being  thus  closed,  it  is  experimented  with  as  in  Dalton's  method. 

The  drum  MN,  being  filled  with  water,  is  gently  heated  by  a  spirit  lamp, 
which  is  separated  from  the  tubes  by  a  wooden  screen.  By  means  of  a 
stirrer,  K,  all  parts  of  the  liquid  are  kept  at  the  same  temperature.  In  the 
side  of  the  drum  is  a  glass  window,  through  which  the  height  of  the  mercury 
in  the  tubes  can  be  read  off  by  means  of  a  cathetometer  ;  from  the  difference 
in  these  heights,  reduced  to  zero,  the  tension  of  vapour  is  deduced.  By 


-357] 


Tension  of  Aqueous  Vapour. 


297 


means  of  this  apparatus,  the  elastic  force  of  vapour  between  o°  and  50°  has 
been  determined  with  accuracy. 

357.  Tension  of  aqueous  vapour  above  one  hundred  degrees.— Two 

methods  have  been  employed  for  determining  the  tension  of  aqueous  vapour 
at  temperatures  above  100° ;  the  one  by  Dulong  and  Arago,  in  1830,  and  the 
other  by  Regnault,  in  1844. 

Fig.  298  represents  a  vertical  section  of  the  apparatus  used  by  Dulong 
and  Arago.     It  consisted  of  a  copper  boiler,  £,  with  very  thick  sides,  and  of 


Fig.  298. 

about  20  gallons  capacity.  Two  gun-barrels,  #,  of  which  only  one  is  seen  in 
the  drawing,  were  firmly  fixed  in  the  sides  of  the  boiler,  and  plunged  in  the 
water.  The  gun-barrels  were  closed  below,  and  contained  mercury,  in  which 
were  placed  thermometers,  /,  indicating  the  temperature  of  the  water  and  of 
the  vapour.  The  tension  of  the  vapour  was  measured  by  means  of  a  mano- 
meter with  compressed  air,  m,  previously  graduated  (178)  and  fitted  into  an 
iron  vessel,  d,  filled  with  mercury.  In  order  to  see  the  height  of  the  mercury 
in  the  vessel,  it  was  connected  above  and  below  with  a  glass  tube,  «,  in  which 
the  level  was  always  the  same  as  in  the  bath.  A  copper  tube,  *',  connected 
the  upper  part  of  the  vessel,  */,  with  a  vertical  tube,  c,  fitted  in  the  boiler. 
The  tube  /  and  the  upper  part  of  the  bath  d  were  filled  with  water,  which 
was  kept  cool  by  means  of  a  current  of  cold  water  flowing  from  a  reservoir, 
and  circulating  through  the  tube  b. 

The  vapour  which  was  disengaged  from  the  tube  c  exercised  a  pressure 
on  the  water  of  the  tube  / ;  this  pressure  was  transmitted  to  the  water  and 
to  the  mercury  in  the  bath  d,  and  the  mercury  rose  in  the  manometer.  By 
noting  on  the  manometer  the  pressures  corresponding  to  each  degree  of  the 
thermometer,  Dulong  and  Arago  were  able  to  make  a  direct  measurement 
of  the  tension  up  to  24  atmospheres,  and  the  tension  from  thence  to  50 
atmospheres  was  determined  by  calculation. 

03 


298 


On  Heat. 


[358- 


358.  Tension   of  vapour  below  and    above  one  hundred  degrees. — 

Regnault  devised  a  method  by  which  the  tension  of  vapour  may  be 
measured  at  temperatures  either  below  or  above  100°.  It  depends  on  the 
principle  that  when  a  liquid  boils,  the  tension  of  the  vapour  is  equal  to  the 
pressure  it  supports  (363).  If,  therefore,  the  temperature  and  the  corre- 
sponding pressure  are  known,  the  question  is  solved,  and  the  method  merely 
consists  in  causing  water  to  boil  in  a  vessel  under  a  given  pressure,  and 
measuring  the  corresponding  temperature. 

The  apparatus  consists  of  a  copper  retort,  C  (fig.  299),  hermetically  sealed 
and  about  two-thirds  full  of  water.     In  the  cover  there  are  four  thermometers, 


Fig   299. 

two  of  which  just  dip  into  the  water,  and  two  descend  almost  to  the  bottom. 
By  means  of  a  tube,  AB,  the  retort  C  is  connected  with  a  glass  globe,  M,  of 
about  6  gallons  capacity,  and  full  of  air.  The  tube  AB  passes  through  a 
metallic  cylinder,  D,  through  which  a  current  of  cold  water  is  constantly 
flowing  from  the  reservoir  E.  To  the  upper  part  of  the  globe  a  tube  with 
two  branches  is  attached,  one  of  which  is  connected  with  a  manometer,  O  ; 
the  other  tube,  HH',  which  is  of  lead,  can  be  attached  either  to  an  exhaust- 
ing or  a  condensing  air-pump,  according  as  the  air  in  the  globe  is  to  be 
rarefied  or  condensed.  The  reservoir  K,  in  which  is  the  globe,  contains 
water  of  the  temperature  of  the  surrounding  air. 

If  the  elastic  force  of  aqueous  vapour  below  100°  is  to  be  measured,  the 
end  H'  of  the  leaden  pipe  is  connected  with  the  plate  of  the  air-pump,  and 
the  air  in  the  globe  M,  and  consequently  that  in  the  retort  C,  is  rarefied. 


-358]  Tension  of  Aqueous  Vapour.  299 

The  retort  being  gently  heated,  the  water  begins  to  boil  at  a  temperature 
below  100°,  in  consequence  of  the  diminished  pressure.  And  since  the 
vapour  is  condensed  in  the  tube  AB,  which  is  always  cool,  the  pressure 
originally  indicated  by  the  manometer  does  not  increase,  and  therefore  the 
tension  of  the  vapour  during  ebullition  remains  equal  to  the  pressure  on  the 
liquid. 

A  little  air  is  then  allowed  to  enter  ;  this  alters  the  pressure,  and  the 
liquid  boils  at  a  new  temperature  ;  both  these  are  read  off,  and  the  experi- 
ment repeated  as  often  as  desired  up  to  100°. 

In  order  to  measure  the  tension  above  100°,  the  tube  H'  is  connected 
with  a  condensing  pump,  by  means  of  which  the  air  in  the  globe  M  and  that 
in  the  vessel  C  are  exposed  to  successive  pressures,  higher  than  the  atmo- 
sphere. The  ebullition  is  retarded  (367),  and  it  is  only  necessary  to  observe 
the  difference  in  the  height  of  the  mercury  in  the  two  tubes  of  the  mano- 
meter O,  and  the  corresponding  temperature,  in  order  to  obtain  the  tension 
for  a  given  temperature. 

The  following  tables  by  Regnault  give  the  tension  of  aqueous  vapour 
from  -  10°  to  101°  : — 


Tensions  of  aqueous  vapour  from  —  10°  to  104°  C. 


Tempe- 
ratures 

Tensions  in 
millimetres 

Tempe- 
ratures 

Tensions  in 
millimetres 

Tempe- 
ratures 

Tensions  in 
millimetres 

Tempe- 
ratures 

Tensions  in 
millimetres 

-10° 

2-078 

12° 

10-457 

29° 

29782 

90° 

525H5 

8 

2-456 

13 

II-062 

30 

3I-548 

91 

54578 

6 

2-890 

14 

I  I  -906 

31 

33-405 

92 

56676 

4 

3387 

15 

12-699 

32 

35359 

93 

588-41 

2 

3-955 

16 

I3-635 

33 

37-4IO 

94 

61074 

0 

4-600 

17 

I4-42I 

34 

39-565 

95 

63378 

+     I 

4-940 

18 

I5-357 

35 

4I-827 

96 

657-54     ' 

2 

5-302 

19 

16-346 

40 

54-906 

97 

682-03 

3 

5-687 

20 

I7-39I 

45 

7I-39I 

98 

707-26 

4 

6-097 

21 

18-495 

50 

91-982 

98-5 

720-I5 

5 

6*534 

22 

19-659 

55 

tI7-479 

99-o 

733-91 

6 

6-998 

23 

20-888 

60 

148791 

99'5 

746-50 

7 

7-492 

24 

22-184 

65 

186-945 

lOO'O 

760-00 

8 

8-017 

25 

23-550 

70 

233-093 

100-5 

77371 

9 

8-574 

26 

24-998 

75 

288-517 

icro 

787-63 

10 

9-165 

27 

26-505 

80 

354^43 

I02'0 

8l6-I7 

ii 

9-792 

28 

28-101 

85 

433-4I 

104-0 

875-69 

In  the  second  table  the  numbers  were  obtained  by  direct  observation 
up  to  24  atmospheres  ;  the  others  were  calculated  by  the  aid  of  a  formula  of 
interpolation. 

This  table  and  the  one  next  following  show  that  the  elastic  force  increases 
much  more  rapidly  than  the  temperature.  It  has  been  attempted  to  express 
the  relation  between  them  by  formulae,  but  none  of  the  formulae  seem  to  have 
the  simplicity  which  characterises  a  true  law. 


300 


On  Heat 


[358- 


Tensions  in  atmospheres  from  100°  to  230-9°. 


Temperatures 

Number 
of  atmo- 
spheres 

Temperatures 

Number 
of  atmo- 
spheres 

Temperatures 

Number 
of  atmo- 
spheres 

Temperatures 

Number 
of  atmo- 
spheres 

100-0° 

I 

I70-80 

8 

198-8° 

15 

2I7-9° 

22 

112-2 

*1 

I75-8 

9 

20I-9 

16 

220-3 

23 

120*6 

2 

180-3 

10 

204-9 

17 

222-5 

24 

J33'9 

3 

184-5 

ii 

2077 

18 

2247 

25 

144-0 

4 

188-4 

12 

2IO-4 

19 

226-8 

26 

152-2 

5 

I92T 

13 

2I3-0 

20 

228-9 

27 

156-2 

6 

I95'5 

14 

2I5-5 

21 

230-9 

28 

165-3 

7 

359.  Tension  of  the  vapours  of  different  liquids. — Regnault  deter- 
mined the  elastic  force,  at  various  temperatures,  of  a  certain  number  of  liquids 
which  are  given  in  the  following  table  : — 


Liquids 

Tempera- 
tures 

Tensions  in 
millimetres 

Liquids 

Tempera- 
tures 

Tensions  in 
millimetres 

Mercury  . 

50° 

100 

o-ii 

0'74 

Ether  .     . 

-20° 
0 

68 
182 

f 

o 

13 

1 

60 

1728 

Alcohol    . 

50 

220 

100 

4950 

I 
Bisulphide 

100 

—  20 
0 

1695 

43 
132 

Sulphurous     I 
acid             1 

-20 
0 
60 

479 
1165 
8124 

of  carbon 

60 

1164 

f 

-30 

876 

I 

100 

3329 

Ammonia       \ 

0 

3163 

( 

30 

8832 

360.  Tension  of  the  vapours  of  mixed  liquids. — Regnault's  experiments 
on  the  tension  of  the  vapour  of  mixed  liquids  prove  that  (i.)  when  two  liquids 
exert  no  solvent  action  on  each  other — such  as  water  and  bisulphide  of  carbon, 
or  water  and  benzole — the  tension  of  the  vapour  which  rises  from  them  is 
nearly  equal  to  the  sum  of  the  tensions  of  the  two  separate  liquids  at  the 
same  temperature  ;  (ii.)  with  water  and  ether,  which  partially  dissolve  each 
other,  the  tension  of  the  mixture  is  much  less  than  the  sum  of  the  tensions  of 
the  separate  liquids,  being  scarcely  equal  to  that  of  the  ether  alone  ;  (iii.) 
when  two  liquids  dissolve  in  all  proportions,  as  ether  and  bisulphide  of  carbon, 
or  water  and  alcohol,  the  tension  of  the  vapour  of  the  mixed  liquid  is  inter- 
mediate between  the  tensions  of  the  separate  liquids. 

Wiillner  has  shown  that  the  tension  of  aqueous  vapour  emitted  from  a 
saline  solution,  as  compared  with  that  of  pure  water,  is  diminished  by  an 
amount  proportional  to  the  quantity  of  anhydrous  salt  dissolved,  when  the 
salt  crystallises  without  water  or  yields  efflorescent  crystals  :  when  the  salt  is 
deliquescent,  or  has  a  powerful  attraction  for  water,  the  reduction  of  tension 
is  proportional  to  the  quantity  of  crystallised  salt. 

361.  Tension  in  two  communicating  vessels  at  different  temperatures. 
—When  two  vessels  containing  the  same  liquid,  but  at  different  temperatures, 


-362] 


Evaporation. 


301 


are  connected  with  each  other,  the  elastic  force  is  not  that  corresponding  to 
the  mean  of  the  two  temperatures,  as  would  naturally  be  supposed.  Thus, 
if  there  are  two  globes  (fig.  290),  one,  A,  containing  water  kept  at  zero  by 
means  of  melting  ice,  the  other,  B,  containing  water  at  100°,  the  tension,  as 
long  as  the  globes  are  not  connected,  is  4  to  6  millimetres  in  the  first,  and 
760  millimetres  in  the  second.  But  when  they  are  connected  by  opening  the 
stopcock  C,  the  vapour  in  the  globe  B,  from  its  greater  tension,  passes  into 
the  other  globe,  and  is  there  condensed,  so  that  the  vapour  in  B  can  never 
reach  a  higher  temperature  than  that  in  the  globe  A.  The  liquid  simply 
distils  from  B  towards  A  without  any  increase  of  tension. 

From  this  experiment  the  general  principle  may  be  deduced  that  when 
two  vessels  containing  the  same  liquid,  but  at  different  temperatures,  are  con- 
nected, the  tension  is  identical  in  both  vessels,  and  is  the  same  as  that  corre- 
sponding to  the  lower  temperature.  An  application  of  this  principle  has  been 
made  by  Watt  in  the  condenser  of  the  steam-engine. 

362.  Evapo- 
ration. Causes 
which  accele- 
rate it. — Evapo- 
ration, as  has 
been  already 
stated  (349),  is  the 
slow  production 
of  vapour  at  the 
surface  of  a  liquid. 
It  is  in  conse- 
quence of  this 
evaporation  that 
wet  clothes  dry 
when  exposed  to 
the  air,  and  that 
open  vessels  con- 
taining water  become  emptied.  The  vapours  which,  rising  in  the  atmo- 
sphere, condense,  and  becoming  clouds,  fall  as  rain,  are  due  to  the  evapora- 
tion from  the  seas,  lakes,  rivers,  and  the  soil. 

Four  causes  influence  the  rapidity  of  the  evaporation  of  a  liquid  :  i.  the  tem- 
perature ;  ii.  the  quantity  of  the  same  vapour  in  the  surrounding  atmosphere  ; 
iii.  the  renewal  of  this  atmosphere  ;  iv.  the  extent  of  the  surface  of  evaporation. 

Increase  of  temperature  accelerates  the  evaporation  by  increasing  the 
elastic  force  of  the  vapours. 

In  order  to  understand  the  influence  of  the  second  cause,  it  is  to  be  ob- 
served that  no  evaporation  could  take  place  in  a  space  already  saturated 
with  vapour  of  the  same  liquid,  and  that  it  would  reach  its  maximum  in 
air  completely  freed  from  this  vapour.  It  therefore  follows  that  between 
these  two  extremes,  the  rapidity  of  evaporation  varies  according  as  the 
surrounding  atmosphere  is  already  more  or  less  charged  with  the  same 
vapour. 

The  effect  of  the  renewal  of  this  atmosphere  is  similarly  explained  ;  for 
if  the  air  or  gas,  which  surrounds  the  liquid,  is  not  renewed,  it  soon  becomes. 


302;  On  Heat.  [362- 

saturated,  and  evaporation  ceases.  Dalton  found  that  the  ratios  of  the 
evaporation  in  a  feeble  medium  and  a  strong  draught  were  as  270  :  347  :  424. 
He  also  observed  that  the  quantity  evaporated  in  perfectly  dry,  almost  still 
air,  in  a  temperature  at  20°,  was  equivalent  to  o-i  of  a  gramme  on  a  square 
decimeter  of  surface  in  a  minute. 

The  influence  of  the  fourth  cause  is  self-evident. 

363.  laws  of  ebullition.— Ebullition,  or  boiling,  is  the  rapid  production 
of  elastic  bubbles  of  vapour  in  the  mass  of  a  liquid  itself. 

When  a  liquid,  water  for  example,  is  heated  at  the  lower  part  of  a 
vessel,  the  first  bubbles  are  due  to  the  disengagement  of  air  which  had 
previously  been  absorbed.  Small  bubbles  of  vapour  then  begin  to  rise 
from  the  heated  parts  of  the  sides,  but  as  they  pass  through  the  upper  layers, 

the  temperature  of  which  is  lower,  they 
condense  before  reaching  the  surface. 
The  formation  and  successive  condensa- 
tion of  these  first  bubbles  occasion  the 
singing  noticed  in  liquids  before  they 
begin  to  boil.  Lastly,  large  bubbles  rise 
and  burst  on  the  surface,  and  this  consti- 
tutes the  phenomenon  of  ebullition  (fig.  30 1 ). 
The  laws  of  ebullition  have  been 
determined  experimentally,  and  are  as 
follows  : — 

I.  The  temperature  of  ebullition,  or  the 
boiling  point,  increases  with  the  pressure. 

II.  For   a  given  pressure   ebullition 
begins   at  a   certain   temperature,   which 
varies  in  different  liquids,  but  which,  for 
eqtial  pressures,  is  always  the  same  in  the 
same  liquid. 

III.  Whatever  be  the  intensity  of  the 
source  of  heat,  as  soon  as  ebullition  begins, 
the  temperature  of  the  liquid  remains  sta- 
tionary. 

Soiling  points  under  the  pressure  0/760  millimetres. 


Fig.  301. 


Carbonic  acid         .         .         .  -  82° 

Chloride  of  methyle        .         .  -23 

Cyanogen       ,         .         .         .  —  20 

Sulphurous  acid     .         .         .  — 10 

Chloride  of  ethyle  .         .         .  +  1 1 
Aldehyde                .         .         .21 

Ether 37 

Bisulphide  of  carbon     .         .  47 

Acetone          ....  56 

Bromine         ....  58 

Methylic  alcohol    ...  66 

Alcohol 78 

Benzole .....  80 

Distilled  water  100 


Acetic  acid 
Amylic  alcohol  . 
Propionic  acid  . 
Butyric  acid 
Turpentine 
Iodine 
Aniline 

Phosphorus         .   • 
Strong  sulphuric  acid 
Mercury     . 
Sulphur 
Cadmium  . 
Zinc    . 


ii7c 
131 
137 
156 

157 
175 
182 
290 
3i8 
358 
448 
860 
1040 


-364]  Theoretical  Explanation  of  Evaporation  and  Ebullition.  303; 

Kopp  has  pointed  out  that  in  homologous  chemical  compounds  the  same 
difference  in  chemical  composition  frequently  involves  the  same  difference 
of  boiling  points  ;  and  he  has  shown  that  in  a  very  extensive  series  of 
compounds,  the  fatty  acids  for  instance,  the  difference  of  CH2  is  attended  by 
a  difference  of  19°  C.  in  the  boiling  point. 

In  other  series  of  homologous  compounds  the  corresponding  difference  irv 
the  boiling  point  is  30°,  and  in  others  24°. 

364.  Theoretical  explanation  of  evaporation  and  ebullition. — From 
what  has  been  said  about  the  nature  of  the  motion  of  the  molecules  in  liquids 
(292),  it  may  readily  be  conceived  that  in  the  great  variety  of  these  motions, 
the  case  occurs  in  which,  by  a  fortuitous  concurrence  of  the  progressive 
vibratory  and  rotatory  motions,  a  molecule  is  projected  from  the  surface  of  the 
liquid  with  such  force  that  it  overleaps  the  sphere  of  the  action  of  its  cir- 
cumjacent molecules,  before,  by  their  attraction,  it  has  lost  its  initial  velocity ; 
and  that  it  then  flies  into  the  space  above  the  liquid. 

Let  us  first  suppose  this  space  limited  and  originally  vacuous,  it  gradu- 
ally fills  with  the  propelled  molecules  which  act  like  a  gas  and  in  their 
motion  are  driven  against  the  sides  of  the  envelope.  One  of  these  sides, 
however,  is  the  surface  of  the  liquid  itself,  and  a  molecule  when  it  strikes 
against  this  surface  will  not  in  general  be  repelled,  but  will  be  retained  by  the 
attraction  which  the  adjacent  ones  exert.  Equilibrium  will  be  established 
when  as  many  molecules  are  dispersed  in  the  surrounding  space  as,  on  the 
average,  impinge  against  the  surface  and  are  retained  by  it  in  the  unit  of 
time.  This  state  of  equilibrium  is  not,  however,  one  of  rest,  in  which  eva- 
poration has  ceased,  but  a  condition  in  which  evaporation  and  condensation, 
which  are  equally  strong,  continually  compensate  each  other. 

The  density  of  a  vapour  depends  on  the  number  of  molecules  which  are 
repelled  in  a  given  time,  and  this  manifestly  depends  on  the  motion  of  the 
molecules  in  the  liquid,  and  therefore  on  the  temperature. 

What  has  been  said  respecting  the  surface  of  the  liquid  clearly  applies  to 
the  other  sides  of  the  vessel  within  which  the  vapour  is  formed  ;  some  vapour 
is  condensed,  this  is  subject  to  evaporation,  and  a  condition  ultimately  occurs 
in  which  evaporation  and  condensation  are  equal.  The  quantity  of  vapour 
necessary  for  this  depends  on  the  density  of  vapour  in  the  closed  space,  on 
the  temperature  of  the  vapour,  and  of  the  sides  of  the  vessel,  and  on  the  force 
with  which  this  attracts  the  molecules.  The  maximum  will  be  reached 
when  the  sides  are  covered  with  a  layer  of  liquid,  which  then  acts  like  the 
free  surface  of  a  liquid. 

In  the  interior  of  a  liquid  it  may  happen  that  the  molecules  repel  each 
other  with  such  force  as  to  momentarily  destroy  the  coherence  of  the  mass. 
The  small  vacuous  space  which  is  thereby  formed  is  entirely  surrounded  by 
a  medium  which  does  not  allow  of  the  passage  of  the  repelled  molecules. 
Hence  it  cannot  increase  and  maintain  itself  as  a  bubble  of  vapour,  unless  so 
many  molecules  are  projected  from  the  inner  sides,  that  the  internal  pressure 
which  thereby  results  can  balance  the  external  pressure  which  tends  to 
condense  the  bubble.  The  expansive  force  of  the  enclosed  vapour  must 
therefore  be  so  much  the  greater,  the  greater  the  external  pressure  on  the 
liquid,  and  thus  we  see  the  dependence  of  pressure  on  the  temperature  of 
boiling. 


304  On  Heat.  [365- 

365.  Influence  of  substances  in  solution  on  the  boiling:  point. — The 

ebullition  of  a  liquid  is  the  more  retarded  the  greater  the  quantity  of  any 
substance  it  may  contain  in  solution,  provided  that  the  substance  be  not 
volatile,  or,  at  all  events,  be  less  volatile  than  the  liquid  itself.  Water,  which 
boils  at  100°  when  pure,  boils  at  the  following  temperatures  when  saturated 
with  different  salts  : — • 

Water  saturated  with  common  salt          .        .  boils  at  102° 

„            „            nitrate  of  potassium  „       116 

„            „            carbonate  of  potassium  „       135 

„            „            chloride  of  calcium  „       179 

Acids  in  solution  present  analogous  results  ;  but  substances  merely 
mechanically  suspended,  such  as  earthy  matters,  bran,  wooden  shavings,  &c., 
do  not  affect  the  boiling  point. 

Dissolved  air  exerts  a  very  marked  influence  on  the  boiling  point  of 
water.  Deluc  first  observed  that  water  freed  from  air  by  ebullition,  and 
placed  in  a  flask  with  a  long  neck,  could  be  raised  to  112°  without  boiling. 
M.  Donny  examined  this  phenomenon  by  means  of  the  apparatus  depicted  in 

figure    302.      It 

A  ^        consists     of     a 

glass  tube  CAB, 
bent  at  one  end 
and  closed  at  C, 

Fig.  302.  while    the    Other 

is  blown   into  a 

pear-shaped  bulb,  B,  drawn  out  to  a  point.  The  tube  contains  water  which 
is  boiled  until  all  air  is  expelled,  and  the  open  end  is  hermetically  sealed.  By 
inclining  the  tube  the  water  passes  into  the  bent  end  CA  ;  this  end  being 
placed  in  a  bath  of  chloride  of  calcium,  the  temperature  may  be  raised  to 
130°  without  any  signs  of  boiling.  At  138°  the  liquid  is  suddenly  converted 
into  steam  and  the  water  is  thrown  over  into  the  bulb,  which  is  smashed  if 
not  sufficiently  strong. 

Boiled  out  water,  covered  with  a  layer  of  oil,  may  be  raised  to  120°  with- 
out boiling,  but  above  this  temperature  it  suddenly  begins  to  boil,  and  with 
almost  explosive  violence. 

When  a  liquid  is  suspended  in  another  of  the  same  specific  gravity,  but  of 
higher  boiling  point,  with  which  it  does  not  mix,  it  may  be  raised  far  beyond 
its  boiling  point  without  the  formation  of  a  trace  of  vapour.  Dufour  has 
made  a  number  of  valuable  experiments  on  this  subject ;  he  used  in  the  case 
of  water  a  mixture  of  oil  of  cloves  and  linseed  oil,  and  placed  in  it  globules 
of  water,  and  then  gradually  heated  the  oil  ;  in  this  way  ebullition  rarely  set 
in  below  110°  or  115°  ;  very  commonly  globules  of  10  millimetres  diameter 
reached  a  temperature  of  120°  or  130°,  while  very  small  globules  of  i  to  3 
millimetres  reached  the  temperature  of  175°,  a  temperature  at  which  the 
tension  of  vapour  on  a  free  surface  is  8  or  9  atmospheres. 

At  these  high  temperatures  the  contact  of  a  solid  body,  or  the  production 
of  gas  bubbles  in  the  liquid,  occasioned  a  sudden  vaporisation  of  the  globule 
accompanied  by  a  sound  like  the  hissing  of  a  hot  iron  in  water. 


-367]  Influence  of  Pressure  on  the  Boiling  Point.  305 

Saturated  aqueous  solutions  of  sulphate  of  copper,  chloride  of  sodium, 
&c.,  remained  liquid  at  a  temperature  far  beyond  their  boiling  point,  when 
immersed  in  melted  stearic  acid.  In  like  manner,  globules  of  chloroform 
(which  boils  at  61°),  suspended  in  a  solution  of  chloride  of  zinc,  could  be 
heated  to  97C  or  98°  without  boiling. 

It  is  a  disputed  question  as  to  what  is  the  temperature  of  the  vapour 
from  boiling  saturated  saline  solutions.  It  has  been  stated  by  Rudberg  to 
be  that  of  pure  water  boiling  under  the  same  pressure.  The  most  recent 
experiments  of  Magnus  seem  to  show,  however,  that  this  is  not  the  case, 
but  that  the  vapour  of  boiling  solutions  is  hotter  than  that  of  pure  water  ; 
and  that  the  temperature  rises  as  the  solutions  become  more  concentrated, 
and  therefore  boil  at  higher  temperatures.  Nethertheless,  the  vapour  was 
always  found  somewhat  cooler  than  the  mass  of  the  boiling  solution,  and  the 
difference  was  greater  at  high  than  at  low  temperatures. 

The  boiling  point  of  a  liquid  is  usually  lowered  when  it  is  mixed  with  a 
more  volatile  liquid  than  itself,  but  raised  when  it  contains  one  which  is  less 
volatile.  Thus  a  mixture  of  two  parts  alcohol  and  one  of  water  boils  at  83°, 
a  mixture  of  two  parts  of  bisulphide  of  carbon  and  one  part  of  ether  boils  at 
38°.  In  some  cases  the  boiling  point  of  a  mixture  is  lower  than  that  of 
either  of  its  constituents.  A  mixture  of  water  and  bisulphide  boils  at  43°, 
the  boiling  point  of  the  latter  being  46°.  On  this  depends  the  following 
curious  experiment.  If  water  and  bisulphide  of  carbon,  both  at  the  tempera- 
ture 45°,  are  mixed  together,  the  mixture  at  once  begins  to  boil  briskly. 

366.  Influence  of  the   nature  of  the  vessel  on  the  boiling:  point.    - 
Gay-Lussac  observed  that  water  in  a  glass  vessel  required  a  higher  tempera- 
ture for  ebullition  than  in  a  metal  one.     Taking  the  temperature  of  boiling 
water  in  a  copper  vessel  at   100°,  its  boiling  point  in  a  glass  vessel  was 
found  to  be  101°  ;  and  if  the  glass  vessel  had  been  previously  cleaned  by 
means  of  sulphuric  acid  and  of  potass,  the  temperature  would  rise  to  105°,  or 
even  to  106°,  before  ebullition  commenced.     A  piece  of  metal  placed  in  the 
bottom  of  the  vessel  was  always  sufficient  to  lower  the  temperature  to  100°, 
and  at  the  same  time  to  prevent  the  violent  concussions  which  accompany 
the  ebullition  of  saline  or  acid  solutions  in  glass  vessels.     Whatever  be  the 
boiling  point  of  water,  the  temperature  of  its  vapour  is  uninfluenced  by  the 
substance  of  the  vessels. 

367.  Influence  of  pressure  on  the  boiling  point. — We  see  from  the 
table  of  tensions  (358)  that  at  100°,  the  temperature  at  which  water  boils 
under  a  pressure  of  760  millimetres,  aqueous  vapour  has  a  tension  exactly 
equal  to  this  pressure.     This  principle  is  general,  and  may  be  thus  enunci- 
ated :  A  liquid  boils  when  the  tension  of  its  vapour  is  equal  to  the  pressure 
it  supports.     Consequently,  as    the   pressure  increases   or  diminishes,  the 
tension  of  the  vapour,  and  therefore  the  temperature  necessary  for  ebulli- 
tion, must  increase  or  diminish. 

In  order  to  show  that  the  boiling  point  is  lower  under  diminished  pres- 
sure, a  small  dish  containing  water  at  30°  is  placed  under  the  receiver  of 
an  air-pump,  which  is  then  exhausted.  The  liquid  soon  begins  to  boil,  the 
vapour  formed  being  pumped  out  as  rapidly  as  it  is  generated. 

A  paradoxical  but  very  simple  experiment  also  well  illustrates  the  de- 
pendence of  the  boiling  point  on  the  pressure.  In  a  glass  flask,  water  is 


306 


On  Heat. 


[367- 


boiled  for  some  time,  and  when  all  air  has  been  expelled  by  the  steam,  the 
flask  is  closed  by  a  cork  and  inverted,  as  shown  in  fig.  303.     If  the  bottom 

is  then  cooled  by  a  stream  of  cold 
water  from  a  sponge,  the  water  begins 
to  boil  again.  This  arises  from  the 
condensation  of  the  steam  above  the 
surface  of  the  water,  by  which  a  partial 
vacuum  is  produced. 

It  is  in  consequence  of  this  diminu- 
tion of  pressure  that  liquids  boil  on 
high  mountains  at  lower  temperatures. 
On  Mont  Blanc,  for  example,  water 
boils  at  84°,  and  at  Quito  at  90°. 

On  the  more  rapid  evaporation  of 
water  under  feeble  pressures  is  based 
the  use  of  the  air-pump  in  concentra- 
ting those  solutions  which  either  can- 
not bear  a  high  degree  of  heat,  or 
which  can  be  more  cheaply  evaporated 
in  an  exhausted  space.  Howard  made 
a  most  important  and  useful  applica- 
tion of  this  principle  in  the  manufac- 
ture of  sugar.  The  syrup,  in  his 
method,  is  enclosed  in  an  air-tight 
vessel,  which  is  exhausted  by  a  steam- 
engine.  The  evaporation  consequently  goes  on  at  a  lower  temperature, 
which  secures  the  syrup  from  injury.  The  same  plan  is  adopted  in  evapo- 
rating the  juice  of  certain  plants  used  in  preparing  medicinal  extracts. 

On  the  other  hand,  ebullition  is  retarded  by  increasing  the  pressure  : 
under  the  pressure  of  two  atmospheres,  for  example,  water  only  boils  at  i2o-°6. 

368.  Franklin's  experiment. — The  influence  of  pressure  on  ebullition 
may  further  be  illustrated  by  means  of  an  experiment  originally  made  by 
Franklin.     The  apparatus  consists  of  a  bulb,  #,  and  a  tube  b,  joined  by  a 

tube  of  smaller  dimensions  (fig. 
304).  The  tube  b  is  drawn  out,  and 
the  apparatus  filled  with  water, 
which  is  then  in  great  part  boiled 
away  by  means  of  a  spirit  lamp. 
When  it  has  been  boiled  sufficiently 
long  to  expel  all  the  air,  the  tube  b 
is  sealed.  There  is  then  a  vacuum 
in  the  apparatus,  or  rather  there  is 
a  pressure  due  to  the  tension  of 
aqueous  vapour,  which  at  ordinary 
temperatures  is  very  small.  Consequently  if  the  bulb,  a,  be  placed  in  the 
hand,  the  heat  is  sufficient  to  produce  a  pressure  which  drives  the  water  into 
the  tube  £,  and  causes  a  brisk  ebullition. 

369.  Measurement  of  heights  by  the  boiling:  point. — From  the  con- 
nection between  the  boiling-point  of  water  and  the  pressure,  the  heights  of 


Fig.  303. 


Fig.  304. 


-370]  Formation  of  Vapour  in  a  Closed  Tube.  307 

mountains  may  be  measured  by  the  thermometer  instead  of  by  the  barometer. 
Suppose,  for  example,  it  is  found  that  water  boils  on  the  summit  of  a 
mountain  at  90°,  and  at  its  base  at  98° ;  at  these  temperatures  the  elastic 
force  or  tension  of  the  vapour  is  equal  to  that  of  the  pressure  on  the  liquid  ; 
that  is,  to  the  pressure  of  the  atmosphere  at  the  two  places  respectively. 
Now  the  tensions  of  aqueous  vapour  for  various  temperatures  have  been 
determined,  and  accordingly  the  tensions  corresponding  to  the  above  tem- 
peratures are  sought  in  the  tables.  These  numbers  represent  the  atmospheric 
pressures  at  the  two  places  :  in  other  words,  they  give  the  barometric  heights, 
and  from  these  the  height  of  the  mountain  may  be  calculated  by  the  method 
already  given  (171).  An  ascent  of  about  1080  feet  produces  a  diminution  of 
i°  C.  in  the  boiling  point. 

The  instruments  used  for  this  purpose  are  called  thermo-barometers  or 
hypsometerS)  and  were  first  applied  by  Wollaston.  They  consist  essentially 
of  a  small  metallic  vessel  for  boiling  water,  fitted  with  very  delicate  ther- 
mometers, which  are  only  graduated  from  80°  to  100°;  so  that  each  degree 
occupying  a  considerable  space  on  the  scale,  the  loths,  and  even  the  icoths, 
of  a  degree  may  be  estimated,  and  thus  it  is  possible  to  determine  the  height 
of  a  place  by  means  of  the  boiling  point  to  within  about  10  feet. 

370.  Formation  of  vapour  in  a  closed  tube. — We  have  hitherto  con- 
sidered vapours  as  being  produced  in  an  indefinite  space,  or  where  they 
could  expand  freely,  and  it  is  only  under  this  condition  that  ebullition  can 
take  place.  In  a  closed  vessel  the  vapours  produced  finding  no  issue,  their 
tension  and  their  density  increase  with  the  temperature,  but  the  rapid  dis- 
engagement of  vapour  which  constitutes  ebullition  is  impossible.  Hence, 
while  the  temperature  of  a  liquid  in  an  open  vessel  can  never  exceed  that  of 
ebullition,  in  a  closed  vessel  it  may  be  much  higher.  The  liquid  state  has, 
nevertheless,  a  limit  ;  for,  according  to  experiments  by  Cagniard-Latour,  if 
either  water,  alcohol,  or  ether  be  placed  in  strong  glass  tubes,  which  are 
hermetically  sealed  after  the  air  has  been  expelled  by  boiling,  and  if  then 
these  tubes  are  exposed  to  a  sufficient  degree  of  heat,  a  moment  is  reached 
at  which  the  liquid  suddenly  disappears,  and  is  converted  into  vapour  at  200°, 
occupying  a  space  less  than  double  its  volume  in  the  liquid  state,  its  tension 
being  then  38  atmospheres. 

Alcohol  which  half  fills  a  tube  is  converted  into  vapour  at  207°  C.  If 
a  glass  tube  about  half  filled  with  water,  in  which  some  carbonate  of  soda 
has  been  dissolved,  to  diminish  the  action  of  the  water  in  the  glass,  be 
heated,  it  is  completely  vaporised  at  about  the  temperature  of  melting 
zinc. 

When  chloride  of  ethyle  is  heated  in  a  very  thick  sealed  tube,  the  upper 
surface  ceases  to  be  distinct  at  170°,  and  is  replaced  by  an  ill-defined 
nebulous  zone.  As  the  temperature  rises  this  zone  increases  in  width  in 
both  directions,  becoming  at  the  same  time  more  transparent ;  after  a  time 
the  liquid  is  completely  vaporised,  and  the  tube  becomes  transparent  and 
seemingly  empty.  On  cooling,  the  phenomena  are  reproduced  in  the  oppo- 
site order.  Similar  appearances  are  observed  on  heating  ether  in  a  sealed 
tube  at  190°. 

Andrews  has  observed  that  when  liquid  carbonic  acid  was  heated  in  a 
closed  tube  to  31°  C  the  surface  of  demarcation  between  the  liquid  and  the 


308 


On  Heat. 


[370- 


gas  became  fainter,  lost  its  curvature,  and  gradually  disappeared.  The 
space  was  then  occupied  by  a  homogeneous  fluid,  which,  when  the  pressure 
was  suddenly 'diminished,  or  the  temperature  slightly  lowered,  exhibited  a 
peculiar  appearance  of  moving  or  flickering  striae  throughout  its  whole  mass. 
Above  30°  no  apparent  liquefaction  of  carbonic  anhydride,  or  separation  into 
two  distinct  forms  of  matter,  could  be  effected,  not  even  when  the  pressure 
of  400  atmospheres  was  applied.  It  would  thus  seem  that  there  exists  for 
every  liquid  a  temperature,  the  critical  point  or  critical  temperature.  While 
below  this  critical  point  a  sudden  transition  from  gas  to  liquid  is  accom- 
panied by  a  sudden  diminution  of  volume,  and  liquid  and  gas  are  separated 
by  a  sharp  line  of  demarcation  ;  above  this  critical  point  the  change  is  con- 
nected with  a  gradual  diminution  of  volume,  and  is  quite  imperceptible.  The 
condensation  can,  indeed,  only  be  recognised  by  a  sudden  ebullition  when 
the  pressure  is  lessened.  Hence,  ordinary  condensation  is  only  possible  at 
a  temperature  below  the  critical  point,  and  it  is  not  surprising,  therefore, 
that  mere  pressure,  however  great,  should  fail  to  liquefy  many  of  the  bodies 
which  usually  exist  as  gases. 

371.  Papin's  dig-ester. — Papin  appears  to  have  been  the  first  to  study 
the  effects  of  the  production  of  vapour  in  closed  vessels.     The  apparatus 

which  bears  his  name  consists  of  a  cylin- 
drical iron  vessel  (fig.  305),  provided  with 
a  cover,  which  is  firmly  fastened  down 
by  the  screw  B.  In  order  to  close  the 
vessel  hermetically,  sheet  lead  is  placed 
between  the  edges  of  the  cover  and  the 
vessel.  At  the  bottom  of  a  cylindrical 
cavity,  which  traverses  the  cylinder  S, 
and  the  tubulure  0,  the  cover  is  perforated 
by  a  small  orifice  in  which  there  is  a  rod 
n.  This  rod  presses  against  a  lever,  A, 
movable  at  a,  and  the  pressure  may  be 
regulated  by  means  of  a  weight  movable 
on  this  lever.  The  lever  is  so  weighted, 
that  when  the  tension  in  the  interior  is 
equal  to  6  atmospheres,  for  example,  the 
valve  rises  and  the  vapour  escapes.  The 
destruction  of  the  apparatus  is  thus 
avoided,  and  this  mechanism  has  hence 
received  the  name  of  safety  valve.  The 
digester  is  filled  about  two-thirds  with 
water,  and  is  heated  on  a  furnace.  The 
water  may  thus  be  raised  to  a  temperature 
far  above  100°,  and  the  tension  of  the  vapour  increased  to  several  atmo- 
spheres, according  to  the  weight  on  the  lever. 

We  have  seen  that  water  boils  at  much  lower  temperatures  on  high 

mountains  (367)  ;  the  temperature  of  water  boiling  in  open  vessels  in  such 

localities  is  not  sufficient  to  soften  animal  fibre  completely  and  extract  the 

nutriment,  and  hence  Papin's  digester  is  used  in  the  preparation  of  food. 

Papin's  digester  is  used  in  extracting  gelatine.     When  bones  are  digested 


Fig.  305- 


-372]  Latent  Heat  of  Vapour.  309 

in  this  apparatus  they  are  softened  so  that  the  gelatine  which  they  contain 
is  dissolved.  The  use  of  the  digester  is  extending  in  Germany  ;  the  part 
through  which  the  screw  B  passes  is  made  of  such  elasticity  that  it  yields 
and  the  lid  opens  when  the  pressure  of  the  vapour  becomes  dangerous. 

372.  latent  heat  of  vapour. — As  the  temperature  of  a  liquid  remains 
constant  during  ebullition,  whatever  be  the  source  of  heat  (363),  it  follows 
that  a  considerable  quantity  of  heat  becomes  absorbed  in  ebullition,  the 
only  effect  of  which  is  to  transform  the  body  from  the  liquid  to  the  gaseous 
condition.  And  conversely  when  a  saturated  vapour  passes  into  the  state  of 
liquid  it  gives  out  a  definite  amount  of  heat. 

These  phenomena  were  first  observed  by  Black,  and  he  described  them 
by  saying  that  during  vaporisation  a  quantity  of  sensible  heat  became  latent, 
and  that  the  latent  heat  again  became  free  during  condensation.  The 
quantity  of  heat  which  a  liquid  must  absorb  in  passing  from  the  liquid  to 
the  gaseous  state,  and  which  it  gives  out  in  passing  from  the  state  of  vapour 
to  that  of  liquid,  is  spoken  of  as  the  latent  heat  of  evaporation. 

The  analogy  of  these  phenomena  to  those  of  fusion  will  be  at  once  seen ; 
the  modes  of  determining  them  will  be  described  in  the  chapter  on  Calori- 
metry  ;  but  the  following  results,  which  have  been  obtained  for  the  latent 
heats  of  evaporation  of  a  few  liquids,  may  be  here  given  : — 

Water 536  Bisulphide  of  carbon        .         .     87 

Alcohol 208  Turpentine        .         .         .         .74 

Acetic  acid       .         .        .         .102  Bromine 49 

Ether 90  Iodine 24 

The  meaning  of  these  numbers  is,  in  the  case  of  water,  for  instance,  that 
it  requires  as  much  heat  to  convert  a  pound  of  water  from  the  state  of  liquid 
at  the  boiling  point  to  that  of  vapour  at  the  same  temperature,  as  would  raise 
a  pound  of  water  through  536  degrees,  or  536  pounds  of  water  through  one 
degree  ;  or  that  the  conversion  of  one  pound  of  vapour  of  alcohol  at  78°  into 
liquid  alcohol  of  the  same  temperature  would  heat  208  pounds  of  water 
through  one  degree. 

Watt,  who  investigated  the  subject,  found  that  the  whole  quantity  of  heat 
necessary  to  raise  a  given  'weight  of  water  from  zero  at  any  temperature  and 
then  to  evaporate  it  entirely,  is  a  constant  quantity.  His  experiments 
showed  that  this  quantity  is  640.  Hence  the  lower  the  temperature  the 
greater  the  latent  heat,  and,  on  the  other  hand,  the  higher  the  temperature 
the  less  the  latent  heat.  The  latent  heat  of  the  vapour  of  water  evaporated 
at  100°  would  be  540,  while  at  50°  it  would  be  590.  At  higher  temperatures 
the  latent  heat  of  aqueous  vapour  would  go  on  diminishing.  Water  evapo- 
rated under  a  pressure  of  1 5  atmospheres  at  a  temperature  of  200°  would 
have  a  latent  heat  of  440,  and  if  it  could  be  evaporated  at  640°  it  would  have 
no  latent  heat  at  all. 

Regnault,  who  examined  this  question  with  great  care,  found  that  the 
total  quantity  of  heat  necessary  for  the  evaporation  of  water  increases  with 
the  temperature,  and  is  not  constant,  as  Watt  had  supposed.  It  is  repre- 
sented by  the  formula. 

Q  =  606-5 +0-305  T> 

in  which  Q  is  the  total  quantity  of  heat,  and  T  the  temperature  of  the  water 


3io 


On  Heat. 


[372- 


during  evaporation,  while  the  numbers  are  constant  quantities.  The  total 
quantity  of  heat  necessary  to  evaporate  water  at  100°  is  606-5  +  (°'3O5  *  100) 
=  637  ;  at  120°  it  is  643  ;  at  150°  it  is  651  ;  and  at  180°  it  is  661. 

Thus  the  heat  required  to  raise  a  pound  of  water  from  zero  and  convert 
it  into  steam  at  100°  represents  a  mechanical  work  of  885430  units,  which 
would  be  sufficient  to  raise  a  ton  weight  through  a  height  of  nearly  400  feet. 

The  total  heat  of  the  evaporation  of  ether  is  expressed  by  a  formula 
similar  to  that  of  water,  namely,  Q  =  64  +  0-045/5  and  that  for  chloroform 


A 


373.  Cold  due  to  evaporation.  Mercury  frozen.  —  Whatever  be  the 
temperature  at  which  a  vapour  is  produced,  an  absorption  of  heat  always 
takes  place.  If,  therefore,  a  liquid  evaporates,  and  does  not  receive  from 
without  a  quantity  of  heat  equal  to  that  which  is  expended  in  producing  the 
vapour,  its  temperature  sinks,  and  the  cooling  is  greater  in  proportion  as  the 
evaporation  is  more  rapid. 

Leslie  succeeded  in  freezing  water  by  means  of  rapid  evaporation. 
Under  the  receiver  of  the  air  pump  is  placed  a  vessel  containing  strong  sul- 
phuric acid,  and  above  it  a  thin  metal  capsule,  A  (fig.  306),  containing  a  small 

quantity  of  water.  By 
exhausting  the  receiver 
the  water  begins  to 
boil  (360),  and  since  the 
vapours  are  absorbed 
by  the  sulphuric  acid 
as  fast  as  they  are 
formed,  a  rapid  evapo- 
ration is  produced, 
which  quickly  effects 
the  freezing  of  the 
water. 

This  experiment  is 
best  performed  by 
using,  instead  of  a  thin 
metallic  vessel,  a  watch 

glass,  coated  with  lampblack  and  resting  on  a  cork.  The  advantage  of  this 
is  twofold  :  firstly,  the  lampblack  is  a  very  bad  conductor  ;  and  secondly,  it 
is  not  moistened  by  the  liquid,  which  remains  in  the  form  of  a  globule  not 
in  contact  with  the  glass.  A  small  porous  dish  may  also  advantageously  be 
used. 

The  same  result  is  obtained  by  means  of  Wollaston's  cryophorus  (fig. 
307),  which  consists  of  a  bent  glass  tube  provided  with  a  bulb  at  each  end. 
The  apparatus  is  prepared  by  introducing  a  small  quantity  of  water,  which 
is  then  boiled  so  as  to  expel  all  air.  It  is  then  hermetically  sealed,  so  that 
on  cooling  it  contains  only  water  and  the  vapour  of  water. 

The  water  being  introduced  into  the  bulb  A,  the  other  is  immersed  in  a 
freezing  mixture.  The  vapours  in  the  tube  are  thus  condensed  ;  the  water  in 
A  rapidly  yields  more.  But  this  rapid  production  of  vapour  requires  a  large 
amount  of  heat,  which  is  abstracted  from  the  water  in  A,  and  its  temperature 
is  so  much  reduced  that  it  freezes. 


?•  306. 


Fi. 


-374]  Carres  Apparatus  for  Freezing  Water.  311 

By  using  liquids  more  volatile  than  water,  more  particularly  liquid  sul- 
phurous acid,  which  boils  at  —  10°,  or  still  better,  chloride  of  methyle,  which 
is  now  prepared  industrially  in  large  quantities,  a  degree  of  cold  is  obtained 
sufficiently  intense  to  freeze  mercury.  The  experiment  may  be  made  by  cover- 
ing the  bulb  of  a  thermometer  with  cotton  wool," and  after  having  moistened 
it  with  the  liquid  in  question,  placing  it  under  the  receiver  of  the  air-pump. 
When  a  vacuum  is  produced  the  mercury  is  quickly  frozen. 

Thilorier,  by  directing  a  jet  of  liquid  carbonic  acid  on  the  bulb  of  an 
alcohol  thermometer,  obtained  a  cold  of  -  100°  without  freezing  the  alcohol. 
We  have  already  seen,  however  (343),  that  with  a  mixture  of  solid  carbonic 
acid,  liquid  protoxide  of  nitrogen  and  ether,  Despretz  obtained  a  sufficient 
degree  of  cold  to  reduce  alcohol  to  the  viscous  state. 

By  means  of  the  evaporation  of  bisulphide  of  carbon  the  formation  of 
ice  may  be  illustrated  without  the  aid  of  an  air-pump.  A  little  water  is 
dropped  on  a  board,  and  a  capsule  of  thin  copper  foil,  containing  bisulphide 
of  carbon,  is  placed  on  the  water.  The  evaporation  of  the  bisulphide  is  ac- 
celerated by  means  of  a  pair  of  bellows,  and  after  a  few  minutes  the  water 
freezes  round  the  capsule,  so  that  the  latter  adheres  to  the  wood. 

In  like  manner,  if  some  water  be  placed  in  a  test  tube,  which  is  then 
dipped  in  a  glass  containing  some  ether,  and  a  current  of  air  be  blown 
through  the  ether  by  means  of  a  glass  tube  fitted  to  the  nozzle  of  a  pair  of 
bellows,  the  rapid  evaporation  of  the  ether  very  soon  freezes  the  water  in  the 
tube.  Richardson's  apparatus  for  producing  local  anaesthesia  also  depends 
on  the  cold  produced  by  the  evaporation  of  ether. 

The  cold  produced  by  evaporation  is  used  in  hot  climates  to  cool  water 
by  means  of  alcarrazas.  These  are  porous  earthen  vessels,  through  which 
water  percolates,  so  that  on  the  outside  there  is  a  continual  evaporation, 
which  is  accelerated  when  the  vessels  are  placed  in  a  current  of  air.  For  the 
same  reason  wine  is  cooled  by  wrapping  the  bottles  in  wet  cloths  and  placing 
them  in  a  draught. 

In  Harrison's  method  of  making  ice  artificially,  a  steam-engine  is  used 
to  work  an  air-pump,  which  produces  a  rapid  evaporation  of  some  ether,  in 
which  is  immersed  the  vessel  containing  the  water  to  be  frozen.  The  ap- 
paratus is  so  constructed  that  the  vaporised  ether  can  be  condensed  and 
used  again. 

The  cooling  effect  produced  by  a  wind  or  draught  does  not  necessarily 
arise  from  the  wind  being  cooler,  for  it  may,  as  shown  by  the  thermometer, 
be  actually  warmer,  but  arises  from  the  rapid  evaporation  it  causes  from  the 
surface  of  the  skin.  We  have  the  feeling  of  oppression,  even  at  moderate 
temperatures,  when  we  are  in  an  atmosphere  saturated  by  moisture,  in  which 
no  evaporation  takes  place. 

374.  Carre's  apparatus  for  freezing:  water. — We  have  already  seen  that 
when  any  liquid  is  converted  into  vapour  it  absorbs  a  considerable  quantity 
of  sensible  heat  ;  this  furnishes  a  source  of  cold  which  is  more  abundant 
the  more  volatile  the  liquid,  and  the  greater  its  heat  of  vaporisation. 

This  property  of  liquids  has  been  utilised  by  M.  Carre\  in  freezing  water 
by  the  distillation  of  ammonia.  The  apparatus  consists  of  a  cylindrical 
boiler  C  (figs.  308,  309),  and  of  a  slightly  conical  vessel  A,  which  is  the  freezer. 
These  two  vessels  are  connected  by  a  tube,  ?//,  and  a  brace,  »,  binds  them 


312 


On  Heat. 


[374- 


firmly.  They  are  made  of  strong  galvanised  iron  plate,  and  can  resist  a 
pressure  of  seven  atmospheres. 

The  boiler  C,  which  holds  about  two  gallons,  is  three  parts  filled  with  a 
strong  solution  of  ammonia.  In  a  tubulure  in  the  upper  part  of  the  boiler 
some  oil  is  placed,  and  in  this  a  thermometer  /.  The  freezer  A  consists  of 
two  concentric  envelopes,  in  such  a  manner  that,  its  centre  being  hollow,  a 
metal  vessel,  G,  containing  the  water  to  be  frozen,  can  be  placed  in  this  space. 
Hence  only  the  annular  space  between  the  sides  of  the  freezer  is  in  commu- 
nication with  the  boiler  by  means  of  the  tube  m.  In  the  upper  part  of  the 
freezer  there  is  a  small  tubulure,  which  can  be  closed  by  a  metal  stopper,  and 
by  which  the  solution  of  ammonia  is  introduced. 

The  formation  of  ice  comprehends  two  distinct  operations.  In  the  first, 
the  boiler  is  placed  in  a  furnace  F,  and  the  freezer  in  a  bath  of  cold  water  of 
about  12°.  The  boiler  being  heated  to  130°,  the  ammoniacal  gas  dissolved 


Fig.  308. 


Fig.  309. 


in  the  water  of  the  boiler  is  disengaged,  and,  in  virtue  of  its  own  pressure,  is 
liquefied  in  the  freezer,  along  with  about  a  tenth  of  its  weight  of  water.  This 
distillation  of  C  towards  A  lasts  about  an  hour  and  a  quarter,  and  when  it  is 
finished  the  second  operation  commences  ;  this  consists  in  placing  the  boiler 
in  the  cold-water  bath  (fig.  309),  and  the  freezer  outside,  care  being  taken  to 
surround  it  with  very  dry  flannel.  The  vessel  G,  about  three-quarters  full 
of  water,  is  placed  in  the  freezer.  As  the  boiler  cools,  the  ammoniacal  gas 
with  which  it  is  filled  is  again  dissolved  ;  the  pressure  thus  being  diminished, 
the  ammonia  which  has  been  liquefied  in  it  is  converted  into  the  gaseous 
form,  and  now  distils  from  A  towards  C,  to  redissolve  in  the  water  which 
has  remained  in  the  boiler.  During  this  distillation  the  ammonia  which  is 
gasified  absorbs  a  great  quantity  of  heat,  which  is  withdrawn  from  the  vessel 
G  and  the  water  it  contains.  Hence  it  is  that  this  water  freezes.  In  order 
to  have  better  contact  between  the  sides  of  the  vessel  G  and  the  freezer, 


-374] 


Carrt ' s  Apparatus  for  Freezing  Water. 


313 


alcohol  is  poured  between  them.     In  about  an  hour  and  a  quarter  a  perfectly 
compact  cylindrical  block  of  ice  can  be  taken  from  the  vessel  G. 

This  apparatus  gives  about  four  pounds  of  ice  in  an  hour,  at  a  price  of 
about  a  farthing  per  pound  ;  large  continuously  working  apparatus  have, 
however,  been  constructed,  which  produce  as  much  as  800  pounds  of  ice  in 
an  hour. 

Carre  has  constructed  an  ice-making  machine  which  is  an  industrial 
application  of  Leslie's  experiment  (373),  and  by  which  considerable  quantities 
of  water  may  be  frozen  in  a  short  time.  It  consists  of  a  cylinder  R  about  15 
inches  long  by  4  in  diameter,  made  of  an  alloy  of  lead  and  antimony 
(fig.  310).  At  one  end  is  a  funnel  E,  by  which  strong  sulphuric  acid  can  be 
introduced  ;  at  the  other  is  a  tubulure  ;;/,  to  which  is  screwed  a  dome  d  that 
supports  a  series  of  obstacles  intended  to  prevent  any  sulphuric  acid  from 
spirting  into  m  and  b.  There  are,  moreover,  on  the  receiver  a  wide  tube  //, 
closed  by  a  thick  glass  disc  O,  and  a  long  tube  //,  to  the  top  of  which  is  fitted 
the  bottle  C  con- 
taining water  to  be 
frozen.  The  dome 
d,  the  disc  O,  and 
the  stopper  i  of  the 
funnel  E  are  all 
sealed  with  wax. 

On  the  side  of 
the  receiver  is  an 
air-pump  P,  con- 
nected with  it  by  a 
tube  £,  and  worked 
by  a  handle  M.  To 
this  handle  is  at- 
tached a  rod  /, 
whi  ch  by  the 
mechanism  repre- 
sented on  the  left 
of  the  figure  works 
a  stirrer  A  in  the 
sulphuric  acid.  A 
lever  x  connected 
with  a  horizontal 
axis  which  tra- 
verses a  small  stuff-  Fig.  310. 
ing-box  n,  trans- 
mits its  backward  and  forward  motion  to  the  rod  e  and  to  the  stirrer.  This 
and  the  stuffing-box  n  are  fitted  in  a  tubulure  on  the  side  of  the  tubulure  /;/. 

The  smallest  size  which  Carr£  makes  contains  2-5  kilogrammes  of  sul- 
phuric acid,  and  the  water-bottle  about  400  grammes,  when  it  is  one-third  full. 
After  about  70  strokes  of  the  piston  the  water  begins  to  boil ;  the  acid  being 
in  continued  agitation,  the  vapour  is  rapidly  absorbed  by  it,  and  the  pump  is 
worked  until  freezing  begins.  For  this  purpose  it  is  merely  necessary  to 
give  a  few  strokes  every  five  minutes.  The  rate  of  freezing  depends  on  the 


314  On  Heat.  [374- 

strength  of  the  acid  ;  when  this  gets  very  dilute  it  requires  renewal :  but  12 
water-bottles  can  be  frozen  with  the  same  quantity  of  acid. 


LIQUEFACTION   OF  VAPOURS   AND   GASES. 

375.  Liquefaction  of  vapours. — The    liqti  ef action    or    condensation  of 
vapours  is  their  passage  from  the  aeriform  to  the  liquid  state.     Condensa- 
tion may  be  due  to  three  causes — cooling,  compression,  or  chemical  affinity. 
For  the  first  two  causes  the  vapours  must  be  saturated  (354),  while   the 
latter  produces  the  liquefaction  of  the  most  rarefied  vapours.     Thus,  a  large 
number  of  salts  absorb  and  condense  the  aqueous  vapour  in  the  atmosphere, 
however  small  its  quantity. 

When  vapours  are  condensed,  their  latent  heat  becomes  free  ;  that  is,  it 
affects  the  thermometer.  This  is  readily  seen  when  a  current  of  steam  at 
100°  is  passed  into  a  vessel  of  water  at  the  ordinary  temperature.  The  liquid 
becomes  rapidly  heated,  and  soon  reaches  100°.  The  quantity  of  heat  given 
up  in  liquefaction  is  equal  to  the  quantity  absorbed  in  producing  the 
vapour. 

376.  Distillation.     Stills. — Distillation   is    an   operation   by  which    a 
volatile  liquid  may  be  separated  from  substances  which  it  holds  in  solution 


Fig.  311. 

or  by  which  two  liquids  of  different  volatilities  may  be  separated.  The 
operation  depends  on  the  transformation  of  liquids  into  vapours  by  the 
action  of  heat,  and  on  the  condensation  of  these  vapours  by  cooling. 

The  apparatus  used  in  distillation  is  called  a  stilL  Its  form  may  vary 
greatly,  but  it  consists  essentially  of  three  parts  :  ist,  the  body,  A  (fig.  311), 
a  copper  vessel  containing  the  liquid,  the  lower  part  of  which  fits  in  the 
furnace  :  2nd,  the  head,  B,  which  fits  on  the  body,  and  from  which  a 


-378]   Apparatus  for  determining  Alcoholic  Value  of  Wines.    315 

lateral  tube,  C,  leads  to  :  3rd,  the  worm,  S,  a  long  spiral  tin  or  copper  tube 
placed  in  a  cistern  kept  constantly  full  of  cold  water.  The  object  of  the 
worm  is  to  condense  the  vapour,  by  exposing  a  greater  extent  of  cold 
surface. 

To  free  ordinary  water  from  the  many  impurities  which  it  contains, 
it  is  placed  in  a  still  and  heated.  The  vapours  disengaged  are  condensed 
in  the  worm,  and  the  distilled  water  arising  from  the  condensation  is  col- 
lected in  the  receiver  D.  The  vapours  in  condensing  rapidly  heat  the 
water  in  the  cistern,  which  must,  therefore,  be  constantly  renewed.  For  this 
purpose  a  continual  supply  of  cold  water  passes  into  the  bottom  of  the 
cistern,  while  the  lighter  heated  water  rises  to  the  surface  and  escapes  by  a 
tube  in  the  top  of  the  cistern. 

377.  Xiiebig's  condenser. — In  distilling  smaller  quantities  of  liquids, 
or  in  taking  the  boiling  point  of  a  liquid,  so  as  not  to  lose  any  of  it,  the 


Fig.  312- 

apparatus  known  as  Liebig's  condenser  is  extremely  useful.  It  consists  of  a 
glass  tube,  //(fig.  312),  about  thirty  inches  long,  fittedin  a  copper  or  tin  tube 
by  means  of  perforated  corks.  A  constant  supply  of  cold  water  from  the 
vessel  a  passes  into  the  space  between  the  two  tubes,  being  conveyed  to  the 
lower  part  of  the  condenser  by  a  funnel  and  tube  f,  and  flowing  out  from  the 
upper  part  of  the  tube  g.  The  liquid  to  be  distilled  is  contained  in  a  retort, 
the  neck  of  which  is  placed  in  the  tube  ;  the  condensed  liquid  drops  quite 
cold  into  a  vessel  placed  to  receive  it  at  the  other  extremity  of  the  con- 
densing tube. 

378.  Apparatus  for  determining:  tne  alcoholic  value  of  wines. — One 
of  the  forms  of  this  apparatus  consists  of  a  glass  flask  resting  on  a  tripod, 
and  heated  by  a  spirit  lamp  (fig.  313).  By  means  of  a  caoutchouc  tube  this 
is  connected  with  a  worm  placed  in  a  copper  vessel  filled  with  cold  water, 
and  below  which  is  a  test-glass  for  collecting  the  distillate.  On  this  are 

P  2 


3i6 


On  Heat. 


[378- 


three  divisions,  one  «,  which  measures  the  quantity  of  wine  taken  ;  the  two 
others  indicating  one-half  and  one-third  of  this  volume. 

The  test-glass  is  filled  with  the  wine  up  to  a  ;  this  is  then  poured  into 
the  flask,  which  having  been  connected  with  the  worm,  the  distillation  is 
commenced.  The  liquid  which  distils  over  is  a  mixture  of  alcohol  and 
water  ;  for  ordinary  wines,  such  as  clarets  and  hocks,  about  one-third  is  dis- 
tilled over,  and  for  wines  richer  in  spirit,  such  as  sherries  and  ports,  one-half 
must  be  distilled  ;  experiment  has  shown  that  under  these  circumstances  all 
the  alcohol  passes  over  in  the  distillate.  The  measure  is  then  filled  up  with 

distilled  water  to 
a  ;  this  gives  the 
mixture  of  alco- 
hol and  water  of 
the  same  volume 
as  the  wine 
taken,  free  from 
all  solid  matters, 
such  as  sugar, 
colouring  mat- 
ter, and  acid,  but 
containing  all 
the  alcohol.  The 
specific  gravity 
of  this  distillate 
is  then  taken  by 
means  of  an  al- 
coholometer 
(129),  and  the 
number  thus  ob- 
tained corresponds  to  a  certain  strength  of  alcohol  as  indicated  by  the 
tables. 

379.  Safety  tube. — In  preparing  gases  and  collecting  them  over  mercury 
or  water,  it  occasionally  happens  that  these  liquids  rush  back  into  the 
generating  vessel,  and  destroy  the  operation.  This 
arises  from  an  excess  of  atmospheric  pressure 
over  the  tension  in  the  vessel.  If  a  gas,  sul- 
phurous acid,  for  example,  be  generated  in  the 
flask  m  (fig.  314),  and  be  passed  into  water  in  the 
vessel  A,  as  long  as  the  gas  is  given  off  freely,  its 
tension  exceeds  the  atmospheric  pressure  and 
the  weight  of  the  column  of  water,  on,  so  that 
the  water  in  the  vessel  cannot  rise  in  the  tube, 
and  absorption  is  impossible.  But  if  the  tension 
decreases  either  through  the  flask  becoming 
cooled  or  the  gas  being  disengaged  too  slowly, 
the  external  pressure  prevails,  and  when  it  exceeds  the  internal  tension  by 
more  than  the  weight  of  the  column  of  water  co,  the  water  rises  into  the 
flask  and  the  operation  is  spoiled.  This  accident  is  prevented  by  means  of 
safety  tubes. 


Fig.  3M- 


-380]  Liquefaction  of  Gases.  317 

These  are  tubes  which  prevent  absorption  by  allowing  air  to  enter  in 
proportion  as  the  internal  tension  decreases.  The  simplest  is  a  tube  C  o 
(fig.  315,)  passing  through  the  cork  which  closes  the  flask  M,  in  which  the  gas 
is  generated,  and  dipping  in  the  liquid.  When  the  tension  of  the  gas 
diminishes  in  M,  the  atmospheric  pressure  on  the  water  in  the  bath  E  causes 
it  to  rise  to  a  certain  height  in  the  tube  DA  ;  but  this  pressure,  acting  also 
on  the  liquid  in  the  tube  C0,  depresses  it  to  the  same  extent,  assuming  that 
the  liquid  has  the  same  density  as  the  water  in  E.  Now  as  the  distance  or 
is  less  than  the  height  DH,  air  enters  by  the  aperture  0,  before  the  water  in 
the  bath  can  rise  to  A,  and  no  absorption  takes  place. 

Fig.  316  represents  another  kind  of  safety  tube.  It  has  a  bulb  a,  con- 
taining a  certain  quantity  of  liquid,  as  does  also  id.  When  the  tension  of 
the  gas  in  the  retort  M  exceeds  the  atmospheric  pressure,  the  level  in  the 
leg  id  rises  higher  than  in  the  bulb  a  ;  if  the  gas  has  the  tension  of  one  atmo- 
sphere, the  level  is  the  same  in  the  tube  as  in  the  bulb.  Lastly,  if  the 
tension  of  the  gas  is  less  than  the  atmospheric  preieure,  the  level  sinks  in 
the  leg  di ;  and,  as  care  is  taken  that  the  height  ia  is  less  than  b  h,  as  soon 
as  the  air  which  enters  through  c  reaches  the  curved  part  *,  it  raises  the 
column  /  a,  and  passes  into  the  retort  before  the  water  in  the  cylinder  can 


Fig-  3*5-  Fig.  316. 

reach  b  ;  the  tension  in  the  interior  is  then  equal  to  the  exterior  pressure, 
and  no  absorption  takes  place. 

380.  liquefaction  of  gases. — We  have  already  seen  that  a  saturated 
vapour,  the  temperature  of  which  is  constant,  is  liquefied  by  increasing  the 
pressure,  and  that,  the  pressure  remaining  constant,  it  is  brought  into  the 
Liquid  state  by  diminishing  the  temperature. 

Unsaturated  vapours  behave  in  all  respects  like  gases.  And  it  is  natural 
to  suppose  that  what  are  ordinarily  called  permanent  gases  are  really  un- 
saturated  vapours.  For  the  gaseous  form  is  accidental,  and  is  not  inherent 
in  the  nature  of  the  substance.  At  ordinary  temperatures  sulphurous  acid  is 
a  gas,  while  in  countries  near  the  poles  it  is  a  liquid  ;  in  temperate  climates 
ether  is  a  liquid,  at  a  tropical  heat  it  is  a  gas.  And  just  as  unsaturated 
vapours  may  be  brought  to  the  state  of  saturation,  and  then  liquefied,  by 
suitably  diminishing  the  temperature  or  increasing  the  pressure,  so  by  the 


318  On  Heat.  [380- 

same  means  gases  may  be  liquefied.  But  as  they  are  mostly  very  far  re- 
moved from  this  state  of  saturation,  great  cold  and  pressure  are  required. 
Some  of  them  may  indeed  be  liquefied  either  by  cold  or  by  pressure  ;  for 
the  majority,  however,  both  agencies  must  be  simultaneously  employed. 
The  late  researches  of  Cailletet  and  Pictet  have 
shown  that  the  distinction  permanent  gas  no 
longer  exists,  now  that  all  are  liquefied. 

Faraday  was  the  first  to  liquefy  some  of  the 
gases.  His  method  consists  in  enclosing  in  a 
bent  glass  tube  (fig.  317)  substances  by  whose 
chemical  action  the  gas  to  be  liquefied  is  pro- 
duced, and  then  sealing  the  shorter  leg.  In 
proportion  as  the  gas  is  disengaged  its  pressure 
increases,  and  it  ultimately  liquefies  and  collects 
Fig.  317.  in  the  shorter  leg,  more  especially  if  its  conden- 

•       sation  is  assisted  by  placing  the  shorter  leg  in  a 

freezing  mixture.     A  small  manometer  may  be  placed  in  the  apparatus  to 
indicate  the  pressure. 

Cyanogen  gas  is  readily  liquefied  by  heating  cyanide  of  mercury  in  a 
bent  tube  of  -this  description  ;  and  carbonic  acid  by  heating  bicarbonate 
of  sodium  ;  other  gases  have  been  condensed  by  taking  advantage  of  special 
reactions,  the  consideration  of  which  belongs  rather  to  chemistry  than  to 
physics.  For  example,  chloride  of  silver  absorbs  about  200  times  its  volume 
of  ammoniacal  gas  ;  when  the  compound  thus  formed  is  placed  in  a 
freezing  tube  and  gently  heated,  while  the  shorter  leg  is  immersed  in  a 
freezing  mixture,  a  quantity  of  liquid  ammoniacal  gas  speedily  collects  in  the 
shorter  leg. 

381.  Apparatus  to  liquefy  and  solidify  gases. — Thilorier  first  con- 
structed an  apparatus  by  which  considerable  quantities  of  carbonic  acid 
could  be  liquefied.  Its  principle  is  the  same  as  that  used  by  Faraday  in 
working  with  glass  tubes  ;  the  gas  is  generated  in  an  iron  cylinder,  and 
passes  through  a  metal  tube  into  another  similar  cylinder,  where  it  con- 
denses. The  use  of  this  apparatus  is  not  free  from  danger  :  many  acci- 
dents have  already  happened  with  it,  and  it  has  been  superseded  by  an 
apparatus  constructed  by  Natterer,  of  Vienna,  which  is  both  convenient  and 
safe. 

A  perspective  view  of  the  apparatus,  as  modified  by  Bianchi,  is  repre- 
sented in  fig.  319,  and  a  section  on  a  larger  scale  in  fig.  318.  It  consists 
of  a  wrought-iron  reservoir  A,  of  something  less  than  a  quart  capacity, 
which  can  resist  a  pressure  of  more  than  600  atmospheres.  A  small  force- 
pump  is  screwed  on  the  lower  part  of  this  reservoir.  The  piston-rod  /  is 
moved  by  the  crank  rod  E,  which  is  worked  by  the  handle  M.  As  the 
compression  of  the  gas  and  the  friction  of  the  piston  produce  a  considerable 
disengagement  of  heat,  the  reservoir  A  is  surrounded  by  a  copper  vessel, 
in  which  ice  or  a  freezing  mixture  is  placed.  The  water  arising  from  the 
melting  of  the  ice  passes  by  a  tube  ;«,  into  a  cylindrical  copper  case  C, 
which  surrounds  the  force-pump,  from  whence  it  escapes  through  the 
tube  ??,  and  the  stopcock  o.  The  whole  arrangement  rests  on  an  iron 
frame,  PQ. 


-381] 


Apparatus  to  Liquefy  and  Solidify  Gases. 


319 


The  gas  to  be  liquefied  is  previously  collected  in  air-tight  bags,  R,  from 
whence  it  passes  into  a  bottle,  V,  containing  some  suitable  drying  substance ; 
it  then  passes  into  the  condensing  pump  through  the  vulcanised  india-rubber 
tube  H.  After  the  apparatus  has  been  worked  for  some  time  the  reservoir 
A  can  be  unscrewed  from  the  pump  without  any  escape  of  the  liquid,  for  it 
is  closed  below  by  a  valve  S  (fig.  318).  In  order  to  collect  some  of  the 


Fig.  319. 

liquid  gas,  the  reservoir  is  inverted,  and  on  turning  the  stopcock  r,  the  liquid 
escapes  by  a  small  tubulure  jr. 

When  carbonic  acid  has  been  liquefied,  and  is  allowed  to  escape  into  the 
air,  a  portion  only  of  the  liquid  volatilises  ;  in  consequence  of  the  heat  ab- 
sorbed by  this  evaporation,  the  rest  is  so  much  cooled  as  to  solidify  in 
white  flakes  like  snow  or  anhydrous  phosphoric  acid. 

Solid  carbonic  acid  evaporates  very  slowly.  By  means  of  an  alcohol 
thermometer  its  temperature  has  been  found  to  be  about  —90°.  A  small 
quantity  placed  on  the  hand  does  not  produce  the  sensation  of  such  great 


320  On  Heat.  [381- 

cold  as  might  be  expected.  This  arises  from  the  imperfect  contact.  But  if 
the  solid  be  mixed  with  ether  the  cold  produced  is  so  intense  that  when  a 
little  is  placed  on  the  skin  all  the  effects  of  a  severe  burn  are  produced.  A 
mixture  of  these  two  substances  solidifies  four  times  its  weight  of  mercury 
in  a  few  minutes.  When  a  tube  containing  liquid  carbonic  acid  is  placed 
in  this  mixture,  the  liquid  becomes  solid,  and  looks  like  a  transparent  piece 
of  ice. 

The  most  remarkable  liquefaction  obtained  by  this  apparatus  is  that  of 
protoxide  of  nitrogen.  The  gas  once  liquefied  only  evaporates  slowly,  and 
produces  a  temperature  of  88°  below  zero.  Mercury  placed  in  it  in  small 
quantities  instantly  solidifies.  The  same  is  the  case  with  water  :  it  must  be 
added  drop  by  drop,  otherwise,  its  latent  heat  being  much  greater  than  that 
of  mercury,  the  heat  given  up  by  the  water  in  solidifying  would  be  sufficient 
to  cause  an  explosion  of  the  protoxide  of  nitrogen. 

Protoxide  of  nitrogen  is  readily  decomposed  by  heat,  and  has  the  pro- 
perty of  supporting  the  combustion  of  bodies  with  almost  as  much  brilliancy 
as  oxygen  ;  and  even  at  low  temperatures  it  preserves  this  property.  When 
a  piece  of  incandescent  charcoal  i-s  thrown  on  liquid  protoxide  of  nitrogen 
it  continues  to  burn  with  a  brilliant  light. 

The  cold  produced  by  the  evaporation  of  ether  (373)  has  been  used  by 
Loir  and  Drion  in  the  liquefaction  of  gases.  By  passing  a  current  of  air 
from  a  blowpipe  bellows  through  several  tubes  into  a  few  ounces  of  ether, 
a  temperature  of  —  34°  C.  can  be  reached  in  five  or  six  minutes,  and  may  be 
kept  up  for  fifteen  or  twenty  minutes.  By  evaporating  liquid  sulphurous 
acid  in  the  same  manner  a  great  degree  of  cold,  —  50°  C.,  is  obtained.  At 
this  temperature  ammoniacal  gas  may  be  liquefied.  By  rapidly  evaporating 
liquid  ammonia  under  the  air-pump,  in  the  presence  of  sulphuric  acid,  a 
temperature  of  —87°  is  attained,  which  is  found  sufficient  to  liquefy  carbonic 
acid  under  the  ordinary  pressure  of  the  atmosphere. 

382.  Cailletet's  and  Pictet's  researches. — Cailletet  and  Pictet,  working 
independently,  but  simultaneously,  have  effaced  the  old  distinction  between 
permanent  and  non-permanent  gases,  by  effecting  the  condensation  of  the 
gases  oxygen  and  hydrogen,  and  other  gases  hitherto  supposed  to  be  in- 
coercible.  This  has  been  accomplished  by  means  of  powerful  material 
appliances  directed  with  great  skill  and  ingenuity. 

The  essential  parts  of  Cailletet's  apparatus  are  represented  in  fig.  320. 
The  gas  to  be  condensed  is  contained  in  the  tube  T  P,  which  is  fitted, 
by  means  of  a  bronze  screw,  A,  into  a  strong  wrought-iron  mercury 
bath,  B.  By  means  of  a  screw,  R  E,  and  a  tube,  U,  this  is  connected  with  a 
hydraulic  or  a  screw  press  not  represented  in  the  figure.  The  capillary  part, 
P,  of  the  tube  T,  is  placed  in  a  vessel  M,  in  which  it  can  be  surrounded 
by  a  freezing  mixture,  and  this  again  is  surrounded  by  a  stout  safety  bell 
jar,  C. 

When  a  pressure  of  250  to  300  atmospheres  is  applied  by  means  of  the 
hydraulic  press,  after  waiting  until  the  heat  due  to  the  compression  has  dis- 
appeared, if  a  screw  arranged  in  the  press  is  suddenly  opened,  the  pressure 
being  diminished,  the  cold  produced  by  the  sudden  expansion  of  the  gas  in 
the  tube  T  P  is  so  great  as  to  liquefy  a  portion  of  the  rest,  as  is  shown  by 
the  production  of  a  mist. 


-382]  Cailletefs  and  Pictet  's  Researches.  3  2  \ 

This  observation  was  first  made  with  binoxide  of  nitrogen,  but  similar 
results  have  been  obtained  with  marsh  gas,  carbonic  acid,  and  oxygen. 

The  principle  of  Pictet's  method  is  that  of 
liberating  the  gas  under  great  pressure  combined 
with  the  application  of  great  degrees  of  cold.  The 
essential  parts  of  the  apparatus  are  the  following  : — 
Two  double-acting  pumps,  A  and  B  (fig.  321),  are  so 
coupled  together  that  they  cause  the  evaporation 
of  liquid  sulphurous  acid  contained  in  the  annular 
receiver  C.  By  the  play  of  the  pumps  the  gas  thus 
evaporated  is  forced  into  the  receiver  D,  where  it 
is  cooled  by  a  current  of  water,  and  again  liquefied 
under  a  pressure  of  three  atmospheres.  Thence 
it  passes  again  by  the  narrow  tube,  d,  to  the  receiver 
C,  to  replace  that  which  is  evaporated. 

In  this  way  the  temperature  of  the  liquid  sul- 
phurous acid  is  reduced  to  —65°.  Its  function  is 
to  produce  a  sufficient  quantity  of  liquid  carbonic 
acid,  which  is  then  submitted  to  a  perfectly  ana- 
logous process  of  rarefaction  and  condensation. 
This  is  effected  by  means  of  two  similar  pumps,  E 
and  F.  The  carbonic  acid  gas,  perfectly  pure  and 
dry,  is  drawn  from  a  reservoir  through  a  tube  not 
represented  in  the  figure,  and  is  forced  into  the 
condenser  K,  which  is  cooled  by  the  liquid  sul- 
phurous acid,  to  a  temperature  of— 65°,  and  is  there 
liquefied. 

H  is  a  tube  of  stout  copper  in  connection  with 

the  condenser  K  by  a  narrow  tube  k.  When  a  sufficient  quantity  of  car- 
bonic acid  has  been  liquefied,  the  connection  with  the  gasholder  is  cut  off, 
and  by  working  the  pumps,  E  and  F,  a  vacuum  is  created  over  the  liquid 
carbonic  acid  in  H,  which  produces  so  great  a  cold  as  to  solidify  it. 

L  is  a  stout  wrought-iron  retort  capable  of  standing  a  pressure  of  1,500 
atmospheres.  In  it  are  placed  the  substances  by  whose  chemical  actions 
the  gas  is  produced  ;  potassium  chlorate  in  the  case  of  oxygen.  This  retort 
is  closed  by  a  strong  copper  tube  in  which  the  actual  condensation  is  effected, 
near  the  end  of  which  is  a  specially-constructed  manometer  R,  and  which  is 
closed  by  a  stopcock  X. 

When  the  four  pumps  are  set  in  action,  for  which  a  steam  engine  of  1 5 
horse-power  is  required,  heat  is  applied  to  the  retort.  Oxygen  is  liberated 
in  a  calculated  quantity,  the  temperature  of  the  retort  being  about  485°. 
Towards  the  close  of  the  decomposition  the  manometer  indicates  a  pressure 
of  500  atmospheres,  and  then  sinks  to  320.  This  diminution  is  due  to  the  con- 
densation of  gas,  and  at  this  stage  the  tube  contains  liquefied  oxygen.  If  the 
cock  N  is  opened,  the  gas  issues  with  violence,  having  the  appearance  of  a 
dazzling  white  pencil.  This  lasts  three  or  four  seconds.  On  closing  the 
stopcock  the  pressure,  which  had  diminished  to  400  atmospheres,  now  rises 
again,  and  again  becomes  stationary,  proving  that  the  gas  is  once  more 
being  condensed. 

P3 


322 


On  Heat. 


[382- 


The  phenomena  presented  by  the  jet  of  oxygen  when  viewed  by  the 
electric  light  showed  that  the  light  it  emits  was  partially  polarised,  indicating 
a  probable  transient  crystallisation  of  the  gas. 

For  hydrogen  the  gas  was  disengaged  by  heating  a  mixture  of  potassic 
formate  and  hydrate.  When  the  pressure  had  reached  650  atmospheres, 
and  the  cock  was  opened,  a  steel-blue  jet  issued  from  the  aperture  with  a 


brisk  noise.  This  suddenly  became  intermittent,  and  resembled  a  shower  of 
hailstones.  As  the  separate  granules  struck  the  ground,  they  produced  a  loud 
noise,  and  Pictet  considers  that  in  all  probability  the  hydrogen  in  the  interior 
was  frozen. 


MIXTURES   OF  GASES   AND  VAPOURS. 

383.  Laws  of  the  mixture  of  gases  and  vapours. — Every  mixture  of  a 
gas  and  a  vapour  obeys  the  following  two  laws  : — 

I.  The  tension,  and,  consequently,  the  quantity  of  vapour  which  saturates 
a  given  space,  are  the  same  for  the  same  temperature,  whether  this  space  con- 
tains a  gas  or  is  a  vacuum. 

II.  The  tension  of  the  mixture  of  a  gas  and  a  vapour  is  equal  to  the 
sum  of  the  tensions  which  each  would  possess  if  it  occupied  the  same  space 
alone. 

These  are  known  as  Daltoils  laws,  from  their  discoverer,  and  are  de- 
monstrated by  the  following  apparatus,  which  was  invented  by  Gay-Lussac  : — 
It  consists  of  a  glass  tube  A  (fig.  322),  to  which  two  stopcocks,  b  and  d,  are 
cemented.  The  lower  stopcock  is  provided  with  a  tubulure,  which  connects 


-383] 


Mixtures  of  Gases  and  Vapours. 


323 


the  tube  A  with  a  tube  B  of  smaller  diameter.     A  scale  between  the  two 

tubes   serves   to  measure  the   heights  of  the  mercurial   columns  in  these 

tubes. 

The  tube  A  is  filled  with  mercury,  and  the  stopcocks  b  and  d  are  closed. 

A  glass  globe  M,  filled  with  dry  air  or  any  other  gas,  is  screwed  on  by  means 

of  a  stopcock  in   the   place  of  the  funnel  C. 

All  three  stopcocks  are  then  opened,  and  a  little 

mercury  is  allowed  to  escape,  which  is  replaced 

by  the  dry  air  of  the  globe.     The  stopcocks  are 

then  closed,  and  as  the  air  in  the  tube  expands 

on  leaving  the  globe,  the  pressure  on  it  is  less 

than  that  of  the  atmosphere.  Mercury  is  ac- 
cordingly poured  into  the  tube  B  until  it  is  at 

the   same  level   in  both  tubes.     The  globe  is 

then  removed,  and  replaced  by  a  funnel  C,  pro- 
vided with  a  stopcock  a  of  a  peculiar  construc- 
tion. It  is  not  perforated,  but  has  a  small 

cavity,  as  represented  in  //,  on  the  left  of  the 

figure.     Some  of  the  liquid  to  be  vaporised  is 

poured  into  C,  and  the  height  of  the  mercury, 

/£,  having  been  noted,  the  stopcock  b  is  opened, 

and  a  turned,  so  that  its  cavity  becomes  filled 

with   liquid ;    being  again   turned,   the   liquid 

enters  the  space  A  and  vaporises.     The  liquid 

is  allowed  to  fall  drop  by  drop  until  the  air  in 

the  tube  is  saturated,  which  is  the  case  when 

the  level  k  of  the  mercury  ceases  to  sink  (353). 
As  the  tension  of  the  vapour  produced  in 

the  space  A  is  added  to  that  of  the  air  already 
present,  the  total  volume  of  gas  is  increased. 
It  may  easily  be  restored  to  its  original  volume 
by  pouring  mercury  into  B.  When  the  mercury 
in  the  large  tube  has  been  raised  to  the  level  k, 
there  is  a  difference  B  <?,  in  the  level  of  the 
mercury  in  the  two  tubes,  which  obviously  re- 
presents the  tension  of  the  vapour  ;  for  as  the  air  has  resumed  its  original 
volume,  its  tension  has  not  changed.  Now,  if  a  few  drops  of  the  same  liquid 
be  passed  into  the  vacuum  of  a  barometric  tube,  a  depression  exactly  equal 
to  B  o  is  produced,  which  proves  that,  for  the  same  temperature,  the  tension 
of  a  saturated  vapour  is  the  same  in  a  gas  as  in  a  vacuum  ;  from  which 
it  is  concluded  that  at  the  same  temperature  the  quantity  of  vapour  is  also 
the  same. 

The  second  law  is  likewise  proved  by  this  experiment,  for,  when  the 
mercury  has  regained  its  level,  the  mixture  supports  the  atmospheric  pres- 
sure on  the  top  of  the  column  B,  in  addition  to  the  weight  of  the  column  of 
mercury  B  o.  But  of  these  two  pressures,  one  represents  the  tension  of  the 
dry  air,  and  the  other  the  tension  of  the  vapour.  The  second  law  is,  more- 
over, a  necessary  consequence  of  the  first. 

Experiments  can  only  be  made  with  this  apparatus  at  ordinary  tempera- 


Fig.  322. 


324  On  Heat.  [383- 

tures  ;  but  Regnault,  by  means  of  an  apparatus  which  can  be  used  at  different 
temperatures,  investigated  the  tensions  of  the  vapours  of  water,  ether,  bisul- 
phide of  carbon,  and  benzole,  both  in  a  vacuum  and  in  air.  He  found  that 
the  tension  in  air  is  less  than  it  is  in  a  vacuum,  but  the  differences  are  so 
small  as  not  to  invalidate  Dalton's  law.  Regnault  was  even  inclined  to 
consider  this  law  as  theoretically  true,  attributing  the  differences  which  he 
observed  to  the  hygroscopic  properties  of  the  sides  of  the  tube. 

384.  Problems  on  mixtures  of  gases  and  vapours.  —  i.  A  volume  of 
dry  air  V,  at  the  pressure  H,  being  given,  what  will  be  its  volume  V,  when 
it  is  saturated  with  vapour,  the  temperature  and  the  pressure  remaining  the 
same  ? 

If  F  be  the  elastic  force  of  the  vapour  which  saturates  the  air,  the 
latter,  in  the  mixture,  only  supports  a  pressure  equal  to  H  —  F  (381).  But 
by  Boyle's  law  the  volumes  V  and  V  are  inversely  as  their  pressures, 
consequently 

V'  =  ff 

ii.  Let  V  be  a  given  volume  of  saturated  air  at  the  pressure  H,  and  the 
temperature  t\  what  will  be  its  volume  V,  also  saturated,  at  the  pressure  H', 
and  the  temperature  t'  ? 

If  /be  the  maximum  tension  of  aqueous  vapour  at  /°,  and/'  its  maximum 
tension  at  /"°,  the  air  alone  in  each  of  the  mixtures  V  and  V  will  be  respec- 
tively under  the  pressures  H  -  f  and  H'  -  f  ;  consequently,  assuming  first 
that  the  temperature  is  constant,  we  obtain 


But  as  the  volumes  V  and  V  of  air,  at  the  temperatures  /'  and  /,  are  in  the 
ratio  of  i  +  at'  to  i  +  a/,  a  being  the  coefficient  of  the  expansion  of  air,  the 
equation  becomes 

V'      H- 


V"     H'-/      I+a/' 

iii.  What  is  the  weight  P  of  a  volume  of  air  V,  saturated  with  aqueous 
vapour  at  the  temperature  /  and  pressure  H  ? 

If  we  call  F  the  maximum  tension  of  the  vapour  at  /°,  the  tension  of  the 
air  alone  will  be  H  -F,  and  the  problem  reduces  itself  to  finding  :  ist,  the 
weight  of  V  cubic  inches  of  dry  air  at  /,  and  under  the  pressure  H  —  F  ;  and 
2nd,  the  weight  of  V  cubic  inches  of  saturated  vapour  at  t°  under  the 
pressure  F. 

To  solve  the  first  part  of  the  problem,  we  know  that  a  cubic  inch  of  dry 
air  at  o°  and  the  pressure  760  millimetres  weighs  0*31  grain,  and  that  at  /°, 

and  the  pressure  H  —  F,  it  weighs  °-3J_(  —  ;  '_)  (330),  consequently  V  cubic 

(i  +a/)7oo 

inches  of  dry  air  weigh 

o-3i(H-F)V  ,, 

(I  +  at]  760     ' 

To  obtain  the  weight  of  the  vapour,  the  weight  of  the  same  volume  of 
dry  air  at  the  same  temperature  and  pressure  must  be  sought,  and  this  is  to 


-385]  Spheroidal  Condition.  325 

be  multiplied  by  the  relative  density  of  the  vapour.  Now  as  V  cubic  inches 
of  dry  air  at  /°,  and  the  pressure  F,  weigh  Q'31  x  VF  y  cubjc  jnches  of 

(I  +  at)  760 

aqueous  vapour,  whose  density  is  \  of  that  of  air  (385),  weigh 

0-31  xVF  ^5 
(I  -fa/)  760     8 (2) 

and  as  the  weight  P  is  equal  to  the  sum  of  the  weights  (i)  and  (2)  we  have 

p_o-3ixV  (H-F)+  0-31  xVF  x5_^  0-31  xVF   /H_3F) 
(I  +a/)700  (I  +  at}  760  X  8     (I  +  at)  760  ^ 

SPHEROIDAL  CONDITION. 

385.  Xieidenfrost's  phenomenon. — Boutigny  s  experiments. — When 
liquids  are  thrown  upon  incandescent  metal  surfaces  they  present  remark- 
able phenomena,  which  were  first  observed  by  Leidenfrost  a  century  ago, 
and  have  been  named  after  their  discoverer.  They  have  since  then  been 
studied  by  other  physicists,  and  more  especially  by  Boutigny. 

Figure  323  represents  an  interesting  method  of  illustrating  this.  F  is  a 
small  copper  flask  which  is  heated  to  dull  redness  over  a  spirit  lamp,  and  a 
small  quantity  of  boiling  hot 
water  is  carefully  introduced  ; 
a  cork  C  having  been  loosely 
fitted,  the  lamp  is  removed, 
and  in  a  short  time  steam  is 
formed  rapidly  with  such  ex- 
plosive violence  as  to  drive 
out  the  cork. 

\Vhen  a  tolerably  thick 
silver  or  platinum  dish  is 
heated  to  redness,  and  a  little 
water,  previously  warmed,  is 
dropped  into  the  dish  by 
means  of  a  pipette,  the  liquid 

does  not  spread  itself  out  on  the  dish,  and  does  not  moisten  it,  as  it  would 
at  the  ordinary  temperature,  but  assumes  the  form  of  a  flattened  globule, 
which  fact  Boutigny  expresses  by  saying  that  it  has  passed  into  the  sphe- 
roidal state.  It  rotates  rapidly  round  on  the  bottom  of  the  dish,  taking 
sometimes  the  form  of  a  star,  and  not  only  does  it  not  boil,  but  its 
evaporation  is  only  about  one-fiftieth  as  rapid  as  if  it  boiled.  As  the  dish 
cools,  a  point  is  reached  at  which  it  is  not  hot  enough  to  keep  the  water  in 
the  spheroidal  state  ;  it  is  accordingly  moistened  by  the  liquid,  and  a  violent 
ebullition  suddenly  ensues. 

All  volatile  liquids  can  assume  the  spheroidal  condition  ;  the  lowest 
temperature  at  which  it  can  be  produced  varies  with  each  liquid,  and  is 
more  elevated  the  higher  the  boiling  point  of  the  liquid.  For  water,  the 
dish  must  have  at  least  a  temperature  of  200°;  for  alcohol,  134°  ;  and  for 
ether,  61°. 


326  On  Heat.  [385- 

The  temperature  of  a  liquid  in  the  spheroidal  state  is  always  below  its 
boiling  point.  This  temperature  has  been  measured  by  Boutigny  by  means 
of  a  very  delicate  thermometer  ;  but  his  method  is  not  free  from  objections, 
and  it  is  probable  that  the  temperatures  he  obtained  were  too  high.  He 
found  that  of  water  to  be  95°  ;  alcohol,  75°  ;  ether,  34°  ;  and  liquid  sulphur- 
ous acid, -11°.  But  the  temperature  of  the  vapour  which  is  disengaged 
appears  to  be  as  high  as  that  of  the  vessel  itself. 

This  property  of  liquids  in  the  spheroidal  state  remaining  below  their 
boiling  point  has  been  applied  by  Boutigny  in  a  remarkable  experiment, 
that  of  freezing  water  in  a  red-hot  crucible.  He  heated  a  platinum  dish  to 
bright  redness,  and  placed  a  small  quantity  of  liquid  sulphurous  acid  in  it. 
It  immediately  assumed  the  spheroidal  condition,  and  its  evaporation  was 
remarkably  slow.  Its  temperature,  as  has  been  stated,  was  about  —  11°,  and 
when  a  small  quantity  of  water  was  added,  it  immediately  solidified,  and  a 
small  piece  of  ice  could  be  thrown  out  of  the  red-hot  crucible.  In  a  similar 
manner  Faraday,  by  means  of  a  mixture  of  solid  carbonic  acid  and  ether, 
succeeded  in  freezing  mercury  in  a  red-hot  crucible. 

In  the  spheroidal  state,  the  liquid  is  not  in  contact  with  the  vessel. 
Boutigny  proved  this  by  heating  a  silver  plate  placed  in  a  horizontal  position 
and  dropping  on  it  a  little  dark-coloured  water.  The  liquid  assumed  the 
spheroidal  condition,  and  the  flame  of  a  candle  placed  at  some  distance 
could  be  distinctly  seen  between  the  drop  and  the  plate.  If  a  plate  perforated 
by  several  fine  holes  be  heated,  a  liquid  will  assume  the  spheroidal  state 
when  projected  upon  it.  This  is  also  the  case  with  a  flat  helix  of  platinum 
wire  pressed  into  a  slightly  concave  shape.  An  experiment  of  another  class, 
due  to  Prof.  Church,  also  illustrates  the  same  fact.  A  polished  silver  dish 
is  made  red-hot,  and  a  few  drops  of  a  solution  of  sulphide  of  sodium  are  pro- 
jected on  it.  The  liquid  passes  into  the  spheroidal  condition,  and  the  silver 
undergoes  no  alteration.  But  if  the  dish  is  allowed  to  cool,  the  liquid  instantly 
moistens  it,  producing  a  dark  spot,  due  to  the  formation  of  sulphide  of  silver. 
In  like  manner  nitric  acid  assumes  the  spheroidal  state  when  projected  on  a 
heated  silver  plate,  and  does  not  attack  the  metal  so  long  as  the  plate  remains 
hot. 

An  analogous  phenomenon  is  observed  when  potassium  is  placed  on 
water.  Hydrogen  is  liberated,  and  burns  with  a  yellow  flame  ;  hydrate  of 
potassium,  which  is  formed  at  the  same  time,  floats  on  the  surface  without 
touching  it,  owing  to  its  high  temperature.  In  a  short  time  it  cools  down, 
and  the  globule  coming  in  contact  with  water  bursts  with  an  explosion. 

Similarly,  liquids  may  be  made  to  roll  upon  liquids,  and  solid  bodies 
which  vaporise  without  becoming  liquid  also  assume  a  condition  analogous 
to  the  spheroidal  state  of  liquids  when  they  are  placed  on  a  surface  whose 
temperature  is  sufficiently  high  to  vaporise  them  rapidly.  This  is  seen  when 
a  piece  of  carbonate  of  ammonium  is  placed  in  a  red-hot  platinum  crucible. 

The  phenomena  of  the  spheroidal  state  seem  to  prove  that  the  liquid 
globule  rests  upon  a  sort  of  cushion  of  its  own  vapour,  produced  by  the  heat 
radiated  from  the  hot  surface  against  its  under  side.  As  fast  as  this  vapour 
escapes  from  under  the  globule,  its  place  'is  supplied  by  a  fresh  quantity 
formed  in  the  same  way,  so  that  the  globule  is  constantly  buoyed  up  by  it, 
and  does  not  come  in  actual  contact  with  the  heated  surface.  When,  how- 


-386] 


Density  of  Vapours. 


327 


ever,  the  temperature  of  the  latter  falls,  the  formation  of  vapour  at  the  under 
surface  becomes  less  and  less  rapid,  until  at  length  it  is  not  sufficient  to  pre- 
vent the  globule  touching  the  hot  metal  or  liquid  on  which  it  rests.  As  soon 
as  contact  occurs,  heat  is  rapidly  imparted  to  the  globule,  it  enters  into  ebul- 
lition, and  quickly  boils  away. 

This  explanation  is  confirmed  by  the  experiments  of  Budde,  who  found 
that  in  an  exhausted  receiver  water  passes  into  the  spheroidal  state,  even 
when  the  temperature  of  the  support  is  not  more  than  80°  or  90° ;  for  then 
the  vapour  has  only  to  support  the  drop,  and  not  the  atmospheric  pressure 
also. 

These  experiments  on  the  spheroidal  state  explain  the  fact  that  the  hand 
may  be  dipped  into  melted  lead,  or  even  melted  iron,  without  injury.  It  is 
necessary  that  the  liquid  metal  be  heated  greatly  above  its  solidifying  point. 
Usually  the  natural  moisture  of  the  hand  is  sufficient,  but  it  is  better  to  wipe 
it  with  a  damp  cloth.  In  consequence  of  the  great  heat  the  hand  becomes 
covered  with  a  layer  of  spheroidal  fluid,  which  prevents  the  contact  of  the 
metal  with  the  hand.  Radiant  heat  alone  operates,  and  this  is  principally 
expended  in  forming  aqueous  vapour  on  the  surface  of  the  hand.  If  the 
hand  is  immersed  in  boiling  water,  the  water  adheres  to  the  flesh,  and  con- 
sequently a  scald  is  produced. 

The  tales  of  ordeals  by  fire  during  the  middle  ages,  of  men  who  could 
run  barefooted  over  red-hot  iron  without  being 
injured,   are   possibly  true  in  some  cases,  and 
would    find    an   explanation   in   the   preceding 
phenomena. 

DENSITY  OF  VAPOURS. 

386.  Gay-Xiussac's  method. — The  density 
of  a  vapour  is  the  relation  between  the  weight 
of  a  given  volume  of  this  vapour  and  that  of 
the  same  volume  of  air  at  the  same  temperature 
and  pressure. 

Two  methods  principally  are  used  in  de- 
termining the  density  of  vapours  :  Gay-Lussac's, 
which  serves  for  liquids  that  boil  at  about  100°, 
and  Dumas',  which  can  be  used  up  at  350°. 

Fig.  324  represents  the  apparatus  used  by 
Gay-Lussac.  It  consists  of  an  iron  vessel  con- 
taining mercury,  in  which  there  is  a  glass  cyl- 
inder, M.  This  is  filled  with  water  or  oil,  and 
the  temperature  is  indicated  by  the  thermo- 
meter, T.  In  the  interior  of  the  cylinder  is  a 
graduated  gas  jar,  C,  which,  at  first,  is  filled 
with  mercury. 

The  liquid  whose  vapour  density  is  to  be  determined  is  placed  in  a  small 
glass  bulb,  A,  represented  on  the  left  of  the  figure.  The  bulb  is  then  sealed 
and  weighed  ;  the  weight  of  the  liquid  taken  is  obviously  the  weight  of  the 
bulb  when  filled,  minus  its  weight  while  empty.  The  bulb  is  then  intro- 


324- 


Let/  be  *r  vegkt  rf tike 


-388]  Dumas  Method. 

in  the  case  of  those  bodies  which  decompose  at  the  boiling  point  under 
ordinary  pressure. 

388.  Dumas'  method. — The  method  just  described  cannot  be  applied  to 
liquids  whose  boiling  point  exceeds  150°  or  160°.  In  order  to  raise  the  oil 
in  the  cylinder  to  this  temperature  it  would  be  necessary  to  heat  the  mercury 
to  such  a  degree  that  the  mercurial  vapours  would  be  dangerous  to  the 
operator.  And,  moreover,  the  tension  of  the  mercurial  vapours  in  the 
graduated  jar  would  increase  the  tension  of  the  vapour  of  the  liquid,  and  so 
far  vitiate  the  result. 

The  following  method,  devised  by  Dumas,  can  be  used  up  to  the  tem- 
perature at  which  glass  begins  to  soften  ;  that  is,  about  400°.  A  glass 
globe  is  used  with  the  neck  drawn  out  to  a  fine  point  (fig.  325).  The  globe, 
having  been  dried  externally  and  internally,  is  weighed,  the  temperature  / 
and  barometic  height  h  being  noted.  This  weight,  W,  is  the  weight  of  the 
glass  G  in  addition  to  /,  the  weight  of  the  air  it  contains.  The  globe  is 
then  gently  warmed  and  its  point  immersed  in  the  liquid  whose  vapour 
density  is  to  be  determined  :  on  cooling,  the  air  contracts,  and  a  quantity 
of  liquid  enters  the  globe.  The  globe  is  then  immersed  in  a  bath,  either 
of  oil  or  fusible  metal,  according  to  the  tempera- 
ture to  which  it  is  to  be  raised.  In  order  to  keep 
the  globe  in  a  vertical  position  a  metal  support, 
on  which  a  movable  rod  slides,  is  fixed  on  the 
side  of  the  vessel.  This  rod  has  two  rings,  be- 
tween which  the  globe  is  placed,  as  shown  in  the 
figure.  There  is  another  rod,  to  which  a  weight 
thermometer,  D,  is  attached. 

The  globe  and  thermometer  having  been  im- 
mersed in  the  bath,  the  latter  is  heated  until 
slightly  above  the  boiling  point  of  the  liquid  in 
the  globe.  The  vapour  which  passes  out  by  the 
point  expels  all  the  air  in  the  interior.  When 
the  jet  of  vapour  ceases,  which  is  the  case  when 
all  the  liquid  has  been  converted  into  vapour,  the 
point  of  the  globe  is  hermetically  sealed,  the 
temperature  of  the  bath  /",  and  the  barometric 
height  //',  being  noted.  When  the  globe  is  cooled, 
it  is  carefully  cleaned  and  again  weighed.  This 

weight,  W,  is  that  of  the  glass,  G,  plus/',  the  weight  of  the  vapour  which  fills 
the  globe  at  the  temperature  /',  and  pressure  h',  or  W'  =  G+/'.  To  obtain 
the  weight  of  the  glass  alone,  the  weight  p  of  air  must  be  known,  which  is 
determined  in  the  following  manner  : — The  point  of  the  globe  is  placed  under 
mercury  and  the  extremity  broken  off  with  a  small  pair  of  pincers  :  the 
vapour  being  condensed,  a  vacuum  is  produced,  and  mercury  rushes  up, 
completely  filling  the  globe,  if,  in  the  experiment,  all  the  air  has  been  com- 
pletely expelled.  The  mercury  is  then  poured  into  a  carefully  graduated 
measure  which  gives  the  volume  of  the  globe.  From  this  result,  the  volume 
of  the  globe  at  the  temperature  f  may  be  easily  calculated,  and  consequently 
the  volume  of  the  vapour.  From  this  determination  of  the  volume  of  the 
globe  the  weight  p  of  the  air  at  the  temperature  /  and  pressure  h  is  readily 


330  On  Heat.  [388- 

calculated,  and  this  result  subtracted  from  W  gives  G,  the  weight  of  the 
glass.  Now  the  weight  of  the  vapour  p'  is  W  —  G.  We  now  know  the 
weight  p'  of  a  given  volume  of  vapour  at  the  temperature  t'  and  pressure  //, 
and  it  is  only  necessary  to  calculate  the  weight  p"  of  the  same  volume  of 
air  under  the  same  conditions,  which  is  easily  accomplished.  The  quotient 

j£  is  the  required  density  of  the  vapour. 

Densities  of  Vapours. 

Air 1-0004  Vapour  of  carbon  bisulphide  2-6447 

Vapour  of  water    .         .         .     0-6235  „          phosphorus.         .  4-3256 

„         alcohol.         .         .1-6138  „          turpentine    .         .  5-0130 

„        acetic  acid    .         .     2-0800  „          sulphur        .         .  6-6542 

„         ether     .         .         .     2-5860  „          mercury       .         .  6-9760 

„         benzole          .         .     2729  „          iodine           .         .  87160 

The  density  of  aqueous  vapour,  when  a  space  is  saturated  with  it,  is  at 
all  temperatures  f,  or,  more  accurately,  0-6225,  of  the  density  of  air  at  the 
same  temperature  and  pressure. 

389.  Modifications  of  Dumas'  method. — Deville  and  Troost  have  modi- 
fied Dumas'  method  so  that  it  can  be  used  for  determining  the  vapour  density 
of  liquids  with  very  high  boiling  points.     The  globe  is  heated  in  an  iron  cylin- 
der in  the  vapour  of  mercury  or  of  sulphur,  the  temperatures  of  which  are 
constant  respectively  at  350°  and  440°.     In  other  respects  the  determination 
is  the  same  as  in  Dumas'  method. 

For  determinations  at  higher  temperatures,  Deville  and  Troost  have 
employed  the  vapour  of  zinc,  the  temperature  of  which  is  1040°.  As  glass 
vessels  are  softened  by  this  heat,  they  use  porcelain  globes  with  finely  drawn- 
out  necks,  which  are  sealed  by  means  of  the  oxyhydrogen  flame. 

In  the  case  of  substances  having  a  high  boiling  point,  Victor  Meyer  has 
advantageously  used  a  non-volatile  substance,  Wood's  fusible  alloy,  which 
melts  at  70°,  instead  of  mercury.  Habermann  has  introduced  into  Dumas' 
method,  Hofmann's  modification  of  Gay-Lussac's,  by  connecting  the  open 
end  of  the  vessel  B  (fig.  325)  with  a  space  in  which  a  partial  vacuum  is  made. 
Thus  the  vapour  density  can  be  determined  for  temperatures  far  below  the 
boiling  point. 

390.  Relation  between  the  volume  of  a  liquid  and  that  of  its  vapour. 
—The  density  of  vapour  being  known,  we  can  readily  calculate  the  ratio 

between  the  volume  of  a  vapour  in  the  saturated  state  at  a  given  temperature, 
and  that  of  its  liquid  at  zero.  We  may  take,  as  an  example,  the  relation 
between  water  at  zero  and  steam  at  100°. 

The  ratio  between  the  weights  of  equal  volumes  of  air  at  zero,  and  the 
normal  barometric  pressure,  and  of  water  under  the  same  circumstances,  is 
as  i  :  773.  But  from  what  has  been  already  said  (332),  the  density  of 
air  at  zero  is  to  its  density  at  100°  as  I  +  at  :  i.  Hence  the  ratio  between  the 
weights  of  equal  volumes  of  air  at  100°  and  water  at  o°  is 

.  +  0-003665  x. 00=    773'  °r   °73'78  =  m' 


-390]  Density  of  Vapours.  331 

Now  from  the  above  table  the  density  of  steam  at  100°  C.,  and  the 
normal  pressure,  compared  with  that  of  air  under  the  same  circumstances, 
is  as  0-6225  •  i-  Hence  the  ratio  between  the  weights  of  equal  volumes  of 
steam  at  100°,  and  water  at  o°,  is 

073178  x  0-6225  :  773,  or  Q'4555  '•  773  or  i  :  l698- 

Therefore,  as  the  volumes  of  bodies  are  inversely  as  their  densities,  one 
volume  of  water  at  zero  expands  into  1698  volumes  of  steam  at  100°  C. 
The  practical  rule  that  a  cubic  inch  of  water  yields  a  cubic  foot  of  steam 
though  not  quite  accurate,  expresses  the  relation  in  a  convenient  form. 


332  On  Heat.  [391- 


CHAPTER  VI. 

HYGROMETRY. 

391.  Province  of  hygrometry. — The  province  of  hygrometry  is  to  deter- 
mine the  quantity  of  aqueous  vapour  contained  in  a  given  volume  of  air. 
This   quantity  is  very  variable  ;    but  the  atmosphere    is  seldom  or  never 
completely  saturated   with   vapour,   even  in  our  climate.     Nor  is  it  ever 
completely  dry  ;  for  if  hygromett  ic  substances — that  is  to  say,  substances  with 
a  great  affinity  for  water,  such  as  chloride  of  calcium,  sulphuric  acid,  &c. — be 
at  any  time  exposed  to  the  air,  they  absorb  aqueous  vapour. 

392.  Hygrometric  state. — As,  in  general,  the  air  is  never  saturated,  the 
ratio  of  the  quantity  of  aqueous  vapour  actually  present  in  the  atmosphere 
to  that  which  it  would  contain  if  it  were  saturated,  the  temperature  remaining 
the  same,  is  called  the  hygrometric  state,  or  degree  of  saturation. 

The  absolute  moisture  is  measured  by  the  weight  of  water  actually  present 
in  the  form  of  vapour  in  the  unit  of  volume. 

We  say  the  'air  is  dry'  when  water  evaporates  and  moist  objects  dry 
rapidly  ;  and  the  *  air  is  moist '  when  they  do  not  dry  rapidly,  and  when 
the  least  lowering  in  temperature  brings  about  deposits  of  moisture.  The 
air  is  dry  or  moist,  according  as  it  is  more  or  less  distant  from  its  point 
of  saturation.  Our  judgment  is,  in  this  respect,  independent  of  the  absolute 
quantity  of  moisture  in  the  air.  Thus,  if  in  summer,  at  a  temperature  of 
25°  C,  we  find  that  each  cubic  metre  of  air  contains  13  grammes  of  vapour, 
we  say  it  is  very  dry,  for,  at  this  temperature,  it  could  contain  22-5  grammes. 
If,  on  the  other  hand,  in  winter  we  find  that  the  same  volume  contains 
6  grammes,  we  call  it  moist,  for  it  is  nearly  saturated  with  vapour,  and  the 
slightest  diminution  of  temperature  produces  a  deposit.  When  a  room  is 
warmed,  the  quantity  of  moisture  is  not  diminished,  but  the  humidity  of  the 
air  is  lessened,  because  its  point  of  saturation  is  raised.  The  air  may  thus 
become  so  dry  as  to  be  injurious  to  the  health,  and  it  is  hence  usual  to  place 
vessels  of  water  on  the  stoves  used  for  heating. 

As  Boyle's  law  applies  to  non-saturated  vapours  as  well  as  to  gases  (354), 
it  follows  that,  with  the  same  temperature  and  volume,  the  weight  of  vapour 
in  a  non-saturated  space  increases  with  the  pressure,  and  therefore  with  the 
tension  of  the  vapour  itself.  Instead,  therefore,  of  the  ratio  of  the  quantities 
of  vapour,  that  of  the  corresponding  tensions  maybe  substituted,  and  it  may 
be  said  that  the  hygrometric  state  is  the  ratio  of  the  elastic  force  of  the  aqueous 
vapour  which  the  air  actually  contains,  to  the  elastic  force  of  the  vapour  which 
it  would  contain  at  the  same  temperature  if  it  were  saturated. 

If/ is  the  actual  tension  of  aqueous  vapour  in  the  air,  and  F  that  of  satu- 


-394]  Chemical  Hygrometer.  333 

rated  vapour  at  the  same  temperature,  and  E  the  hygrometric  state,  we  have 
E  -   *  ;  whence  f-  F  x  E. 

As  a  consequence  of  this  second  definition,  it  is  important  to  notice  that, 
the  temperature  having  varied,  the  air  may  contain  the  same  quantity  of 
vapour  and  yet  not  have  the  same  hygrometric  state.  For,  when  the  tem- 
perature rises,  the  tension  of  the  vapour  which  the  air  would  contain,  if  satu- 
rated, increases  more  rapidly  than  the  tension  of  the  vapour  actually  present 
in  the  atmosphere,  and  hence  the  ratio  between  the  two  forces — that  is  to  say, 
the  hygrometric  state — becomes  smaller. 

It  will  presently  be  explained  (401)  how  the  weight  of  the  vapour  con- 
tained in  a  given  volume  of  air  may  be  deduced  from  the  hygrometric  state. 

393.  Different  kinds  of  hygrometers. — Hygrometers  are  instruments 
for  measuring  the  hygrometric  state  of  the  air.     There  are  numerous  varie- 
ties of  them — chemical  hygrometers,  condensing  hygrometers,  and  psychro- 
meters. 

394.  Chemical  hygrometer. — The  method  of  the  chemical  hygrometer 
consists  in  passing  a  known  volume  of  air  over  a  substance  which  readily 
absorbs  moisture — chloride  of  calcium,  for  instance.     The  substance  having 
been  weighed  before  the  passage  of  air,  and  then  afterwards,  the  increase  in 
weight  represents  the  amount  of  aqueous  vapour  present  in  the  air.     By 
means  of  the  apparatus  represented  in  fig.  326,  it  is  possible  to  examine  any 


Fig.  326. 

given  volume  of  air.  Two  brass  reservoirs,  A  and  B,  of  the  same  size  and 
construction,  act  alternately  as  aspirators,  by  being  fixed  to  the  same  axis, 
about  which  they  can  turn.  They  are  connected  by  a  central  tubulure,  and 
by  means  of  two  tubulures  in  the  axis  the  lower  reservoir  is  always  in  con- 
nection with  the  atmosphere,  while  the  upper  one,  by  means  of  a  caoutchouc 


334 


On  Heat. 


[394-^ 


tube,  is  connected  with  two  tubes  M  and  N,  filled  either  with  chloride  of 
calcium,  or  with  pumice-stone  impregnated  with  sulphuric  acid.  The  first 
absorbs  the  vapours  in  the  air  drawn  through,  while  the  other,  M,  stops  any 
vapour  which  might  diffuse  from  the  reservoirs  to  the  tube  N. 

The  lower  reservoir  being  full  of  water,  and  the  upper  one  of  air,  the 
apparatus  is  inverted  so  that  the  liquid  flows  slowly  from  A  to  B.  A  vacuum 
being  formed  in  A,  air  enters  by  the  tubes  NM,  in  the  first  of  which  all  the 
vapour  is  absorbed.  When  all  the  water  is  run  into  B  it  is  inverted  ;  the 
same  flow  recommences,  and  the  same  volume  of  air  is  drawn  through  the 
tube  N.  Thus,  if  each  reservoir  holds  a  gallon,  for  example,  and  the  ap- 
paratus has  been  turned  five  times,  6  gallons  of  air  have  traversed  the 
tube  N,  and  have  been  dried.  If  then,  before  the  experiment,  the  tube  with 
its  contents  has  been  weighed,  the  increase  in  weight  gives  the  weight  of 
aqueous  vapour  present  in  6  gallons  of  air  at  the  time  of  the  experiment. 

Edelmann  has  devised  a  new  form  of  hygrometer  the  principle  of  which 
is  to  enclose  a  given  volume  of  air,  and  then  to  absorb  the  aqueous  vapour 
present  by  means  of  strong  sulphuric  acid  ;  in  this  way  a  diminution  in  the 
pressure  is  produced  which  is  determined  and  which  is  a  direct  measure  of 
the  tension  of  the  aqueous  vapour  previously  present. 

395.  Condensing:  hygrometers. — When  a  body  gradually  cools  in  a 
moist  atmosphere,  as,  for  instance,  when  a  lump  of  ice  is  placed  in  water 
contained  in  a  polished  metal  vessel,  the  layer  of  air  in  immediate  contact 

with  it  cools  also,  and  a  point  is  ultimately 
reached  at  which  the  vapour  present  is  just 
////  sufficient  to  saturate  the  air  ;  the  least  dim- 
inution of  temperature  then  causes  a  precipi- 
tation of  moisture  on  the  vessel  in  the  form 
of  dew.  When  the  temperature  rises  again, 
the  dew  disappears.  The  mean  of  these 
two  temperatures  is  taken  at  the  dew  point, 
and  the  object  of  condensing  hygrometers 
is  to  observe  this  point.  Daniell's  and  Reg- 
nault's  hygrometers  belong  to  this  class. 

396.  Daniell's  hygrometer. — This  con- 
sists of  two  glass  bulbs  at  the  extremities  of 
a  glass  tube  bent  twice  (fig.  327).  The  bulb 
A  is  two-thirds  full  of  ether,  and  a  very  deli- 
cate thermometer  plunges  in  it ;  the  rest  of 
the  space  contains  nothing  but  the  vapour 
of  ether,  the  ether  having  been  boiled  before 
the  bulb  B  was  sealed.  The  bulb  B  is  covered 
with  muslin  and  ether  is  dropped  upon  it. 
The  ether  in  evaporating  cools  the  bulb,  and 
the  vapour  contained  in  it  is  condensed. 
The  internal  tension  being  thus  diminished, 

In 

proportion  as  the  liquid  distils  from  the  lower  to  the  upper  bulb,  the  ether 
in  A  becomes  cooler,  and  ultimately  the  temperature  of  the  air  in  immediate 
contact  with  A  sinks  to  that  point  at  which  its  vapour  is  more  than  sufficient 


Fig.  327. 

the  ether  in  A  forms  vapours  which  condense  in  the  other  bulb  B. 


-397] 


Regnault  's  Hygrometer. 


335 


to  saturate  it,  and  it  is,  accordingly,  deposited  on  the  outside  as  a  ring  of 
dew  corresponding  to  the  surface  of  the  ether.  The  temperature  of  this 
point  is  noted  by  means  of  the  thermometer  in  the  inside.  The  addition 
of  ether  to  the  bulb  B  is  then  discontinued,  the  temperature  of  A  rises  and 
the  temperature  at  which  the  dew  disappears  is  noted.  In  order  to  render 
the  deposition  of  dew  more  perceptible,  the  bulb  A  is  made  of  black  glass. 

These  two  points  having  been  determined,  their  mean  is  taken  as  that  of 
the  dew  point.  The  temperature  of  the  air  at  the  time  of  the  experiment  is 
indicated  by  the  thermometer  on  the  stem.  The  tension/  corresponding  to 
the  temperature  of  the  dew  point,  is  then  found  in  the  table  of  tensions  (358). 
This  tension  is  exactly  that  of  the  vapour  present  in  the  air  at  the  time  of 
the  experiment.  The  tension  F  of  vapour  saturated  at  the  temperature  of 
the  atmosphere  is  found  by  means  of  the  same  table ;  the  quotient  obtained 
by  dividing  /  by  F  represents  the  hygrometric  state  of  the  air  (392).  For 
instance,  the  temperature  of  the  air  being  1 5°,  suppose  the  dew  point  is  5°. 
From  the  table  the  corresponding  tensions  are  /=  6-534  millimetres,  and 
F  =  12-699  millimetres,  which  gives  0-514  for  the  ratio  of /to  F,  or  the 
hygrometric  state. 

There  are  many  sources  of  error  in  Daniell's  hygrometer.  The  principal 
are  :  ist,  that  as  the  evaporation  in  the  bulb  A  only  cools  the  liquid  on  the 
surface,  the  thermometer  dipping  on  it  does  not  exactly  give  the  dew  point ; 
2nd,  that  the  observer 
standing  near  the  in-  \t 

strument  modifies  the 
hygrometric  state  of 
the  surrounding  air, 
as  well  as  its  tempera- 
ture ;  the  cold  ether 
vapour  too  flowing 
from  the  upper  bulb 
may  cause  inaccuracy. 

397.  Reg-nault's 
hygrometer.  —  Reg- 
nault's  hygrometer  is 
free  from  the  sources 
of  error  incidental  to 
the  use  of  Daniell's. 
It  consists  of  two  very 
thin  polished  silver 
thimbles  175  inch  in 
height,  and  0-75  inch 
in  diameter  (fig.  328). 
In  these  are  fixed  two 
glass  tubes,  D  and  E, 
in  each  of  which  is  a 

thermometer.  A  bent  tube,  A,  open  at  both  ends,  passes  through  the  cork 
of  the  tube  D,  and  reaches  nearly  to  the  bottom  of  the  thimble.  There  is  a 
tubulure  on  the  side  of  D,  fitting  in  a  brass  tube  which  forms  a  support  for 
the  apparatus.  The  end  of  this  tube  is  connected  with  an  aspirator  G. 


336 


On  Heat. 


[397- 


The  tube  E  is  not  connected  with  the  aspirator ;  its  thermometer  simply 
indicates  the  temperature  of  the  atmosphere. 

The  tube  D  is  then  half  filled  with  ether,  and  the  stopcock  of  the  aspirator 
opened.  The  water  contained  in  it  runs  out,  and  just  as  much  air  enters 
through  the  tube  A,  bubbling  through  the  ether,  and  causing  it  to  evaporate. 
This  evaporation  produces  a  diminution  of  temperature,  so  that  dew  is  de- 
posited on  the  silver  just  as  on  the  bulb  in  Daniell's  hygrometer  ;  the  ther- 
mometer T  is  then  instantly  to  be  read,  and  the  stream  from  the  aspirator 
stopped.  The  dew  will  soon  disappear  again,  and  the  thermometer  T  is 
again  to  be  read  ;  the  mean  of  the  two  readings  is  taken  ;  the  thermometer 
/  gives  the  corresponding  temperature  of  the  air,  and  hence  there  are  all  the 
elements  necessary  for  calculating  the  hygrometric  state. 

As  in  this  instrument  all  the  ether  is  at  the  same  temperature  in  con- 
sequence of  the  agitation,  and  the  temperatures  are  read  off  at  a  distance 
by  means  of  a  telescope,  the  sources  of  error  in  Daniell's  hygrometer  are 
avoided. 

A  much  simpler  form  of  the  apparatus  may  be  constructed  out  of  a 
common  test-tube  containing  a  depth  of  i^  inch  of  ether.  The  tube  is 
provided  with  a  loosely  fitting  cork  in  which  is  a  delicate  thermometer  and 
a  narrow  bent  tube  dipping  in  the  ether.  On  blowing  into  the  ether,  through 
a  caoutchouc  tube  of  considerable  length,  a  diminution  of  temperature  is 
caused,  and  dew  is  ultimately  deposited  on  the  glass  ;  after  a  little  practice 
the  whole  process  can  be  conducted  almost  as  well  as  in  Regnault's  more 
complete  instrument.  The  temperature  of  the  air  is  indi- 
cated by  a  detached  thermometer. 

398.  Psychrometer.  Wet  bulb  hygrometer.— A  moist 
body  evaporates  in  the  air  more  rapidly  in  proportion  as  the 
air  is  drier,  and  in  consequence  of  this  evaporation  the  tem- 
perature of  the  body  sinks.  The  psychrometer,  or  wet  bulb 
hygrometer,  is  based  on  this  principle,  the  application  of  which, 
to  this  purpose,  was  first  suggested  by  Leslie.  The  form 
usually  adopted  in  this  country  is  due  to  Mason.  It  consists 
of  two  delicate  thermometers  placed  on  a  wooden  stand  (fig. 
329).  One  of  the  bulbs  is  covered  with  muslin,  and  is  kept 
continually  moist  by  being  connected  with  a  reservoir  of  water 
by  means  of  a  string.  Unless  the  air  is  saturated  with  moisture 
the  wet  bulb  thermometer  always  indicates  a  lower  temperature 
than  the  other,  and  the  difference  between  the  indications  of 
I  |K?SJ/|  |  the  two  thermometers  is  greater  in  proportion  as  the  air  can 
take  up  more  moisture.  The  tension  e  of  the  aqueous  vapour 
in  the  atmosphere  may  be  calculated  from  the  indications  of 
the  two  thermometers  by  means  of  the  following  empirical 
formula  : — 

e  =  e  —  0-00077  (f  —  t^ht 

Fig  329<        in  which  e'  is  the   maximum  tension    corresponding   to   the 
temperature  of  the  wet  bulb  thermometer,  h  is  the  barometric 
height,  and  /  and  f  the  respective  temperatures  of  the  dry  and  wet  bulb 
thermometers.     If,  for  example,  72  =  750  millimetres,  /=  15°  C.,  /'=io°  C.  ; 


-398] 


Hygrometers  of  A  bsorption. 


337 


according  to  the  table  of  tensions  (358),  ^'  =  9-165,  and  we  have 
e  =  9-165  —  0-00077  x  5  x  75°  =  6-278. 

This  tension  corresponds  to  a  dew  point  of  about  4-5°  C.  If  the  air  had 
been  saturated,  the  tension  would  have  been  12-699,  an^  the  air  is  therefore 
about  half  saturated  with  moisture. 

This  formula  expresses  the  result  with  tolerable  accuracy,  but  the  above 
constant  0*00077  requires  to  be  controlled  for  different  positions  of  the  instru- 
ment ;  in  small  closed  rooms  it  is  0-00128,  in  large  rooms  it  is  o-ooioo,  and 
in  the  open  air  without  wind  it  is  0-00090  :  the  number  0-00077  is  its  value 
in  a  large  room  with  open  windows.  Regnault  found  that  the  difference, 
in  temperature  of  the  two  bulbs  depends  on  the  rapidity  of  the  current  of 
air  ;  he  also  found  that  at  a  low  temperature,  and  in  very  moist  air,  the 
results  obtained  with  the  psychrometer  differed  from  those  yielded  by  his 
hygrometer.  It  is  probable  that  the  indications  of  the  psychrometer  are 
only  true  for  mean  and  high  temperatures,  and  when  the  atmosphere  is  not 
too  moist. 

According  to  Glaisher  the  temperature  of  the  dew  point  may  be  obtained 
by  multiplying  the  difference  between  the  temperatures  of  the  wet  and  dry 
bulb  by  a  constant  depending  on  the  temperature  of  the  air  at  the  time  of 
observation,  and  subtracting  the  product  thus  obtained  from  this  last-named 
temperature.  The  following  are  the  numbers  : — 


Dry  bulb 
Temperature  F.° 

Factor 

Dry  bulb 
Temperature  F.9 

Factor 

Below  24° 

8-5 

34  to  35 

2-8 

241025 

6-9 

35—40 

2'5 

25—26 

6-5 

40—45 

2'2 

26—27 

6-1 

45—50 

2-1 

27—28 

5-6 

50—55 

2-0 

28—29 

5'i 

55—60 

I'9 

29—30 

4-6 

60-65 

1-8 

30—31 

4'  i 

65—70 

1-8 

31—32 

37 

70—75 

1-7 

32—33 

3'3 

75—80 

1-7 

33—34 

3-0 

80—85 

1-6 

These  are  often  known  as  Glaisher 's  factors. 

A  formula  frequently  used  in  this  country  is  that  given  by  Dr.  Apjohn. 
It  is 

88     30'  96     30 

in  which  d  is  the  difference  of  the  wet  and  dry  bulb  thermometers  in 
Fahrenheit  degrees ;  //  the  barometric  height  in  inches  ;  f  the  tension  of 
vapour  for  the  temperature  of  the  wet  bulb,  and  F  the  elastic  force  of  vapour 
at  the  dew  point,  from  which  the  dew  point  may  if  necessary  be  found  from 
the  tables.  The  constant  coefficient  88,  for  the  specific  heats  of  air  and 
aqueous  vapour,  is  to  be  used  when  the  reading  of  the  wet  bulb  is  above  32° 
F.,  and  96  when  it  is  below. 

Q 


338 


On  Heat. 


[399- 


399.  Hygrometers  of  absorption — These   hygrometers  are  based  on 
the  property  which  organic  substances  have,  of  elongating  when  moist,  and 
of  again  contracting  as  they  become  dry.     The  most  common  form  is  the 
hair  or  Saussure's  hygrometer. 

It  consists  of  a  brass  frame  (fig.  330),  on  which  is  fixed  a  hair,  c,  fastened 
at  its  upper  extremity  in  a  clamp,  a,  provided  with  a  screw,  d.  This  clamp 
is  moved  by  a  screw  b.  The.  lower  part  of  the  hair  passes 
round  a  pulley,  0,  and  supports  a  small  weight,  p.  On  the 
pulley  there  is  a  needle,  which  moves  along  a  graduated 
scale.  When  the  hair  becomes  shorter  the  needle  rises, 
when  it  becomes  longer  the  weight  p  makes  it  sink. 

The  scale  is  graduated  by  calling  that  point  zero  at  which 
the  needle  would  stand  if  the  air  were  completely  dry,  and 
100  the  point  at  which  it  stands  in  air  completely  saturated 
with  moisture.  The  distance  between  these  points  is  divided 
into  100  equal  degrees. 

Regnault  has  devoted  much  study  in  order  to  render  the 
hair  hygrometer  scientifically  useful,  but  without  much  suc- 
cess. And  the  utmost  that  can  be  claimed  for  it  is  that  it 
can  be  used  as  a  hygroscope  ;  that  is,  an  instrument  which 
shows  approximately  whether  the  air  is  more  or  less  moist, 
without  giving  any  indication  as  to  the  quantity  of  moisture 
present.  To  this  class  of  hygroscopes  belong  the  chimney 
ornaments,  one  of  the  most  common  forms  of  which  is  that 
of  a  small  male  and  female  figure,  so  arranged  in  reference 
Fig-  330.  to  a  little  house,  with  two  doors,  that  when  it  is  moist  the 

man  goes  out,  and  the  woman  goes  in,  and  vice  versa  when  it  is  fine.  They 
are  founded  on  the  property  which  twisted  strings  or  pieces  of  catgut  possess 
of  untwisting  when  moist,  and  of  twisting  when  dry. 

As  these  hygroscopes  only  change  slowly,  their  indications  are  always 
behindhand  with  the  state  of  the  weather;  nor  are  they,  moreover,  very 
exact. 

400.  Moisture  of  the  atmosphere. — The  absolute  moisture  varies  with 
the  temperature  both  in  the  course  of  the  year  and  of  the  day.     In  summer 
there  is  a  maximum  at  eight  in  the  morning  and  evening,  and  a  minimum  at 
3  P.M.  and  at  3  A.M.,  because  the  ascending  current  of  air  carries  the  moisture 
upwards.     The  absolute  moisture  is  greatest  in  the  tropics,  where  it  represents 
a  pressure  of  25mm,  while  in  our  latitudes  it  does  not  exceed  iomm.     The 
relative  moisture,  on  the  other  hand,  is  at  its  minimum  in  the  hottest  and  at 
its  maximum  in  the  coolest  part  of  the  day.     It  varies  also  in   different 
regions.     It  is  greater  in  the  centre  of  continents  than  it  is  on  the  sea  or 
the  sea  coast.     That  the  dryness  diminishes  with  the  distance  from  the  sea 
is  shown  by  the  clearer  skies  of  continental  regions.      In    Platowskya  in 
Siberia  the  air,  at  a  temperature  of  24°,  was  found  to  contain  a  quantity  of 
moisture  only  sufficient  to  saturate  it  at  —  3°  ;  the  air  might  therefore  have 
been  cooled  through  27°  without  any  deposit  of  moisture.     In  some  parts 
of  East  Africa  the  springs  of  powder-flasks  exposed  to  the  damp  snap  like 
twisted  quills,  paper  becomes  soft  and  sloppy  by  the  loss  of  its  glaze,  and 
gunpowder,  if  not  kept  hermetically  sealed,  refuses  to  ignite.     On  the  other 


-402]  Problem  on  Hygrometry.  339 

hand,  in  North  America,  where  the  south-west  winds  blow  over  large  tracts 
of  land,  the  relative  moisture  is  less  than  in  Europe  ;  evaporation  is  there 
far  more  rapid  than  in  Europe  ;  clothes  dry  quickly,  bread  soon  becomes 
hard,  newly  built  houses  can  be  at  once  inhabited,  European  pianos  soon 
give  way  there,  while  American  ones  are  very  durable  on  this  side  of  the 
ocean.  As  regards  the  animal  economy,  the  liquids  evaporate  more  rapidly, 
by  which  the  circulation  and  the  assimilation  is  accelerated,  and  the  whole 
character  is  more  nervous.  For  evaporation  is  quicker  the  drier  the  air,  and 
the  more  frequently  it  is  renewed  ;  it  is,  moreover,  more  rapid  the  higher 
the  temperature,  and  the  less  the  pressure.  This  is  not  in  disaccord  with  the 
statement  that  the  quantity  of  vapour  which  saturates  a  given  space  is  the 
same  however  this  be  filled  with  air  ;  a  certain  space  takes  up  the  same 
weight  of  vapour  whether  it  is  vacuous,  or  filled  with  rarefied  or  dense  air  ; 
the  saturation  with  vapour  takes  place  the  more  rapidly  the  smaller  the 
pressure  of  the  air. 

401.  Problem  on  nygrrometry. — To  calculate  the  weight  P  of  a  volume 
of  moist  air  V,  the  hygrometric  state  of  which  is  E,  the  temperature  /,  and 
the  pressure  H,  the  density  of  the  vapour  being  \  that  of  air. 

From  the  second  law  of  the  mixture  of  gases  and  vapours,  it  will  be  seen 
that  the  moist  air  is  nothing  more  than  a  mixture  of  V  cubic  inches  of  dry 
air  at  /°,  under  the  pressure  H  minus  that  of  the  vapour,  and  of  V  cubic 
inches  of  vapour  at  t°  and  the  tension  given  by  the  hygrometric  state  ;  these 
two  values  must,  therefore,  be  found  separately. 

The  formula/=-F  x  E  (392)  gives  the  tension/of  the  vapour  in  the  air, 
for  E  has  been  determined,  and  F  is  found  from  the  tables.     The  tension/ 
being  known,  if/'  is  the  tension  of  the  air,/+/'=  H,  from  which 
/'  =  H-/=H-FE. 

The  question  consequently  resolves  itself  into  calculating  the  weight  of 
V  cubic  inches  of  dry  air  at  ^,  and  the  pressure  H  —  FE,  and  then  that  of  V 
cubic  inches  of  aqueous  vapour  also  at  /°,  but  under  the  pressure  FE. 

Now  V  cubic  inches  of  dry  air  under  the  given  conditions  weigh 
0-31  V  (H-FE)^  and  we  readily  see  from  problem  III.  art.  384  that  V 

cubic  inches  of  vapour  at  /°,  and  the  pressure  FE,  weigh  -J  x  ^1 

8      (i+a/)7oo 

Adding  these  two  weights,  and  reducing,  we  get 

p_o-3iV(H-!-FE) 
(l+a/)  760 

If  the  air  were  saturated  we  should  have  E  =  I,  and  the  formula  would  thus 
be  changed  into  that  already  found  for  the  mixture  of  gases  and  saturated 
vapours  (384). 

This  formula  contains,  besides  the  weight  P,  many  variable  quantities  V, 
E,  H,  and  /,  and  consequently,  by  taking  successively  each  of  these  quantities 
as  unknown,  as  many  different  problems  might  be  proposed. 

402.  Correction  for  the  loss  of  weight  experienced  by  bodies  weighed 
in  the  air. — It  has  been  seen  in  speaking  of  the  balance  that  the  weight 
which  it  indicates  is  only  an  apparent  weight,  and  is  less  than  the  real 

Q2 


340  On  Heat.  [402- 

weight.  The  latter  may  be  deduced  from  the  former  when  it  is  remembered 
that  every  body  weighed  in  the  air  loses  a  weight  equal  to  that  of  the  dis- 
placed air  (185).  This  problem  is,  however,  very  complicated,  for  not  only 
does  the  weight  of  the  displaced  air  vary  with  the  temperature,  the  pres- 
sure, and  the  hygrometric  state,  but  the  volume  of  the  body  to  be  weighed, 
and  that  of  the  weights,  vary  also  with  the  temperature  ;  so  that  a  double 
correction  has  to  be  made  ;  one  relative  to  the  weights,  the  other  to  the  body 
weighed. 

Correction  relative  to  the  weights.  —  In  order  to  make  this  correction  let 
P  be  their  weight  in  air,  and  n  their  weight  in  vacuo  ;  further,  let  V  be 
the  volume  of  these  weights  at  o°,  D  the  density  of  the  substance  of  which 
they  are  made,  and  K  its  coefficient  of  linear  expansion. 

The  volume  V  becomes  V  (i  +  3K/)  at  /°,  hence  this  is  the  volume  of  air 
displaced  by  the  weights.  If  /u  be  the  weight  of  a  cubic  inch  of  air  at  /,  and 
the  pressure  H  at  the  time  of  weighing,  we  have 


From  the   formula  P  =  VD   (125)  V  may  be  replaced  by   —,    and    the 
formula  becomes 


n[,  - 


which  gives  the  value,  in  air,  of  a  weight  n,  when  p,  is  replaced  by  its  value. 
But  since  /z  is  the  weight  of  a  cubic  inch  of  air  more  or  less  moist,  at  the 
temperature  t  and  the  pressure  H,  its  value  may  be  calculated  by  means  of 
the  formula  in  the  foregoing  paragraph. 

Correction  relative  to  the  body  weighed.  —  Let  p  be  the  apparent  weight  of 
the  body  to  be  weighed,  rr  its  real  weight  in  vacuo,  d  its  density,  k  its  co- 
efficient of  expansion,  and  /  its  temperature  ;  by  the  same  reasoning  as  above 
we  have 


By  using  the  method  of  double  weighing,  and  of  a  counterpoise  whose 
apparent  weight  is  p',  the  real  weight  n',  the  density  d',  and  the  coefficient  k', 
and  assuming  that  the  pressure  does  not  change,  which  is  usually  the  case, 
we  have  again 

.  (3) 


If  a  and  b  are  the  two  arms  of  the  beam,  we  have  in  the  first  weighing  ap  =pb  ; 
and  in  the  second  «P  =  bp^  whence  p  =  P.  Replacing  P  and/  by  their  values 
deduced  from  the  above  equations,  we  have 


I  - 


which  solves  the  problem. 


-404]  Conductivity  of  Solids.  341 


CHAPTER  VII. 

CONDUCTIVITY  OF  SOLIDS,   LIQUIDS,   AND  GASES. 

403.  Transmission  of  beat. — When  we  stand  at  a  little  distance  from  a 
fire  or  other  source  of  heat  we  experience  the  sensation  of  warmth.     The 
heat  is  not  transmitted  by  the  intervening  air  ;  it  passes  through  it  without 
raising  its  temperature,  for  if  we  place  a  screen  before  the  fire  the  sensation 
ceases  to  be  felt.     The  heat  from  the  sun  reaches  us  in  the  same  manner. 
The  heat,  which,  as  in  this  case,  is  transmitted  to  a  body  from  the  source  of 
heat  without  affecting  the  temperature  of  the  intervening  medium,  is  said  to 
be  radiated. 

That  heat  can  be  transmitted  through  a  medium  without  raising  its  tem- 
perature is  proved  by  a  remarkable  experiment  of  Prevost  in  1811.  Water 
from  a  spring  was  allowed  to  fall  in  a  thin  sheet ;  on  one  side  of  this  was  held 
a  red-hot  iron  ball,  and  on  the  other  a  delicate  thermometer.  The  tempera- 
ture of  the  latter  was  observed  to  rise  steadily,  a  result  which  could  not  have 
been  due  to  any  heating  effect  of  the  water  itself,  as  this  was  cold,  and  was 
continually  renewed.  It  could  only  have  been  due  to  heat  which  traversed 
the  water  without  raising  its  temperature.  A  similar  experiment  has  been 
made  by  a  hollow  glass  lens  through  which  cold  water  flowed  in  a  constant 
stream.  The  sun's  rays  concentrated  by  this  arrangement  ignited  a  piece  of 
wood  placed  in  the  focus. 

Heat  is  transmitted  in  another  way.  When  the  end  of  a  metal  bar  is 
heated,  a  certain  increase  of  temperature  is  presently  observed  along  the 
bar.  Where  the  heat  is  transmitted  in  the  mass  of  the  body  itself,  as  in  this 
case,  it  is  said  to  be  conducted.  We  shall  first  consider  the  transmission  of 
heat  by  conduction. 

404.  Conductivity  of  solids. — Bodies  conduct  heat  with  different  de- 
gress of  facility.     Good  conductors  are   those 

which  readily  transmit  heat,  such  as  are  the 
metals;  while  bad  conductors,  to  which  class 
belong  the  resins,  glass,  wood,  and  more 
especially  liquids  and  gases,  offer  a  greater  or 
less  resistance  to  the  transmission  of  heat. 

In  order  to  compare  roughly  the  conducting 
power  or  conductivity  of  different  solids,  Ingen- 
haus  constructed  the  apparatus  which  bears  his 
name  and  which  is  represented  in  fig.  331.  It  Fig.  33i. 

is  a  metal  trough,  in  which,  by  means  of  tubu- 

lures  and   corks,  are  fixed   rods  of  the  same  dimensions,  but  of  different 
materials  ;  for  instance,  iron,  copper,  wood,  glass.     These  rods  extend  to  a 


342  On  Heat.  [404- 

slight  distance  in  the  trough,  and  the  parts  outside  are  coated  with  wax 
which  melts  at  61°.  The  box  being  filled  with  boiling  water,  it  is  observed 
that  the  wax  melts  to  a  certain  distance  on  the  metal  rods,  while  on  the 
others  there  is  no  trace  of  fusion.  The  conducting  power  is  evidently 
greater  in  proportion  as  the  wax  has  fused  to  a  greater  distance.  The 
experiment  is  sometimes  modified  by  attaching  glass  balls  or  marbles  to 
the  ends  of  the  rods  by  means  of  wax.  As  the  wax  melts,  the  balls  drop 
off,  and  this  in  the  order  of  their  respective  conductivities.  The  quickness 
with  which  melting  takes  place  is,  however,  only  a  measure  of  the  conduct- 
ing power,  in  case  the  metals  have  the  same  or  nearly  the  same  specific  heat. 
Despretz  compared  the  conducting  powers  of  solids  by  forming  them  into 
a  bar  (fig.  332),  in  which  small  cavities  are  made  at  short  intervals  :  these 


Fig.  332- 

cavities  contain  mercury,  and  a  delicate  thermometer  is  placed  in  each  of 
them.  This  bar  is  exposed  at  one  end  to  a  constant  source  of  heat ;  the 
thermometers  gradually  rise  until  they  indicate  fixed  temperatures,  which 
are  less  according  as  the  thermometers  are  farther  from  the  source  of  heat. 
By  this  method  Despretz  verified  the  following  law  : — If  the  distances  from 
the  source  of  heat  increase  in  arithmetical  progression,  the  excess  of  tem- 
perature over  that  of  the  surrounding  air  decreases  in  geometrical  pro-, 
gression. 

This  law,  however,  only  prevails  in  the  case  of  very  good  conductors, 
such  as  gold,  platinum,  silver,  and  copper ;  it  is  only  approximately  true  for 
iron,  zinc,  lead,  and  tin,  and  does  not  apply  at  all  to  non:metallic  bodies, 
such  as  marble,  porcelain,  £c. 

Taking  the  conducting  power  of  gold  at  1000,  Despretz  constructed  the 
following  table  of  conductivities  : — 

•  304 

•  179 
.       23 

.          12. 
II 


Platinum  . 
Silver 
Copper 
Iron  . 
Zinc  . 

.         .         .     981 
-     973 
•     897 
•     374 
afa 

Tin  . 
Lead 
Marble     . 
Porcelain 
Brick  earth 

-405]  Coefficient  of  Conductivity.  343 

By  making  cavities  in  the  bars,  as  in  Despretz's  method,  their  form  is 
altered,  and  the  continuity  partially  destroyed.  Wiedemann  and  Franz 
avoided  this  source  of  error  by  measuring  the  temperature  of  the  bars  in 
different  places  by  applying  to  them  the  junction  of  a  thermo-electric  couple 
(412).  The  metal  bars  were  made  as  regular  as  possible,  one  of  the  ends 
was  heated  to  100°,  the  rest  of  the  bar  being  surrounded  by  air  at  a  constant 
temperature.  The  thermo-electric  couple  was  of  small  dimensions,  in  order 
not  to  abstract  too  much  heat. 

By  this  method  Wiedemann  and  Franz  obtained  results  which  differ  con- 
siderably from  those  of  Despretz.  Representing  the  conductivity  of  silver 
by  100°,  they  found  for  the  other  metals  the  following  numbers  :  — 

Silver    ....     IOCTO  Steel        .         .         .         .     ir6 

Copper  ....       73-6  Lead        ....      8-5 

Gold      .....       53-2  Platinum          .        .        .8-4 

Tin         ....       14-5  Rose's  alloy     .         .        .2*8 

Iron        .         .         .         .11-9  Bismuth  .         .         .         .1-8 

These  experimenters  found  that  the  conducting  power  of  the  pure  metals 
for  heat  and  electricity  is  the  same. 

Organic  substances  conduct  heat  badly.  De  la  Rive  and  De  Candolle 
have  shown  that  woods  conduct  better  in  the  direction  of  their  fibres  than 
in  a  transverse  direction  ;  and  have  remarked  upon  the  influence  which  this 
feeble  conducting  power,  in  a  transverse  direction,  exerts  in  preserving  a  tree 
from  sudden  changes  of  temperature,  enabling  it  to  resist  alike  a  sudden 
abstraction  of  heat  from  within,  and  the  sudden  accession  of  heat  from  with- 
out. Tyndall  has  also  shown  that  this  tendency  is  aided  by  the  low  conduct- 
ing power  of  the  bark,  which  is  in  all  cases  less  than  that  of  the  wood. 
Cotton,  wool,  straw,  bran,  £c.,  are  all  bad  conductors. 

405.  Coefficient  of  conductivity.  —  The  numbers  given  in  the  foregoing 
article  only  express  the  relative  conducting  powers  of  the  respective  sub- 
stances. Numerous  experiments  have  been  made  to  determine  the  quantity 
of  heat  W  which  passes,  for  instance,  through  a  plate  the  two  sides  of  which 
are  kept  at  a  constant  difference  of  temperature.  This  will  clearly  be  pro- 
portional to  the  area  of  the  plate  A  and  to  the  time  /.  It  is  further  propor- 
tional to  the  excess  of  the  temperature  of  the  one  face  01  over  that  of  the 
other  —  that  is,  to  01  —  ^-,  and  as  the  flow  of  heat  is  different  in  different  sub- 
stances, it  will  be  proportional  to  a  constant  k. 

On  the  other  hand  it  will  be  inversely  proportional  to  the  thickness  of 
the  plate  d.  These  results  are  expressed  by  the  formula 

W 


Adopting  the  C  G  S  system  of  units,,  we  may  define  the  coefficient  of 
thermal  conductivity  as  the  quantity  of  heat  which  passes  in  a  second  of 
time  between  the  two  opposite  faces,  of  a  cube  of  the  substance  one  centi- 
metre in  thickness,  and  which  are  kept  at  a  constant  difference  of  one 
degree. 

The  mean  values  are  as  follows  :  —  copper,  I  -108  ;  zinc,  0-307  ;  iron,  0-163  ; 
german  silver,  0-109  ;  tin,  0-0057. 


344  On  Heat.  [405- 

Thus  if  the  two  opposite  faces  of  a  cube  of  iron  one  centimetre  in  thick- 
ness are  kept  at  a  constant  difference  of  i°  C.,  the  quantity  of  heat  which 
passes  in  each  second  of  time  will  be  sufficient  to  raise  0-163  gramme 
of  water  through  i°  C. 

From  this,  which  is  often  called  the  calorimetrical  measure  of  conductivity, 
we  must  distinguish  the  thermometric  measure  of  conductivity  ;  that  is  to  say, 
the  number  of  degrees  through  which  the  above  cube  would  be  heated  when 
the  above  quantity  of  heat  passes  through  it  under  the  given  conditions. 
This  is  obtained  from  the  above  constants  by  dividing  them  by  the  reduced 
value  of  the  cube  ;  that  is,  by  the  product  of  its  specific  heat  in  toits  specific 
gravity. 

406.  Senarmont  s  experiment. — It  is  only  in  homogeneous  bodies  that 
heat  is  conducted  with  equal  facility  in  all  directions.  If  an  aperture  be 
made  in  a  circular  piece  of  ordinary  glass  covered  with  a  thin  layer  of  wax, 
and  a  platinum  wire  ignited  by  a  voltaic  current  be  held  through  the  aperture, 
the  wax  will  be  melted  round  the  hole  in  a  circular  form.  Senarmont 
made,  on  this  principle,  a  series  of  experiments  on  the  conductivity  of  heat 
in  crystals.  A  plate  cut  from  a  crystal  of  the  regular  system  was  covered  with 
wax,  and  a  heated  metallic  point  was  held  against  it.  The  part  melted  had 
a  circular  form  ;  but  when  plates  of  crystals  belonging  to  other  systems  were 
investigated  in  a  similar  manner,  it  was  found  that  the  form  of  the  isothermal 
line  or  line  of  equal  temperature— that  is,  the  limit  of  the  melted  part— varied 
with  the  different  systems  and  with  the  position  of 
the  axes.  In  plates  of  uniaxial  crystals  cut  parallel 
to  the  principal  axis  it  was  an  ellipse,  the  major  axis 
of  which  was  in  the  direction  of  the  principal  axis. 
In  plates  cut  perpendicular  to  the  principal  axis  it 
was  a  circle.  In  biaxial  crystals  the  line  was  always 
an  ellipse. 

Instead  of  wax  the  plate  may  be  coated  with  the 
double  iodide  of  mercury  and  copper ;  this  substance 
is  of  a  brick-red  colour,  which  when  heated  is  changed 
into  a  purplish  black. 

407.  Conductivity  of  liquids. — The  conductivity 
of  liquids  is  very  small,  as  is  seen  from  the  following 
experiment : — A  delicate  thermoscope  B,  consisting 
p-    3  3  of  two  glass  bulbs,  joined  by  a  tube,  m,  in  which 

there  is  a  small  index  of  coloured  liquid,  is  placed  in 

a  large  cylindrical  glass  vessel,  D  (fig.  333).  This  vessel  is  filled  with  water 
at  the  ordinary  temperature,  and  a  tin  vessel,  A,  containing  oil  at  a  tempe- 
rature of  two  or  three  hundred  degrees,  is  dipped  in  it.  The  bulb  near  the 
vessel  A  is  only  very  slightly  heated,  and  the  index  m  moves  through  a  very 
small  distance.  Other  liquids  give  the  same  result.  That  liquids  conduct 
very  badly  is  also  demonstrated  by  a  simpler  experiment.  A  long  test-tube 
is  half  filled  with  water  and  some  ice  so  placed  in  it  that  it  cannot  rise  to  the 
surface.  By  inclining  the  tube  and  heating  the  surface  of  the  liquid  by 
means  of  a  spirit  lamp,  the  liquid  at  the  top  may  be  made  to  boil,  while  the 
ice  at  the  bottom  remains  unmelted. 

Despretz  made  a  series  of  experiments  with  an  apparatus  analogous  to 


-407]  Conductivity  of  Liquids.  345 

that  here  described,  but  he  kept  the  liquid  in  the  vessel,  A,  at  a  constant 
temperature,  and  arranged  a  series  of  thermometers  one  below  the  other  in 
the  vessel  D.  In  this  manner  he  found  that  the  conductivity  of  heat  in 
liquids  obeys  the  same  laws  as  in  solids,  but  is  much  more  feeble.  For  ex- 
ample, the  conductivity  of  water  is  ^  that  of  copper. 

Paalzow  states  that  in  regard  to  conducting  power  the  following  liquids 
stand  in  the  order  given  of  their  decreasing  conductivity  for  heat :  mercury, 
water,  solution  of  sulphate  of  copper,  sulphuric  acid,  solution  of  sulphate  of 
zinc,  solution  of  common  salt. 

Guthrie  has  examined  the  conductivity  of  liquids  in  the  following  man- 
ner :— Two  hollow  brass  cones  are  placed  near  each  other  so  that  the  top  of 
one  points  upwards,  that  of  the  other  downwards  (fig.  334).  The  distance 


Fig-  334- 

of  the  bases,  which  are  of  platinum,  can  be  regulated  by  a  micrometer  screw. 
Between  the  bases  the  liquid  to  be  examined  is  introduced  by  means  of  a 
pipette.  The  lower  cone  is  fitted  with  a  glass  tube  which  dips  in  a  coloured 
liquid,  and  thus  constitutes  an  air  thermometer.  The  base  of  the  upper  cone 
is  kept  at  a  constant  temperature  by  means  of  a  current  of  hot  water  ;  it  thus 
warms  the  liquid,  and  the  base  of  the  lower  cone,  in  consequence  of  which 
the  air  in  the  interior  is  expanded  and  the  column  of  liquid  in  the  stem 
depressed. 

The  bases  of  the  cones  were  first  brought  in  contact  and  the  depression 
of  the  column  of  liquid  was  observed.  A  column  of  liquid  of  a  given  thick- 
ness was  then  interposed  and  the  depression  observed  after  a  certain  time. 
The  same  thicknesses  of  other  liquids  were  then  successively  introduced,  and 
the  corresponding  depressions  noted.  The  difference  of  the  depressions  was 
a  measure  for  the  resistance  which  the  liquid  offered  to  the  passage  of  heat. 


346 


On  Heat. 


[407- 


The  following  numbers  give  the  ratios  of  the  resistance  of  the  respective 
liquids  to  that  of  an  equal  thickness  of  water  : — 

Water  .  .  .  .  I'oo  Alcohol  ....  9-08 
Glycerine  .  .  .  3-84  Oil  of  turpentine  .  .  1175 
Sperm  oil  .  -3*85  Chloroform  .  .  .  12*10 

It  was  also  observed  that  water  conducts  better  the  hotter  it  is  ;  and  any 
salt  dissolved  increases  the  conductivity. 

408.  Manner  in  which  liquids  are  heated. — When  a  column  of  liquid 
is  heated  at  the  bottom,  ascending  and  descending  currents  are  produced.   It 
is  by  these  that  heat  is  mainly  distributed  through  the  liquid,  and  not  by  its 
conductivity.     These  currents  arise  from  the  expansion  of  the  inferior  layers, 
which,  becoming  less  dense,  rise  in  the  liquid,  and  are  replaced  by  colder 
and  denser  layers.     They  may  be  made  visible  by  projecting  bran  or  wooden 
shavings  into  water,  which  rise  and  descend  with  the  currents.     The  experi- 
ment is  arranged  as  shown  in  fig.  335.     The  mode  in  which  heat  is  thus 
propagated  in  liquids  and  in  gases  is  said  to  be  by  convection. 

409.  Conductivity  of  gases. — It  is  a  disputed  question  whether  gases 
have  a  true  conductivity ;  but  certainly  when  they  are  restrained  in  their 
motion  their  conductivity  is  very  small.     All  substances,  for  instance,  be- 
tween whose  particles  air  remains  stationary,  offer  great  resistance  to  the 
propagation  of  heat.     This  is  well  seen  in  straw,  eider-down,  and  furs.     The 
propagation  of  heat  in  a  gaseous  mass  is  effected  by  means  of  the  ascending 
and  descending  currents  formed  in  it,  as  is  the  case  with  liquids. 

Stefan  has  found  the  value  of  k  for  air  to  be  0-0000558,  so  that  it  is 

nearly  20,000  times  worse  conductor  than  copper  (405). 

The  following  experiment,  originally  devised  by  Grove,  is  considered  to 

prove  that  gases  have  a  certain  conductivity  : — In  a  glass  vessel  provided 

with  delivery  tubes  by  which  any  gases  can  be 
introduced,  or  by  which  it  can  be  exhausted, 
is  a  platinum  wire  which  can  be  heated  to  red- 
ness by  a  voltaic  battery.  When  the  vessel  is 
exhausted  the  platinum  wire  is  gradually  raised 
to  a  bright  redness  ;  on  then  allowing  air  to 
enter,  the  luminosity  is  greatly  diminished,  and 
if  the  vessel  be  exhausted  and  then  hydrogen 
admitted,  the  luminosity  quite  disappears. 
This  greater  chilling  of  the  wire  in  hydrogen 
than  in  air  is  considered  by  Magnus  to  be  an 
effect  of  conduction  ;  while  Tyndall  ascribes  it 
to  the  greater  mobility  of  the  particles  of 
hydrogen. 

410.  Applications. — The  greater  or  less 
conductivity  of  bodies  meets  with  numerous 
applications.  If  a  liquid  is  to  be  kept  warm 
for  a  long  time,  it  is  placed  in  a  vessel  and 


Fig.  335- 


packed  round  with  non-conducting  substances,  such  as  shavings,  straw,  or 
bruised  charcoal.  For  this  purpose  water-pipes  and  pumps  are  wrapped  in 
straw  at  the  approach  of  frost.  The  same  means  are  used  to  hinder  a  body 


-410]  Conductivity  of  Gases.  347 

from  becoming  heated.     Ice  is  transported  in  summer  by  packing  it  in  bran 
or  folding  it  in  flannel. 

Double  walls  constructed  of  thick  planks  having  between  them  any  finely 
divided  materials,  such  as  shavings,  sawdust,  dry  leaves,  &c.,  retain  heat 
extremely  well  ;  and  are  likewise  advantageous  in  hot  countries,  for  they 
prevent  its  access.  Pure  silica  in  the  state  of  rock  crystal  is  a  better  con- 
ductor than  lead,  but  in  a  state  of  powder  it  conducts  very  badly.  If  a  layer 
of  asbestos  is  placed  on  the  hand  a  red-hot  iron  ball  can  be  held  without 
inconvenience.  Red-hot  cannon  balls  can  be  wheeled  to  the  gun's  mouth  in 
wooden  barrows  partially  filled  with  sand.  Lava  has  been  known  to  flow 
over  a  layer  of  ashes  underneath  which  was  a  bed  of  ice,  and  the  non- 
conducting power  of  the  ashes  has  prevented  the  ice  from  fusion. 

The  clothes  which  we  wear  are  not  warm  in  themselves  ;  they  only 
hinder  the  body  from  losing  heat,  in  consequence  of  their  spongy  texture 
and  the  air  they  enclose.  The  warmth  of  bed-covers  and  of  counterpanes 
is  explained  in  a  similar  manner.  Double  windows  are  frequently  used  in 
cold  climates  to  keep  a  room  warm — they  do  this  by  the  non-conducting 
layer  of  air  interposed  between  them.  During  the  night  the  windows  are 
opened,  while  during  the  day  they  are  kept  closed.  It  is  for  the  same  reason 
that  two  shirts  are  warmer  than  one  of  the  same  material  but  of  double  the 
thickness.  Hence,  too,  the  warmth  of  furs,  eider-down,  &c. 

The  small  conducting  power  of  felt  is  used  in  the  North  of  Europe  in  the 
construction  of  the  Norwegian  stove,  which  consists  merely  of  a  wooden 
box  with  a  thick  lining  of  felt  on  the  inside.  In  the  centre  is  a  cavity  in 
which  can  be  placed  a  stew-pan  provided  with  a  cover.  On  the  top  of  this 
is  a  lid,  also  made  of  felt,  so  that  the  pan  is  surrounded  by  a  very  badly 
conducting  envelope.  Meat,  with  water  and  suitable  additions,  is  placed  in 
the  pan,  and  the  contents  are  then  raised  to  boiling.  The  whole  is  then 
enclosed  in  the  box  and  left  to  itself ;  the  cooking  will  go  on  without  fire, 
and  after  the  lapse  of  several  hours  it  will  be  quite  finished.  The  cooling 
down  is  very  slow,  owing  to  the  bad  conducting  power  of  the  lining ;  at  the 
end  of  three  hours  the  temperature  is  usually  not  found  to  have  sunk  more 
than  from  10°  to  15°. 

That  water  boils  more  rapidly  in  a  metallic  vessel  than  in  one  of  porcelain 
of  the  same  thickness  ;  that  a  burning  piece  of  wood  can  be  held  close  to 
the  burning  part  with  the  naked  hand,  while  a  piece  of  iron  heated  at  one 
end  can  only  be  held  at  a  great  distance,  are  easily  explained  by  reference  to. 
their  various  conductivities. 

The  sensation  of  heat  or  cold  which  we  feel  when  in  contact  with  certain 
bodies  is  materially  influenced  by  their  conductivity.  If  their  temperature  is 
lower  than  ours,  they  appear  colder  than  they  really  are,  because  from  their 
conductivity  heat  passes  away  from  us.  If,  on  the  contrary,  their  temperature 
is  higher  than  that  of  our  body,  they  appear  warmer  from  the  heat  which 
they  give  up  at  different  parts  of  their  mass.  Hence  it  is  clear  why  carpets, 
for  example,  are  warmer  than  wooden  floors,  and  why  the  latter  again  are 
warmer  than  stone  floors. 


348  On  Heat.  [411- 


CHAPTER   VIII. 

RADIATION    OF   HEAT 

411.  Radiant  neat. — It  has  been  already  stated  (403)  that  heat  can  be 
transmitted  from  one  body  to  another  without  altering  the  temperature  of  the 
intervening  medium.  If  we  stand  in  front  of  a  fire  we  experience  a  sensation 
of  warmth  which  is  not  due  to  the  temperature  of  the  air,  for  if  a  screen  be 
interposed  the  sensation  immediately  disappears,  which  would  not  be  the 
case  if  the  surrounding  air  had  a  high  temperature.  Hence  bodies  can  send 
out  rays  which  excite  heat,  and  which  penetrate  through  the  air  without 
heating  it,  as  rays  of  light  through  transparent  bodies.  Heat  thus  propagated 
is  said  to  be  radiated',  and  we  shall  use  the  terms  ray  of  heat,  or  thermal,  or 
calorific  ray,  in  a  similar  sense  to  that  in  which  we  use  the  term  ray  of  light 
or  hnninous  ray. 

We  shall  find  that  the  property  of  radiating  heat  is  not  confined  to 
luminous  bodies,  such  as  a  fire  or  a  red-hot  ball,  but  that  bodies  of  all  tem- 
peratures radiate  heat.  It  will  be  convenient  to  make  a  distinction  between 
luminous  and  obscure  rays  of  heat. 

412,  Detection  and  measurement  of  radiant  heat. — In  demonstrating 
the  phenomena  of  radiant  heat,  very  delicate  thermometers  are  required,  and 
the  thermo-electrical  multiplier  of  Melloni  is  used  for  this  purpose  with  great 
advantage  ;  for  it  not  only  indicates  minute  differences  of  temperature,  but 
it  also  measures  them  with  accuracy. 

This  instrument  cannot  be  properly  understood  without  a  knowledge  of 
the  principles  of  thermo-electricity,  for  which  Book  X.  must  be  consulted. 
It  may,  however,  be  stated  here  that  when  two  different  metals  A  and  B  are 
soldered  together  at  one  end  (fig.  336),  the  free  ends  being  joined  by  a  wire, 
when  the  soldering  C  is  heated  a  current  of  electricity  circulates  through  the 
system  ;  if,  on  the  contrary,  the  soldering  be  cooled,  a  current  is  also  pro- 
duced, but  it  circulates  in  exactly  the  opposite  direction.  This  is  called  a 

thermo-electric  couple  or 
pair.  If  a  number  of  such 
pairs  be  alternately  sol- 
dered together,  as  repre- 
sented in  fig.  337,  the 
intensity  of  the  current 
produced  by  heating  the 

Fig.  336.  Fig.  337.  ends    is    increased ;    or, 

what  amounts  to  the  same 
thing,  a  smaller  degree  of  heat  will  produce  the  same  effect.  Such  an 
arrangement  of  a  number  of  thermo-electric  pairs  is  called  a  thermo-electric 
battery  or  pile. 


-413] 


Laws  of  Radiation. 


349 


Melloni's  thermo-multiplier  consists  of  a  thermo-electric  pile  connected 
with  a  delicate  galvanometer.  The  thenno-electric  pile  is  constructed  of  a 
number  of  minute  bars  of  bismuth  and  antimony  soldered  together  alternately, 
though  kept  insulated  from  each  other,  and  contained  in  a  rectangular  box 
P  (fig-  338).  The  terminal  bars  are  connected  with  two  binding  screws  m  and 
?/,  which  in  turn  are  connected  with  the  galvanometer  G  by  means  of  the 
wires  a  and  b. 

The  galvanometer  consists  of  a  quantity  of  fine  insulated  copper  wire 
coiled  round  a  frame,  in  the  centre  of  which  a  delicate  magnetic  needle  is 
suspended  by  means  of  a  silk  thread.  When  an  electric  current  is  passed 
through  this  coil,  the  needle  is  deflected  through  an  angle  which  depends  on 
the  intensity  of  the  current.  The  angle  is  measured  on  a  dial  by  an  index 
connected  with  the  needle. 

It  may  then  be  sufficient  to  state  that  the  thermo-electric  pile  being  con- 
nected with  the  galvanometer  by  means  of  the  wires  a  and  b,  an  excess  of 


Fig.  338. 

temperature  at  one  end  of  the  pile  causes  the  needle  to  be  deflected  through 
an  angle  which  depends  on  the  extent  of  this  excess  ;  and  similarly  if  the 
temperature  is  depressed  below  that  of  the  other  end,  a  corresponding 
deflection  is  produced  in  the  opposite  direction.  By  arrangements  of  this 
kind  Melloni  was  able  to  measure  differences  of  temperature  of  s^th  of  a 
degree. 

The  object  of  the  cone  C  is  to  concentrate  the  thermal  rays  on  the  face 
of  the  pile. 

413.  &aws  of  radiation.— The  radiation  of  heat  is  governed  by  three 
laws  : — 

I.  Radiation  takes  place  in  all  directions  round  a  body.     If  a  thermometer 
be  placed  in  different  positions  round  a  heated  body,  it  indicates  everywhere 
a  rise  in  temperature. 

II.  In  a  homogeneous  medium,  radiation  takes  place  in  a  right  line.     For, 
if  a  screen  be  placed  in  a  right  line  which  joins  the  source  of  heat  and  the 
thermometer,  the  latter  is  not  affected. 


350  On  Heat.  [413- 

But  in  passing  obliquely  from  one  medium  into  another,  as  from  air  into 
a  glass,  calorific-like  luminous  rays  become  deviated,  an  effect  known  as 
refraction.     The  laws  of  this   phenomenon  are  the  same   for 
heat  as  for  light,  and  they  will  be  more  fully  discussed  under 
the  latter  subject. 

III.  Radiant  heat  is  propagated  in  vacuo  as  well  as  in  air. 
This  is  demonstrated  by  the  following  experiment  :— 
)  In  the  bottom  of  a  glass  flask  a  thermometer  is  fixed  in  such 

a  manner  that  its  bulb  occupies  the  centre  of  the  flask  (fig.  339). 
The  neck  of  the  flask  is  carefully  narrowed  by  means  of  the 
blowpipe,  and  then  the  apparatus  having  been  suitably  attached 
to  an  air-pump,  a  vacuum  is  produced  in  the  interior.  This 
having  been  done,  the  tube  is  sealed  at  the  narrow  part.  On 
immersing  this  apparatus  in  hot  water,  or  on  bringing  near  it 
some  hot  charcoal,  the  thermometer  is  at  once  seen  to  rise. 
This  could  only  arise  from  radiation  through  the  vacuum  in 
the  interior,  for  glass  is  so  bad  a  conductor  that  the  heat  could 
not  travel  with  this  rapidity  through  the  sides  of  the  flask  and  the  stem  of 
the  thermometer. 

414.  Causes  which  modify  the  intensity  of  radiant  heat. — By  the 
intensity  of  radiant  heat  is  understood  the  quantity  of  heat  received  on  the 
unit  of  surface.  Three  causes  are  found  to  modify  this  intensity  :  the  tem- 
perature of  the  source  of  heat,  its  distance,  and  the  obliquity  of  the  calorific 
rays  in  reference  to  the  surface  which  emits  them.  The  laws  which  regulate 
these  modifications  may  be  thus  stated  : — 

I.  The  intensity  of  radiant  heat  is  proportional  to  the  temperature  of  the 
source. 

II.  The  intensity  is  inversely  as  the  square  of  the  distance. 

III.  The  intensity  is  less,  the  greater  the  obliquity  of  the  rays  with  respect 
to  the  radiating  surface. 

The  first  law  is  demonstrated  by  placing  a  metal  box  containing  water 
at  10°,  20°,  or  30°  successively  at  equal  distances  from  the  bulb  of  a  differen- 
tial thermometer.  The  temperatures  indicated  by 
the  latter  are  then  found  to  be  in  the  same  ratio 
as  those  of  the  box  :  for  instance,  if  the  tempera- 
ture of  that  corresponding  to  the  box  at  10°  be  2°, 
those  of  others  will  be  4°  and  6°  respectively. 

The  truth  of  the  second  law  follows  from  the 
geometrical  principle  that  the  surface  of  a  sphere 
increases  as  the  square  of  its  radius.  Suppose  a 
hollow  sphere  ab  (fig.  340)  of  any  given  radius, 
and  a  source  of  heat  C,  in  its  centre  ;  each  unit 
Fig.  340.  of  surface  in  the  interior  receives  a  certain  quan- 

tity of  heat.     Now  a   sphere,  ef,  of  double  the 

radius  will  present  a  surface  four  times  as  great ;  its  internal  surface  con- 
tains, therefore,  four  times  as  many  units  of  surface,  and  as  the  quantity  of 
heat  emitted  is  the  same,  each  unit  must  receive  one-fourth  the  quantity. 

To  demonstrate  the  same  law  experimentally,  a  narrow  tin  plate  box  is 
taken  (fig.  341),  filled  with  hot  water,  and  coated  on  one  side  with  lampblack. 


-414]       Causes  which  modify  Intensity  of  Radiant  Heat.          351 

The  thermo-pile  with  its  conical  reflector  is  placed  so  that  its  face  is  at 
a  certain  definite  distance,  co,  say  9  inches,  from  this  box,  and  the  cover 


Fig.  341- 

having  been  lowered,  the  needle  of  the  galvanometer  is  observed  to  be  de- 
flected through  80°,  for  example. 

If  now  the  pile  is  removed  to  a  distance,  CO  (fig.  342),  double  that  of  <:<?, 
the  deflection  of  the  galvanometer  remains  the  same,  which  shows  that  the 
battery  receives  the  same  amount  of  heat;  the  same  is  the  case  if  the 


342- 


battery  is  removed  to  three  or  four  times  the  distance.  This  result,  though 
apparently  in  opposition  to  the  second  law,  really  confirms  it.  For  at  first 
the  battery  only  receives  heat  from  the  circular  portion  ab  of  the  side  of  the 
box,  while,  in  the  second  case,  the  circular  portion  AB  radiates  towards  it. 
But,  as  the  two  cones  ACB  and  acb  are  similar,  and  the  height  of  ACB  is 
double  that  of  acb,  the  diameter  AB  is  double  that  of  ab,  and  therefore  the 


352  On  Heat.  [414- 

area  AB  is  four  times  as  great  as  that  of  ab,  for  the  areas  of  circles  are 
proportional  to  the  squares  of  the  radii.  But  since  the  radiating  surface 
increases  as  the  square  of  the  distance,  while  the  galvanometer  is  stationary, 
the  heat  received  by  the  battery  must  be  inversely  as  this  same  square. 

The  third  law  is  demonstrated  by  means  of  the  following  experiment, 
which  is  a  modification  of  one  originally  devised  by  Leslie  (fig.  343)  : — P 


M 


Fig.  343- 

represents  the  thermo-multiplier  which  is  connected  with  its  galvanometer, 
and  A  a  metal  cube  full  of  hot  water.  The  cube  being  first  placed  in  such 
a  position,  A,  that  its  front  face,  ac,  is  vertical,  the  deflection  of  the  galvano- 
meter is  noted.  Supposing  it  amounts  to  45°,  this  represents  the  radiation 
from  ac.  If  this  now  be  turned  in  the  direction  represented  by  A',  the 
galvanometer  is  still  found  to  mark  45°. 

The  second  surface  is  larger  than  the  first,  and  it  therefore  sends  more 
rays  to  the  mirror.  But  as  the  action  on  the  thermometer  is  no  greater 
than  in  the  first  case,  it  follows  that  in  the  second  case,  where  the  rays 
are  oblique,  the  intensity  is  less  than  in  the  first  case,  where  they  are 
perpendicular. 

In  order  to  express  this  in  a  formula,  let  i  be  the  intensity  of  the  rays 
emitted  perpendicularly  to  the  surface,  and  ir  that  of  the  oblique  rays. 
These  intensities  are  necessarily  inversely  as  the  surfaces  ac  and  a'c',  for  the 
effect  is  the  same  in  both  cases,  and  therefore  i'  x  surface  a'c'  =  i  x  surface  ac ; 

hence  if -i —  '   ,     =*'  -'—  =  i  cos.  aoa' \  which  signifies  that  the  intejisity 
surf,  ac'          a'c'  * 

of  oblique  ray  sis  proportional  to  the  cosine  of  the  angle  which  these  rays  form 
with  the  normal  to  the  surface  ;  for  this  angle  is  equal  to  the  angle  aoa'. 
This  law  is  known  as  the  law  of  the  cosine ;  it  is,  however,  not  general  ; 
Desains  and  De  la  Provostaye  have  shown  that  it  is  only  true  within 
very  narrow  limits  ;  that  is,  only  with  bodies  which,  like  lampblack,  are 
entirely  destitute  of  reflecting  power  (423). 

415.  Mobile  equilibrium.  Theory  of  exchanges. —  Prevost  of  Geneva 
suggested  the  following  hypothesis  in  reference  to  radiant  heat,  known  as 
Prevost's  theory  of  exchanges,  which  is  now  universally  admitted.  All  bodies, 
whatever  their  temperatures,  constantly  radiate  heat  in  all  directions.  If 
we  imagine  two  bodies  at  different  temperatures  placed  near  one  another, 
the  one  at  a  higher  temperature  will  experience  a  loss  of  heat,  its  temperature 
will  sink,  because  the  rays  it  emits  are  of  greater  intensity  than  those  it 
receives  ;  the  colder  body,  on  the  contrary,  will  rise  in  temperature,  because 
it  receives  rays  of  greater  intensity  than  those  which  it  emits.  Ultimately 
the  temperature  of  both  bodies  becomes  the  same,  but  heat  is  still  exchanged 


-417]  Reflection  of  Heat.  353 

between  them,  only  each  receives  as  much  as  it  emits,  and  the  temperature 
remains  constant.  This  state  is  called  the  mobile  equilibi  ium  of  temperature. 

416.  Newton  s  law  of  cooling:. — A  body  placed  in  a  vacuum  is  only 
cooled  or  heated  by  radiation.  In  the  atmosphere  it  becomes  cooled  or 
heated  by  its  contact  with  the  air  according  as  the  latter  is  colder  or  hotter 
than  the  radiating  body.  In  both  cases  the  velocity  of  cooling  or  of  heating 
— that  is,  the  quantity  of  heat  lost  or  gained  in  a  second — is  greater  accord- 
ing as  the  difference  of  temperature  is  greater. 

Newton  has  enunciated  the  following  law  in  reference  to  the  cooling  or 
heating  of  a  body  : — The  quantity  of  heat  lost  or  gained  by  a  body  in  a  second 
is  proportional  to  the  difference  between  its  temperature  and  that  of  the  sur- 
rounding medium.  Dulong  and  Petit  have  proved  that  this  law  is  not  so 
general  as  Newton  supposed,  and  only  applies  where  the  differences  of 
temperature  do  not  exceed  1 5°  to  20°.  Beyond  that,  the  quantity  of  heat 
lost  or  gained  is  greater  than  that  required  by  this  law. 

Two  consequences  follow  from  Newton's  law  : — 

I.  When  a  body  is  exposed  to  a  constant  source  of  heat,  its  temperature 
does  not  increase  indefinitely,  for  the  quantity  which  it  receives  in  the  same 
time  is  always  the  same  ;  while  that  which  it  loses  increases  with  the  excess 
of  its  temperature  over  that  of  the  surrounding  medium.     Consequently  a 
point  is  reached  at  which  the  quantity  of  heat  emitted  is  equal  to  that 
absorbed,  and  the  temperature  then  remains  stationary. 

II.  Newton's  law,  as  applied  to  the  differential  thermometer,  shows  that 
its  indications  are  proportional  to  the  quantities  of  heat  which  it  receives. 
If  one  of  the  bulbs  of  a  differential  thermometer  receives  rays  of  heat  from 
a  constant  source,  the  instrument  exhibits,  first,  increasing  temperatures,  but 
afterwards  becomes  stationary.     In  this  case,  the  quantity  of  heat  which  it 
receives  is  equal  to  that  which  it  emits.     But  the  latter  is  proportional  to  the 
excess  of  the  temperature  of  the  bulb  above  that  of  the  surrounding  atmo- 
sphere— that  is,  to  the  number  of  degrees  indicated  by  the  thermometer ; 
consequently,  the  temperature  indicated  by  the  differential  thermometer  is 
proportional  to  the  quantity  of  heat  it  receives. 


REFLECTION   OF  HEAT. 

417.  Laws  of  reflection. — When  thermal  rays  fall  upon  a  body  they  are, 
speaking  generally,  divided  into  two  parts,  one  of  which  penetrates  the  body 
while  the  other  rebounds  as  if  repelled  from  the 
surface  like  an  elastic  ball.  This  is  said  to  be 
reflected. 

If  ;;/;/  be  a  plane  reflecting  surface  (fig.  344), 
CB  an  incident  ray,  BD  a  line  perpendicular  to 
the  surface  called  the  normal,  and  BA  the  re- 
flected ray  \  the  angle  CBD  is  called  the  angle 
of  incidence,  and  DBA  the  angle  of  reflection.  Fig.  344. 

The  reflection  of  heat,  like  that  of  light,  is  governed  by  the  two  following 
laws  : — 

I.   The  angle  of  reflection  is  equal  to  the  angle  of  incidence. 


354 


On  Heat. 


[417- 


II.  Both  the  incident  and  the  reflected  ray  are  in  the  same  plane  with  the 
normal  to  the  reflecting  surface. 

418.   Experimental  demonstration  of  the  laws  of  reflection  of  neat. 

—This  may  be  effected  by  means  of  Melloni's  thermo-pile  and  also  by  the 
conjugate  mirrors  (420).  Fig.  345  represents  the  arrangement  adopted  in 
the  former  case.  MN  is  a  horizontal  bar,  about  a  metre  in  length  graduated 


Fig.  345- 

in  millimetres,  on  which  slide  various  parts,  which  can  be  clamped  by  means 
of  screws.  The  source  of  heat,  S,  is  a  platinum  spiral,  kept  at  a  white  heat 
in  a  spirit  lamp.  A  screen  K,  when  raised,  cuts  off  the  radiation  from  the 
source  ;  a  second  screen,  F,  with  an  aperture  in  the  centre,  gives  the  rays  a 
parallel  direction.  At  the  other  end  is  an  upright  rod,  I,  with»a  graduated 
dial,  the  zero  of  which  is  in  the  direction  of  MN,  and  therefore  parallel  to 
the  pencil  S;;z.  In  the  centre  of  the  dial  is  an  aperture,  in  which  turns  an 
axis  that  supports  a  metallic  mirror  ;//.  About  this  axis  turns  an  index,  R, 
on  which  is  fixed  the  thermo-pile,  P,  in  connection  with  the  galvanometer,  G. 
H  is  a  screen,  the  object  of  which  is  to  cut  off  any  direct  radiation  from  the 
source  of  heat  towards  the  pile.  In  order  not  to  mask  the  pile,  it  is  not  re- 
presented in  the  position  it  occupies  in  the  experiment. 

By  lowering  the  screen  K.  a  pencil  of  parallel  rays,  passing  through  the 
aperture  F,  falls  upon  the  mirror  mt  and  is  there  reflected.  If  the  index  R 
is  not  in  the  direction  of  the  reflected  pencil,  this  latter  does  not  impinge  on 
the  pile,  and  the  needle  of  the  galvanometer  remains  stationary ;  but  by 
slowly  turning  the  index  R,  a  position  is  found  at  which  the  galvanometer 
attains  its  greatest  deviation,  which  is  the  case  when  the  pile  receives  the 
reflected  pencil  perpendicularly  to  its  surface.  Reading  off  then  on  the 
dial  the  position  of  a  small  needle  perpendicular  to  the  mirror,  it  is  observed 
that  this  bisects  the  angle  formed  by  the  incident  and  the  reflected  pencil, 
which  demonstrates  the  first  law. 

The  second  law  is  also  proved  by  the  same  experiment,  for  the  various 
pieces  of  the  apparatus  are  arranged  so  that  the  incident  and  reflected  rays 
are*  in  the  same  horizontal  plane,  and  therefore  at  right  angles  to  the  reflect- 
ing surface,  which  is  vertical. 


-420]  Verification  of  the  Laws  of  Reflection.  355 

419.  Reflection  from  concave  mirrors. — Concave  mirrors  or  reflectors 
are  polished  spherical  or  parabolic  surfaces  of  metal  or  of  glass,  which  are 
used  to  concentrate  luminous  or  calorific  rays  in  the  same  point. 

We  shall  only 
consider  the  case 
of  spherical 

mirrors.  Fig.  347       ,,  ^..  B 

represents     two  H//'1^V.' p 

of  these  mirrors;    J[—     ^^, ;;:••:>. 

fig-  346  gives  a    T\^~S.   '-'•'-'•'-•      c 

medial     section,     15\^_ 

which   is   called 
the  principal  sec- 
tion. The  centre  Fig>  346> 
C  of  the  sphere 

to  which  the  mirror  belongs  is  called  the  centre  of  cuivature  ;  the  point  A, 
the  middle  of  the  reflector,  is  the  centre  of  the  figure  ;  the  straight  line  AB 
passing  through  these  points,  is  the  principal  axis  of  the  mirror. 

In  order  to  apply  to  spherical  mirrors  the  laws  of  reflection  from  plane 
surfaces,  they  are  considered  to  be  composed  of  an  infinite  number  of  in- 
finitely small  plane  surfaces,  each  belonging  to  the  corresponding  tangent 
plane  ;  the  normals  to  these  small  surfaces  are  all  radii  of  the  same  sphere, 
and  therefore  meet  at  its  centre,  the  centre  of  curvature  of  the  mirror. 

Suppose  now,  on  the  axis  AB  of  the  mirror  MN,  a  source  of  heat  so 
distant  that  the  rays  EK,  PH  .  .  .  .  which  emanate  from  it  may  be  con- 
sidered as  parallel.  From  the  hypothesis  that  the  mirror  is  composed  of 
an  infinitude  of  small  planes,  the  ray  EK  is  reflected  from  the  plane  K  just 
as  from  a  plane  mirror  ;  that  is  to  say,  CK  being  the  normal  to  this  plane, 
the  reflected  ray  takes  a  direction  such  that  the  angle  CKF  is  equal  to  the 
angle  CKE.  The  other  rays,  PH,  GI  .  .  .  .  are  reflected  in  the  same 
manner,  and  all  converge  approximately  towards  the  same  point  F,  on  the 
line  AC.  There  is  then  a  concentration  of  the  rays  in  this  point,  and  conse- 
quently a  higher  temperature  than  at  any  other  point.  This  point  is  called 
the  focus,  and  the  distance  from  the  focus  to  the  mirror  at  A  is  the  focal 
distance. 

In  the  above  figure  the  heat  is  propagated  along  the  lines  EKF,  LDF,  in 
the  direction  of  the  arrows  ;  but,  conversely,  if  the  heated  body  be  placed  at 
F,  the  heat  is  propagated  along  the  lines  FKE,  FDL,  so  that  the  rays  emitted 
from  the  focus  are  nearly  parallel  after  reflection. 

420.  Verification  of  the  laws  of  reflection. — The  following  experiment, 
which  was  made  for  the  first  time  by  Pictet  and  Saussure,  and  which  is 
known  as  the  experiment  of  the  conjugate  mirrors,  demonstrates  not  only 
the  existence  of  the  foci,  but  also  the  laws  of  reflection.  Two  reflectors, 
M  and  N  (fig.  347),  are  arranged  at  a  distance  of  4  to  5  yards,  and  so  that 
their  axes  coincide.  In  the  focus  of  one  of  them,  A,  is  placed  a  small  wire 
basket  containing  a  red-hot  iron  ball.  In  the  focus  of  the  other  is  placed 
B,  an  inflammable  body,  such  as  gun-cotton  or  phosphorus.  The  rays 
emitted  from  the  focus  A  are  first  reflected  from  the  mirror  M,  in  a  direction 
parallel  to  the  axis  (419),  and  impinging  on  the  other  mirror,  N,  are  reflected 
so  that  they  coincide  in  the  focus  B.  That  this  is  so  is  proved  by  the  fact 


356 


On  Heat. 


[420- 


that  the  gun-cotton  at  this  point  takes  fire,  which  is  not  the  case  if  it  is  above 
or  below  it. 

The  experiment  also  serves  to  show  that  light  and  heat  are  reflected  in 
the  same  manner.  For  this  purpose  a  lighted  candle  is  placed  in  the  focus 
of  A,  and  a  ground-glass  screen  in  the  focus  of  B,  when  a  luminous  focus 
is  seen  on  it  exactly  in  the  spot  where  the  gun-cotton  ignites.  Hence  the 
luminous  and  the  calorific  foci  are  produced  at  the  same  point,  and  the 
reflection  takes  place  in  both  cases  according  to  the  same  laws,  for  it  will 


be  afterwards  shown  that  for  light  the  angle  of  reflection  is  equal  to  the 
angle  of  incidence,  and  that  both  the  incident  and  the  reflected  rays  are  in 
the  same  plane  perpendicular  to  the  plane  reflecting  surface. 

In  consequence  of  the  high  temperature  produced  in  the  foci  of  concave 
mirrors  they  have  been  called  burning  mirrors.  It  is  stated  that  Archi- 
medes burnt  the  Roman  vessels  before  Syracuse  by  means  of  such  mirrors. 
Buffon  constructed  burning  mirrors  of  such  power  as  to  prove  that  the  feat 
attributed  to  Archimedes  was  not  impossible.  The  mirrors  were  made  of  a 
number  of  silvered  plane  mirrors  about  8  inches  long  by  5  broad.  They 
could  be  turned  independently  of  each  other  in  such  a  manner  that  the 
rays  reflected  from  each  coincided  in  the  same  point.  With  128  mirrors 
and  a  hot  summer's  sun  Buffon  ignited  a  plank  of  tarred  wood  at  a  distance 
of  70  yards. 

421.  Reflection  in  a  vacuum. — Heat  is  reflected  in  a  vacuum  as  well  as 
in  air,  as  is  seen  from  the  following  experiment  (fig.  348),  due  to  Sir  Hum- 
phry Davy.  Two  small  concave  reflectors  were  placed  opposite  each  other 
under  the  receiver  of  an  air-pump.  In  the  focus  of  one  was  placed  a  delicate 
thermometer,  and  in  the  focus  of  the  other  a  platinum  wire  made  incan- 


-423] 


Reflecting  Power. 


357 


Fig.  348. 


descent  by  means  of  a  galvanic  current.  The  thermometer  was  immedi- 
ately seen  to  rise  several  degrees,  which  could  only  be  due  to  reflected  heat, 
for  the  thermometer  did  not  show  any 
increase  of  temperature  if  it  were  not 
exactly  in  the  focus  of  the  second  re- 
flector. 

422.  Apparent  reflection  of  cold. — 
If  two   mirrors   are  arranged   as   repre- 
sented in  fig.  347,  and  a  piece  of  ice  is 
placed  in  one  of  the  foci  instead  of  the 
red-hot  ball,    the   surrounding  tempera- 
ture being  greater  than  zero,  a  differential 
thermometer  placed  in  the  focus  of  the 
second  reflector  would  exhibit  a  decrease 
in  temperature  of  several  degrees.     This 
appears    at    first    to    be   caused   by   the 
emission  of  frigorific  rays  from  ice.     It 
is,  however,  easily  explained  from  what 
has   been    said   about   the  mobile   equi- 
librium of  temperature  (415).     There  is 
still  an  exchange  of  temperature,  but  here 

the  thermometer  is  the  warmest  body.  As  the  rays  which  the  thermometer 
emits  are  more  intense  than  those  emitted  by  the  ice,  the  former  gives  out 
more  heat  than  it  receives,  and  hence  its  temperature  sinks. 

The  sensation  of  cold  experienced  when  we  stand  near  a  plaster  or  stone 
wall  whose  temperature  is  lower  than  that  of  our  body,  or  when  we  stand  in 
front  of  a  wall  of  ice,  is  explained  in  the  same  way. 

423.  Reflecting:  power. — The  reflecting  power of  a  substance  is  its  pro- 
perty of  throwing  off  a  greater  or  less  proportion  of  incident  heat. 

This  power  varies  in  different  substances.  In  order  to  study  this  power 
in  different  bodies  without  having  recourse  to  as  many  reflectors,  Leslie 
arranged  his  experiment  as  shown  in  fig.  349.  The  source  of  heat  is  a 
cubical  canister,  M,  now  known  as  Leslies  cube,  filled  with  hot  water.  A 
plate,  a,  of  the  substance  to  be  experimented  upon  is  placed  on  the  axis  of  a 
reflecting  mirror  between  the  focus  and  the  mirror.  In  this  manner  the  rays 
emitted  by  the  source  are  first  reflected  from  the  mirror  and  impinge  on  the 
plate  a,  where  they  are  again  reflected  and  converge  to  the  focus  between  the 
plate  and  the  mirror,  in  which  point  a  differential  thermometer  is  placed. 
The  reflector  and  the  thermometer  are  always  in  the  same  position,  and  the 
water  of  the  cube  is  always  kept  at  100°,  but  it  is  found  that  the  temperature 
indicated  by  the  thermometer  varies  with  the  nature  of  the  plate.  This 
method  gives  a  means  of  determining,  not  the  absolute  reflecting  power  of  a 
body,  but  its  power  relatively  to  that  of  some  body  taken  as  a  standard  of 
comparison.  For  from  what  has  been  said  on  the  application  of  Newton's 
law  to  the  differential  thermometer,  the  temperatures  which  this  instrument 
indicates  are  proportional  to  the  quantities  of  heat  which  it  receives.  Hence, 
if  in  the  above  experiment  a  plate  of  glass  causes  the  temperature  to  rise  i° 
and  a  plate  of  lead  6°,  it  follows  that  the  quantity  of  heat  reflected  by  the 
latter  is  six  times  as  great  as  that  reflected  by  the  former.  For  the  heat 


353 


On  Heat. 


[423- 


emitted  by  the  source  remains  the  same,  the  concave  reflector  receives  the 
same  portion,  and  the  difference  can  only  arise  from  the  reflecting  power  of 
the  plate  a. 


By  this  method  Leslie  determined  the  reflecting  powers  of  the  following 
substances,  relatively  to  that  of  brass,  taken  as  100  : — 


Polished  brass 
Silver  . 
Steel    . 
Lead 


100  Indian  ink 

90  Glass 

70  Oiled  glass 

60  Lampblack 


13 
10 

5 
o 


The  numbers  only  represent  the  relative  reflecting  power  as  compared 
with  that  of  brass.  Their  absolute  power  is-  the  relation  of  the  quantity  of 
heat  reflected  to  the  quantity  of  heat  received.  Desains  and  De  la  Provostaye, 
who  examined  the  absolute  reflecting  power  of  certain  metals,  obtained 
the  following  results  by  means  of  Melloni's  thermo-multiplier  (412),  the  heat 
being  reflected  at  an  angle  of  50°  : — 


Silver  plate 
Gold  . 
Brass 
Platinum  . 


0-97  Steel 

0-95  Zinc 

o%93  Iron 

0*83  Cast  iron 


0-82 
0-8 1 
077 
074 


424.  Absorbing-  power. — The  absorbing  power  of  a  body  is  its  property 
of  allowing  a  greater  or  less  quantity  of  incident  heat  to  pass  into  its  mass. 
Its  absolute  value  is  the  ratio  of  the  quantity  of  heat  absorbed  to  the  quantity 
of  heat  received. 

The  absorbing  power  of  a  body  is  always  inversely  as  its  reflecting 
power  :  a  body  which  is  a  good  absorbent  is  a  bad  reflector,  and  vice  versa. 


-425]  Radiating  Power.  359 

It  was  formerely  supposed  that  the  two  powers  were  exactly  complementary, 
that  the  sum  of  the  reflected  and  absorbed  heat  was  equal  to  the  total  quan- 
tity of  incident  heat.  This  is  not  the  case  ;  it  is  always  less  :  the  incident 
heat  is  divided  into  three  parts — ist,  one  which  is  absorbed;  2nd,  another 
which  is  reflected  regularly — that  is,  according  to  laws  previously  demon- 
strated (417) ;  and  a  third,  which  is  irregularly  reflected  in  all  directions, 
and  which  is  called  scattered  or  diffused  heat. 

In  order  to  determine  the  absorbing  power  of  bodies,  Leslie  used  the 
apparatus  which  he  employed  in  determining  the  reflecting  powers  (423). 
But  he  suppressed  the  plate  a,  and  placed  the  bulb  of  the  thermometer  in 
the  focus  of  the  reflector.  This  bulb  being  then  covered  successively  with 
lampblack,  or  varnish,  or  with  gold,  silver,  or  copper  foil,  &c.,  the  thermo- 
meter exhibited  a  higher  temperature  under  the  influence  of  the  source  of 
heat,  M,  according  as  the  substance  with  which  the  bulb  was  covered 
absorbed  more  heat.  Leslie  found  in  this  way  that  the  absorbing  power  of 
a  body  is  greater  the  less  its  reflecting  power.  In  these  experiments, 
however,  the  relation  of  the  absorbing  powers  cannot  be  deduced  from 
that  of  the  temperatures  indicated  by  the  thermometer,  for  Newton's 
law  is  not  exactly  applicable  in  this  case,  as  it  only  prevails  for  bodies 
whose  substance  does  not  vary,  and  here  the  covering  of  the  bulb  varied 
with  each  observation.  But  we  shall  presently  show  (426)  how  the  com- 
parative absorbing  powers  may  be  deduced  from  the  ratios  of  the  emissive 
powers. 

Taking,  as  a  source  of  heat,  a  canister  filled  with  water  at  100°,  Melloni 
found  by  means  of  the  thermo-multiplier  the  following  relative  absorbing 
powers  : — 

Lampblack        ....     100     Indian  ink 85 

White  lead        .         .         .         .     100     Shellac 72 

Isinglass 91     Metals 13 

425.  Radiating:  power. — The  radiating  or  emissive  power  of  a  body  is 
its  capability  of  emitting,  at  the  same  temperature,  and  with  the  same  extent 
of  surface,  greater  or  less  quantities  of  heat. 

The  apparatus  represented  in  fig.  349  was  also  used  by  Leslie  in  deter- 
mining the  radiating  power  of  bodies.  For  this  purpose  the  bulb  of  the 
thermometer  was  placed  in  the  focus  of  the  reflector,  and  the  faces  of  the 
canister  M  were  formed  of  different  metals,  or  covered  with  different 
substances  such  as  lampblack,  paper,  &c.  The  cube  being  filled  with  hot 
water,  at  100°,  and  all  other  conditions  remaining  the  same,  Leslie  turned 
each  face  of  the  cube  successively  towards  the  reflectors,  and  noted  the 
temperature  each  time.  That  face  which  was  coated  with  lampblack  caused 
the  greatest  elevation  of  temperature,  and  the  metal  faces  the  least.  Applying 
Newton's  law,  and  representing  the  heat  emitted  by  lampblack  as  100,  Leslie 
formed  the  following  table  of  radiating  powers  : — 
Lampblack  .  .  .  .100  Tarnished  lead  .  .  .  .45 

White  lead         .         .         .         .100     Mercury 20 

Paper 98     Polished  lead      .        .        .        .19 

Ordinary  white  glass         .         .       90     Polished  iron       .         .         .         .15 
Isinglass 80     Tin,  gold,  silver,  copper,  £c.       .12 


On  Heat.  [425- 

It  will  be  seen  that,  in  this  table,  the  order  of  the  bodies  is  exactly  the 
reverse  of  that  in  the  tables  of  reflecting  powers. 

The  radiating  powers  of  several  substances  were  determined  by  Desains 
and  De  la  Provostaye,  who  used  the  thermo-multiplier.  They  found  in  this 
manner  the  following  numbers  compared  with  lampblack  as  100  : — 


Platinum  foil   . 
Burnished  platinum 
Silver  deposited  chemically 
Copper  foil 
Gold  leaf 


Pure  silver  laminated 

„  burnished 

„  deposited  chemi- 

cally and  bur- 
nished 


3-00 
2-50 


10-80 
9-50 
5-36 
4-90 
4-28 

It  appears,  therefore,  that  the  radiating  power  found  by  Leslie  for  the 
metals  is  too  large. 

426.  Identity  of  the  absorbing  and  radiating:  powers. — The  absorb- 
ing power  of  a  body  cannot  be  accurately  deduced  from  its  reflecting  power, 
because  the  two  are  not  exactly  complementary.  But  the  absorbing  power 
would  be  determined  if  it  could  be  shown  that  in  the  same  body  it  is  equal 
to  the  radiating  power.  This  conclusion  has  been  drawn  by  Dulong  and 
Petit  from  the  following  experiments  : — In  a  large  glass  globe,  blackened  on 
the  inside,  was  placed  a  thermometer  at  a  certain  temperature,  1 5°  for  ex- 
ample ;  the  globe  was  kept  at  zero  by  surrounding  it  with  ice,  and  having 
been  exhausted  by  means  of  a  tubulure  connected  with  the  air-pump,  the  time 
was  noted  which  elapsed  while  the  thermometer  fell  through  5°.  The  experi- 
ment was  then  made  in  the  contrary  direction  ;  that  is,  the  sides  of  the  globe 
were  heated  to  1 5°,  while  the  thermometer  was  cooled  to  zero  :  the  time  was 
then  observed  which  the  thermometer  occupied  in  rising  through  5°.  It  was 
found  that  this  time  was  exactly  the  same  as  that  which  the  thermometer 

had  taken  in  sinking  through  5°,  and  it  was 
thence  concluded  that  the  radiating  power  is 
equal  to  the  absorbing  power  for  the  same 
body,  and  for  the  same  difference  between  its 
temperature  and  the  temperature  of  the  sur- 
rounding medium,  because  the  quantities  of 
heat  emitted  or  absorbed  in  the  same  time  are 
equal. 

This  point  may  also  be  demonstrated  by 
means  of  the  following  apparatus  devised  by 
Ritchie.  Fig.  350  represents  what  is  virtually  a 
differential  thermometer,  the  two  glass  bulbs  of 
which  are  replaced  by  two  cylindrical  reservoirs 
B  and  C,  of  metal,  and  full  of  air.  Between 
them  is  a  third  and  larger  one  A,  which  can  be 
filled  with  hot  water  by  means  of  a  tubulure. 
The  ends  of  B  and  of  A,  which  face  the  right, 
are  coated  with  lampblack ;  those  of  C  and  of  A, 
which  face  the  left,  are  either  painted  white,  or 
are  coated  with  silver  foil.  Thus  of  the  two 
faces  opposite  each  other,  one  is  black  and  the  other  white ;  hence  when 
the  cylinder  A  is  filled  with  hot  water,  its  white  face  radiates  towards  the 


-427]  Radiating  Power.  361 

black  face  of  B,  and  its  black  face  towards  the  white  face  of  C.  Under 
these  circumstances  the  liquid  in  the  stem  does  not  move,  indicating  that 
the  two  reservoirs  are  at  the  same  temperature.  On  the  one  hand,  the 
greater  emissive  power  of  the  black  face  of  A  is  compensated  by  the  smaller 
absorptive  power  of  the  white  face  of  C  ;  while,  on  the  other  hand,  the 
feebler  radiating  power  of  the  white  face  of  A  is  compensated  by  the  greater 
absorbing  power  of  the  black  face  of  B. 

The  experiment  may  be  varied  by  replacing  the  two  white  faces  by  discs 
of  paper,  glass,  porcelain,  £c. 

427.  Causes  which  modify  the  reflecting-,  absorbing-,  and  radiating: 
powers. — As  the  radiating  and  absorbing  powers  are  equal,  any  cause 
which  affects  the  one  affects  the  other  also.  And  as  the  reflecting  power 
varies  in  an  inverse  manner,  whatever  increases  it  diminishes  the  radiating 
and  absorbing  powers,  and  vice  versA. 

It  has  been  already  stated  that  these  different  powers  vary  with  different 
bodies,  and  that  metals  have  the  greatest  reflecting  power,  and  lampblack 
the  least.  In  the  same  body  these  powers  are  modified  by  the  degree  of 
polish,  the  density,  the  thickness  of  the  radiating  substance,  the  obliquity  of 
the  incident  or  emitted  rays,  and,  lastly,  by  the  nature  of  the  source  of  heat. 

It  has  been  usually  assumed  that  the  reflecting  power  increases  with  the 
polish  of  the  surface,  and  that  the  other  powers  diminish  therewith.  But 
Melloni  showed  that  by  scratching  a  polished  metallic  surface  its  reflecting 
power  was  sometimes  diminished  and  sometimes  increased.  This  pheno- 
menon he  attributed  to  the  greater  or  less  density  of  the  reflecting  surface. 
If  the  plate  had  been  originally  hammered,  its  homogeneity  would  be 
destroyed  by  this  process,  the  molecules  would  be  closer  together  on  the 
surface  than  in  the  interior,  and  the  reflecting  power  would  be  increased. 
But  if  the  surface  is  scratched,  the  internal  and  less  dense  mass  becomes 
exposed,  and  the  reflecting  power  diminished.  On  the  contrary,  in  a  plate 
which  has  not  been  hammered,  and  which  is  homogeneous,  the  reflecting 
power  is  increased  when  the  plate  is  scratched,  because  the  density  at  the 
surface  is  increased  by  the  scratches. 

Melloni  found  that  when  the  faces  of  a  cube  filled  with  water  at  a  constant 
temperature  were  varnished,  the  emissive  power  increased  with  the  number 
of  layers  up  to  16  layers,  while  above  that  point  it  remained  constant, 
whatever  the  number.  The  thickness  of  the  16  layers  was  calculated  to  be 
0-04  mm.  With  reference  to  metals,  gold  leaves  of  0*008,  0-004,  and  0-002 
of  a  millimetre  in  thickness,  having  been  successively  applied  on  the  sides 
of  a  cube  of  glass,  the  diminution  of  radiant  heat  was  the  same  in  each  case. 
It  appears,  therefore,  that,  beyond  certain  limits,  the  thickness  of  the  radiat- 
ing layer  of  metal  is  without  influence. 

The  absorbing  power  is  greatest  when  the  rays  are  at  right  angles  ;  and 
it  diminishes  in  proportion  as  the  incident  rays  deviate  from  the  normal. 
This  is  one  of  the  reasons  why  the  sun  is  hotter  in  summer  than  in  winter, 
because,  in  the  former  case,  the  sun's  rays  are  less  oblique. 

The  radiating  power  of  gaseous  bodies  in  a  state  of  combustion  is  very 
weak,  as  is  seen  by  bringing  the  bulb  of  a  thermometer  near  a  hydrogen 
flame,  the  temperature  of  which  is  very  high.  But  if  a  platinum  spiral  be 
placed  in  this  flame,  it  assumes  the  temperature  of  the  flame,  and  radiates 

R 


362 


On  Heat. 


[427- 


a  great  amount  of  heat,  as  is  shown  by  the  thermometer.  For  a  similar 
reason  the  flames  of  oil  and  of  gas  lamps  radiate  more  than  a  hydrogen 
flame,  in  consequence  of  the  excess  of  carbon  which  they  contain,  and 
which,  not  being  entirely  burned,  becomes  incandescent  in  the  flame. 

428.  Ittelloni's    researches   on  radiant  heat. — For  our  knowledge  of 
the  phenomena  of  the  reflection,  emission,  and  absorption  of  heat  which 
have  up  to  now  been  described,  science  is  indebted  mainly  to  Leslie.     But 
since  his  time  the  discovery  of  other  and  far  more  delicate  modes  of  de- 
tecting and  measuring  heat  has  not  only  extended  and  corrected  our  pre- 
vious knowledge,  but  has  led  to  the  discovery  of  other  phenomena  of  radiant 
heat,  which,  without  such  improved  means,  must  have  remained  unknown. 

This  advance  in  science  is  due  to  an  Italian  philosopher,  Melloni,  who 
first  applied  the  thermo-electric  pile,  invented  by  Nobili,  to  the  measurement 
of  very  small  differences  of  temperature  ;  a  method  of  which  a  preliminary 
account  has  already  been  given  (412). 

In  his  experiments  Melloni  used  five  sources  of  heat — ist,  a  Locatelli's 
lamp — one,  that  is,  without  a  glass  chimney,  but  provided  with  a  reflector 

<p-?s  (fig-  350;  2nd,  an 
\(ffi  Argand  lamp,  that 
is,  one  with  a  chim- 
ney and  a  double 
draught  ;  3rd,  a 
platinum  spiral, 
kept  red-hot  by  a 
spirit  lamp  (fig. 
352) ;  4th,  a  black- 
ened copper  plate, 
kept  at  a  tem- 
perature of  about 
400  degrees  by  a 
spirit  lamp  (fig. 
353);  5th,  a  copper 
tube,  blackened  on  the  outside  and  filled  with  water  at  100°  (fig.  354). 

429.  Dynamical  theory  of  heat. — Before  describing  the  results  arrived 
at  by  Melloni  and  others,  it  will  be  convenient  to  explain  here  the  view  now 
generally  taken  as  to  the  mode  in  which  heat  is  propagated.     For  additional 
information  the  chapter  on  the  Mechanical  Theory  of  Heat  and  the  book  on 
Light  should  be  read.     According  to  what  has  been  already  stated,  a  hot 
body  is  nothing  more  than  one  whose  particles  are  in  a  state  of  vibration. 
The  higher  the  temperature  of  the  body,  the  more  rapid  are  these  vibrations, 
and  a  diminution  in  temperature  is  but  a  diminished  rapidity  of  vibration  of 
the  particles.     The  propagation  of  heat  through  a  bar  is  due  to  a  gradual 
communication  of  this  vibratory  motion  from  the  heated  part  to  the  rest  of 
the  bar.     A  good  conductor  is  one  which  readily  takes  up  and  transmits  the 
vibratory  motion  from  particle  to  particle,  while  a  bad  conductor  is  one  which 
takes  up  and  transmits  the  motion  with  difficulty.    But  even  through  the  best 
conductors  the  propagation  of  this  motion  is  comparatively  slow.     How  then 
are  we  to  explain  the  instantaneous  perception  of  heat  experienced  when  a 
screen  is  removed  from  a  fire,  or  when  a  cloud   drifts   from   the  face  of 
the  sun  ?     In  this  case,  the  heat  passes  from  one  body  to  another  without 


Fig.  351- 


Fig.  352- 


Fig.  353- 


Fig.  354- 


-430]  Dynamical  Theory  of  Heat.  363 

affecting  the  temperature  of  the  medium  which  transmits  it.  In  order  to 
explain  these  phenomena,  it  is  imagined  that  all  space,  the  interplanetary 
spaces  as  well  as  the  interstices  in  the  hardest  crystal  or  the  heaviest  metal, 
in  short,  matter  of  any  kind,  is  permeated  by  a  medium  having  the  properties 
of  a  fluid  of  infinite  tenuity,  called  ether.  The  particles  of  a  heated  body 
being  in  a  state  of  intensely  rapid  vibration,  communicate  their  motion  to 
the  ether  around  them,  throwing  it  into  a  system  of  waves  which  travel 
through  space  and  pass  from  one  body  to  another  with  the  velocity  of  light. 
When  the  undulations  of  the  ether  reach  a  given  body,  the  motion  is  again 
delivered  up  to  the  particles  of  that  body,  which  in  turn  begin  to  vibrate  ; 
that  is,  the  body  becomes  heated.  This  passage  of  motion  through  the 
hypothetical  ether  is  termed  radiation,  and  a  so-called  ray  of  heat  is  merely 
the  direction  of  the  motion  of  one  series  of  waves. 

It  will  facilitate  the  understanding  of  this  to  consider  the  analogous  mode 
in  which  sound  is  produced  and  propagated.  A  sounding  body  is  one  whose 
entire  mass  is  in  a  state  of  vibration  ;  the  more  rapid  the  rate  of  vibration, 
the  more  acute  the  sound  ;  the  slower  the  rate  of  vibration,  the  deeper  the 
sound.  This  vibratory  motion  is  communicated  to  the  surrounding  air,  by 
means  of  which  the  vibrations  reach  the  auditory  nerve,  and  there  produce 
the  sensation  of  sound.  If  a  metal  ball-  be  heated,  say,  to  the  temperature 
of  boiling  water,  we  can  ascertain  that  it  radiates  heat,  although  we  cannot 
see  any  luminosity ;  and  if  its  temperature  be  gradually  raised,  we  see  it 
become  successively  of  a  dull  red,  bright  red,  and  dazzling  white.  At  each 
particular  temperature  the  heated  body  emits  waves  of  a  definite  length  ;  in 
other  words,  its  particles  vibrate  in  a  certain  period.  As  its  temperature 
rises  it  sends  out  other  and  more  rapid  undulations,  which  coexist,  how- 
ever, with  all  those  which  it  had  previously  emitted.  Thus  the  motion  at 
each  successive  temperature  is  compounded  of  all  preceding  ones. 

It  has  been  seen  that  vibrations  of  the  air  below  and  above  a  certain  rate 
do  not  affect  the  auditory  nerve  (244) ;  it  can  only  take  up  and  transmit  to  the 
brain  vibrations  of  a  certain  periodicity.  So  too  with  the  vibrations  which 
produce  light.  The  optic  nerve  is  insensible  to  a  large  number  of  wave- 
lengths. It  can  apprehend  only  those  waves  that  form  the  visible  spectrum. 
If  the  rate  of  undulation  be  slower  than  the  red  or  faster  than  the  violet, 
though  intense  motion  may  pass  through  the  humours  of  the  eye  and  fall 
upon  the  retina,  yet  we  shall  be  utterly  unconscious  of  the  fact,  for  the 
optic  nerve  cannot  take  up  and  respond  to  the  rate  of  vibrations  which  exist 
beyond  the  visible  spectrum  in  both  directions.  Hence  these  are  termed 
invisible  or  obscure  rays.  A  vast  quantity  of  these  obscure  rays  is  emitted 
by  flames  which,  though  intensely  hot,  are  yet  almost  non-luminous,  such  as 
the  oxy-hydrogen  flame,  or  that  of  a  Bunsen's  burner ;  for  the  vibrations 
which  these  emit,  though  capable  in  part  of  penetrating  the  media  of  the 
eye,  are  incapable  of  exciting  in  the  optic  nerve  the  sensation  of  light. 

430.  Thermal  analysis  of  solar  light. — When  a  solar  ray  (fig.  355), 
admitted  through  an  aperture  in  a  dark  room,  is  concentrated  on  a  prism 
of  rock  salt  by  means  of  a  lens  of  the  same  material,  and  then,  after  emerging 
from  the  prism,  is  received  on  a  screen,  it  will  be  found  to  present  a  band  of 
colours  in  the  following  order  :  red,  orange,  yellow,  green,  blue,  and  violet 
This  is  called  the  spectrum  (564). 

R  2 


364  On  Heat.  [430- 

If  now  a  narrow  and  delicate  thermo-pile  be  placed  successively  on  the 
space  occupied  by  each  of  the  colours,  it  will  be  scarcely  affected  on  the 


r 


Fig.  355- 

violet,  but  in  passing  over  the  other  colours  it  will  indicate  a  gradual  rise  of 
temperature,  which  is  greatest  at  the  red.  Painters,  thus  guided  by  a  cor- 
rect but  unconscious  feeling,  always  speak  of  blue  and  green  colours  as  cold, 
and  of  red  and  orange  as  warm  tones.  If  the  pile  be  now  moved  in  the 
same  direction  beyond  the  limits  of  the  luminous  spectrum,  the  temperature 
will  gradually  rise  up  to  CP,  at  which  it  attains  its  maximum.  From  this 
point  the  pile  indicates  a  decrease  of  temperature  until  it  reaches  a  point,  O, 
where  it  ceases  to  be  affected.  This  point  is  about  as  distant  from  R  as  the 
latter  is  from  V  ;  that  is,  there  is  a  region  in  which  thermal  effects  are  pro- 
duced extending  as  far  beyond  the  red  end  of  the  spectrum  in  one  direction 
as  the  entire  length  of  the  visible  spectrum  is  in  the  other.  In  accordance 
with  what  we  have  stated,  the  sun's  light  consists  of  rays  of  different  rates  of 
vibration  ;  by  their  passage  through  the  prism  they  are  unequally  broken  or 
refracted  ;  those  of  greatest  wave-length  or  slowest  vibrating  period  are  least 
bent  aside,  or  are  said  to  be  the  least  refrangible,  while  those  with  shorter 
wave-lengths  are  the  most  refrangible. 

These  non-luminous  rays  outside  the  red  are  called  the  extra  or  ultra-red 
rays,  or  sometimes  the  Herschelian  rays,  from  Sir  W.  Herschel,  who  first 
discovered  their  existence. 

If,  in  the  above  case,  prisms  of  other  materials  than  rock  salt  be  used,  the 
position  of  maximum  heat  will  be  found  to  vary  with  the  nature  of  the  prism, 
a  fact  first  noticed  by  Seebeck.  Thus  with  a  prism  of  water  it  is  in  the  yellow ; 
with  one  of  crown  glass,  in  the  middle  of  the  red,  and  so  on.  These  changes 
are  due  to  the  circumstance  that  prisms  of  different  materials  absorb  rays  of 
different  refrangibility  to  unequal  extents.  But  rock  salt  practically  allows  heat 
of  all  kinds  to  pass  with  equal  facility,  and  thus  gives  a  normal  spectrum. 

431.  Tyndall's  researches. — Tyndall  investigated  the  spectrum  pro- 
duced by  the  electric  light,  by  the  following  mode  of  experimenting  : — The 
electric  light  was  produced  between  charcoal  points  by  a  Grove's  battery  of 
fifty  cells.  The  beam,  rendered  parallel  by  a  double  rock-salt  lens,  was 
caused  to  pass  through  a  narrow  slit,  and  then  through  a  second  lens  of  rock 
salt ;  the  slices  of  white  light  thus  obtained  being  decomposed  by  a  prism 
of  the  same  material.  To  investigate  the  thermal  conditions  of  the  spec- 
trum a  linear  thermo-electric  pile  was  used ;  that  is,  one  consisting  of  a 


-431] 


TyndaWs  Researches. 


365 


number  of  elements  arranged  in  a  line,  and  in  front  of  which  was  a  slit  that 
could  be  narrowed  to  any  extent.  The  instrument  was  mounted  on  a 
movable  bar  connected  with  a  fine  screw,  so  that  by  turning  a  handle  the 
pile  could  be  pushed  forward  through  the  smallest  space.  On  placing  this 
apparatus  successively  in  each  part  of  the  spectrum  of  the  electric  light, 
the  heating  effected  at  various  points  near  each  other  was  determined  by  the 
indications  of  a  very  delicate  galvanometer.  As  in  the  case  of  the  solar 
spectrum,  the  heating  effect  gradually  increased  from  the  violet  end  towards 
the  red,  and  was  greatest  in  the  dark  space  beyond  the  red.  The  position 
of  the  greatest  heat  was  about  as  far  from  the  limit  of  the  visible  red  as  the 
latter  was  from  the  green,  and  the  total  extent  of  the  invisible  spectrum  was 
found  to  be  twice  that  of  the  visible. 

The  increase  of  temperature  in  the  dark  space  is  very  considerable.  If 
thermal  intensities  are  represented  by  perpendicular  lines  of  proportionate 
length,  erected 
at  those  parts  of 
the  spectrum  to 
which  they  cor- 
respond, on  pass- 
ing beyond  the 
red  end  these 
lines  increase 
rapidly  and 

greatly  in  length, 
reach  a  maxi- 
mum, and  then 
fall  somewhat 
more  suddenly. 
If  these  lines  are 

connected,  they  form  a  curve  (fig.  356),  which  beyond  the  red  represents 
a  massive  peak,  quite  dwarfing  by  its  magnitude  that  of  the  visible 
spectrum.  In  fig.  357,  the  dark  parts  at  the  end  represent  the  obscure 
radiation.  The  curve  is  based,  in  the  manner  above  stated,  on  the  results 
obtained  by  Tyndall  with  the  electric  light.  The  upper  curve  in  fig.  357  re- 
presents the  spectrum  of  sun  light  from  the  experiments  of  Miiller  with  a 
rock-salt  prism,  while  the  lower  curve  represents  the  results  obtained  with 
the  use  of  a  flint-glass  prism,  which  is  thus  seen  to  absorb  some  of  the  ultra- 
red  radiation. 

Tyndall  found  that  by  interposing  various  substances,  more  especially 
water,  in  certain  thicknesses,  in  the  path  of  the  electric  light,  the  ultra-red 
radiation  was  greatly  diminished.  Now  aqueous  vapour  would,  like  water, 
absorb  the  obscure  rays.  And  most  probably  the  reason  why  the  obscure 
part  of  the  spectrum  of  sun  light  is  not  so  intense  as  in  the  case  of  the 
electric  light  is  that  the  obscure  rays  have  been  already  partially  absorbed 
by  the  aqueous  vapour  of  the  atmosphere.  If  a  solar  spectrum  could  be 
produced  outside  the  atmosphere,  it  doubtless  would  give  a  spectrum  more 
like  that  of  the  electric  light,  which  is  uninfluenced  by  the  atmospheric 
absorption. 

This  has  been  remarkably  confirmed  in  other  ways.     Melloni  observed 


366 


On  Heat. 


[431- 


that  the  position  of  the  maximum  in  the  solar  spectrum  differs  on  different 
days  ;  which  is  probably  due  to  the  varying  absorption  of  the  atmosphere,  in 
consequence  of  its  varying  hygrometric  state.  Secchi,  in  Rome,  found  the 

same  shifting  of 
the  maximum  to 
occur  in  the 
different  seasons 
of  the  year;  for 
in  winter,  when 
there  is  least 
moisture  in  the 
atmosphere,  the 
maximum  is  far- 

ther  from  the  red 

than  in  summer, 
when  the  aqueous 

vapour  in  the  air  is  most  abundant.  An  important  observation  on  the 
luminous  rays  has  also  been  made  by  Cooke,  in  America,  who  found  that 
the  faint  black  lines  in  the  solar  spectrum  attributed  to  the  absorption  of 
light  by  our  atmosphere  ("see  book  on  Optics)  are  chiefly  caused  by  the 
presence  of  aqueous  vapour. 

432.  Luminous  and  obscure  radiation. — The  radiation  from  a  luminous 
object,  a  gas  flame  for  example,  is  of  a  composite  character ;  a  portion  con- 
sists of  what  we  term  light,  but  a  far  greater  part  consists  of  heat  rays, 
which  are  insensible  to  our  eyes,  being  unable  to  affect  the  optic  nerve. 
When  this  mixed  radiation  falls  upon  the  blackened  face  of  a  thermo-electric 
pile,  the  whole  of  it  is  taken  to  be  absorbed,  the  light  by  this  act  being 
converted  into  heat,  and  affecting  the  instrument  proportionally  with  the 
purely  calorific  rays.  The  total  radiation  of  a  luminous  source,  expressed 
in  units  of  heat  or  force,  can  thus  be  measured.  By  introducing  into  the 
path  of  the  rays  a  body  capable  of  stopping  either  the  luminous  or  the 
obscure  radiation,  we  can  ascertain  by  the  comparative  action  on  the  pile 
the  relative  quantities  of  heat  and  light  radiated  from  the  source.  Melloni 
sought  to  do  this  by  passing  a  luminous  beam  through  a  layer  of  water 
containing  alum  in  solution  ;  a  liquid  which  he  found  in  previous  experi- 
ments absorbed  all  the  radiation  from  bodies  heated  under  incandescence. 
Comparing  the  transmission  through  this  liquid — which  allowed  the  luminous 
part  of  the  beam  to  pass,  but  quenched  the  obscure  portion — with  the  trans- 
mission through  a  plate  of  rock  salt — which  affected  neither  the  luminous  nor 
the  obscure  radiation,  but  gave  the  loss  due  to  reflection — Melloni  found 
that  90  per  cent,  of  the  radiation  from  an  oil  flame  and  99  per  cent,  of  the 
radiation  from  an  alcohol  flame  consist  of  invisible  calorific  rays.  This  pro- 
portion has  been  still  further  increased  by  the  experiments  of  Tyndall,  who 
employed  a  solution  of  iodine  in  bisulphide  of  carbon,  which  he  found  to  be 
impervious  to  the  most  intense  light,  but  very  pervious  to  radiant  heat  ;  only 
a  slight  absorption  being  effected  by  the  bisulphide.  By  successively  com- 
paring the  transmission  through  the  transparent  bisulphide,  and  the  trans- 
mission through  the  same  liquid  rendered  opaque  by  iodine,  the  value  of  the 
luminous  radiation  from  various  sources  was  found  to  be  as  follows  : — 


-434]  Transmutation  of  Obscure  Rays.  367 

Source  Luminous        Obscure 

Red-hot  spiral o  100 

Hydrogen  flame o  100 

Oil  flame 3  97 

Gas  flame 4  96 

White-hot  spiral 4-6  95-4 

Electric  light 10  90 

Here  by  direct  experiment  the  ratio  of  luminous  to  obscure  rays  in  the 
electric  light  is  found  to  be  10  per  cent,  of  the  total  radiation.  By  prismatic 
analysis,  the  curve  shown  in  fig.  356  was  obtained,  graphically  representing 
the  proportion  of  luminous  to  obscure  rays  in  the  electric  light ;  by  calculating 
the  areas  of  the  two  spaces  in  the  diagram,  the  obscure  portion,  D  C  B  A,  is 
found  to  be  nearly  10  times  as  large  as  the  luminous  one,  D  C  E. 

433.  Transmutation  of  obscure  rays. — We  shall  find,  in  speaking  of 
the  luminous  spectrum,  that  beyond  the  violet  there  are  rays  which  are  in- 
visible to  the  eye,  but  which  are  distinguished  by  their  chemical  action,  and 
are  spoken  of  as  the  actinic  or  chemical  rays  ;  they  are  also  known  as  the 
Ritteric  rays,  from  the  philosopher  who  first  discovered  their  existence. 

As  we  shall  afterwards  see  in  the  book  on  Optics,  Stokes  has  succeeded 
in  converting  these  rays  into  rays  of  lower  refrangibility,  which  then  become 
visible  ;  so  Tyndall  has  effected  the  corresponding  but  inverse  change,  and 
has  increased  the  refrangibility  of  the  Herschelian  or  extra  red  rays,  and 
thus  rendered  them  visible.  The  charcoal  points  of  the  electric  light  were 
placed  in  front  of  a  concave  silvered  glass  mirror  in  such  a  manner,  that 
the  rays  from  the  points  after  reflection  were  concentrated  to  a  focus  about 
6  inches  distant.  On  the  path  of  the  beam  was  interposed  a  cell  full  of  a 
solution  of  iodine  in  bisulphide  of  carbon,  which  (441)  has  the  power  of  com- 
pletely stopping  all  luminous  radiation,  but  gives  free  passage  to  the  non- 
luminous  rays.  On  now  placing  in  the  focus  of  the  beam,  thus  sifted,  a  piece 
of  platinum,  it  was  raised  to  incandescence  by  the  impact  of  perfectly  invisible 
rays.  In  like  manner  a  piece  of  charcoal  in  vacuo  was  heated  to  redness. 

By  a  proper  arrangement  of  the  charcoal  points  a  metal  may  be  raised  to 
whiteness,  and  the  light  now  emitted  by  the  metal  yields  on  prismatic 
analysis  a  brilliant  luminous  spectrum,  which  is  thus  entirely  derived  from 
the  invisible  rays  beyond  the  red.  To  the  new  phenomena  here  described, 
to  this  transmutation  of  non-luminous  into  luminous  heat,  Tyndall  has 
applied  the  word  calorescence. 

When  the  eye  was  cautiously  placed  in  the  focus,  guarded  by  a  small 
hole  pierced  in  a  metal  screen,  so  that  the  converged  rays  should  only  enter 
the  pupil  and  not  affect  the  surrounding  part  of  the  eye,  no  impression  of 
light  was  produced,  and  there  was  scarcely  any  sensation  of  heat.  A  con- 
siderable portion  was  absorbed  by  the  humours  of  the  eye,  but  yet  a  power- 
ful beam  undoubtedly  reached  the  retina  ;  for,  as  Tyndall  showed  by  a 
separate  experiment,  about  18  per  cent,  of  the  obscure  radiation  from  the 
electric  light  passed  through  the  humours  of  an  ox's  eye. 

434.  Transmission  of  thermal  rays. — Melloni   was   the  first  who  ex- 
amined  extensively  and  accurately  the  absorption  of  heat  by  solids  and 
liquids.     The  apparatus  he  employed  is  represented  in  the  annexed  figure 
(358),  where  A  B  is  the  thermo-electric  pile  ;  a  is  a  support  for  the  source  of 


368 


On  Heat. 


[434- 


heat,  in  this  case  a  Locatelli's  lamp ;  F  and  E  are  screens,  and  C  is  a 
support  for  the  body  experimented  on  ;  while  m  is  the  support  for  the  pile, 
and  D  the  galvanometer. 


The  various  sources  of  heat  used  by  Melloni  in  his  experiments  have 
been  already  (428)  enumerated. 

To  express  the  power  which  bodies  have  of  transmitting  heat,  Melloni 
used  the  term  diathermancy  :  diathermancy  bears  the  same  relation  to 
radiant  heat  that  transparency  does  to  light  ;  and  in  like  manner  the  power 
of  stopping  radiant  heat  is  called  athermancy,  which  thus  corresponds  to 
opacity  for  light.  In  experimenting  on  the  diathermancy  of  liquids,  Melloni 
used  glass  troughs  with  parallel  sides,  the  thickness  of  the  liquid  layer  being 
0-36  in.  The  radiant  heat  of  an  Argand  lamp  with  a  glass  chimney  was 
first  allowed  to  fall  directly  on  the  face  of  the  pile,  and  the  deflection  pro- 
duced in  the  galvanometer  taken  as  the  total  radiation  ;  the  substance  under 
examination  was  then  interposed,  and  the  deflection  noted.  This  corre- 
sponded to  the  quantity  of  heat  transmitted  by  the  substance.  If  /  indicate 
this  latter  number,  and  f  the  total  radiation,  then 


which  is  the  percentage  of  rays  transmitted. 
tion  100,  Melloni  found  that 

Bisulphide  of  carbon  transmitted  . 

Olive  oil 

Ether 

Sulphuric  acid 

Alcohol 

Solution  of  alum  or  sugar 

Distilled  water 


Thus,  calling  the  total  radia- 

.         .         .         .         63 
30 

*7  T 

17 
15 

12 
II 


In  experimenting  with  solids  they  were  cut  into  plates  o-i   inch  in  thick- 
ness, and  it  was  found  that  of  every  100  rays  there  was  transmitted  by 


-434] 


Transmission  of  Thermal  Rays. 


369 


Rock  salt 92 

Smoky  quartz      ,         .         .         .67 
Transparent  carbonate  of  lead   .     52 


Selenite 

Alum  . 

Sulphate  of  copper 


20 

12 

o 


The  transmission  of  heat  through  liquids  has  been  re-examined  by 
Tyndall  in  the  following  way  : — Instead  of  employing  a  glass  vessel  to  hold 
the  liquids  under  examination,  he  made  use  of  a  little  cell  whose  ends  were 
stopped  by  parallel  plates  of  rock  salt.  The  plates  were  separated  by  a  ring 
of  brass  with  an  aperture  on  the  top  through  which  the  liquid  could  be 
poured.  As  this  plate  could  be  changed  at  will,  liquid  layers  of  various 
thicknesses  were  easily  obtainable,  the  apparatus  being  merely  screwed 
together  and  made  liquid-tight  by  paper-washers.  The  instrument  was 
mounted  on  a  support  before  an  opening  in  a  brass  screen  placed  in  front 
of  the  pile.  The  source  of  heat  employed  was  a  spiral  of  platinum  wire 
raised  to  incandescence  by  an  electric  current ;  the  spiral  being  inclosed  in 
a  small  glass  globe  with  an  aperture  in  front,  through  which  the  radiation 
passed  unchanged  in  its  character,  a  point  of  essential  importance  overlooked 
by  Melloni.  The  following  table  contains  the  results  of  experiments  made 
with  liquids  in  the  various  thicknesses  indicated,  the  numbers  expressing 
the  absorption  per  cent,  of  the  total  radiation.  The  transmission  per  cent,  can 
be  found  in  each  case  by  subtracting  the  absorption  from  100.  Thus  a  layer 
of  water  0*2  inch  thick  absorbs  807  and  transmits  19-3  per  cent,  of  the 
radiation  from  a  red-hot  spiral. 

Absorption  of  heat  by  liquids. 


Thickness  of  liquid  in  parts  of  an  inch. 

O'O2 

0,4 

0*07 

0-14 

0-27 

Bisulphide  of  carbon 

5*5 

8-4 

12-5 

15-2 

I7'3 

Chloroform 

1  6*6 

25-0 

35'° 

40*0 

44-8 

Iodide  of  methyl        .         .       36*1 

46-5 

53-2 

65-2 

68-6 

Benzole      .... 

43'4 

557 

62-5 

71-5 

73-6 

Amylene    .... 

58-3 

65-2 

73-6 

777 

82-3 

Ether         .... 

63-3 

73'5 

76-1 

78-6 

85-2 

Alcohol      .... 

673 

78-6 

83-6 

85-3 

89-1 

Water        .... 

807 

86-1 

88-8 

91-0 

91-0 

It  appears  from  these  tables  that  there  is  no  connection  between  dia- 
thermancy and  transparency.  The  liquids,  except  olive  oil,  are  all  colourless 
and  transparent,  and  yet  vary  as  much  as  75  per  cent,  in  the  amount  of 
heat  transmitted.  Among  solids,  smoky  quartz,  which  is  nearly  opaque  to 
light,  transmits  heat  very  well ;  while  alum,  which  is  perfectly  transparent, 
cuts  off  88  per  cent,  of  heat  rays.  As  there  are  different  degrees  of  trans- 
parency, so  there  are  different  degrees  of  diathermancy  ;  and  the  one  cannot 
be  predicated  from  the  other. 

By  studying  the  transmission  of  heat  from  different  parts  of  the  spec- 
trum separately,  the  connection  between  light  and  heat  becomes  manifest. 
With  this  view  Masson  and  Jamin  received  the  spectrum  of  the  solar 

R  3 


370  On  Heat.  [434- 

light  given  by  a  prism  of  rock  salt  on  a  movable  screen  provided  with  an 
aperture,  so  that  by  raising  or  lowering  the  screen  the  action  of  any  given 
part  of  the  spectrum  on  different  plates  could  be  investigated.  They  thus 
found — 

That  glass,  rock  crystal,  ice,  and  generally  substances  transparent  for 
light,  are  also  diathermanous  for  all  kinds  of  himinous  heat ; 

That  a  coloured  glass,  red,  for  instance,  which  only  transmits  the  red  rays 
of  the  spectrum,  and  extinguishes  the  others,  also  extinguishes  every  kind  of 
luminous  heat,  excepting  that  of  the  red  rays  ; 

That  glass  and  rock  crystal,  which  are  diathermanous  for  luminous  heat, 
also  transmit  the  obscure  heat  near  the  red — that  is,  the  most  refrangible — 
but  extinguish  the  extreme  obscure  rays,  or  those  which  are  the  least  de- 
flected by  the  prism. 

Alum  extinguishes  a  still  greater  proportion  of  the  obscure  spectrum,  and 
ice  stops  it  altogether. 

Knoblauch  has  shown  that  very  thin  layers  of  gold,  silver,  and  platinum, 
which  are  known  to  transmit  luminous  rays  of  a  definite  colour,  also  allow 
rays  of  heat  to  pass  ;  so  that  these  substances  are  diathermanous,  though  in 
a  small  degree. 

435.  Influence  of  the  nature  of  the  heat. — The  diathermanous  power 
differs  greatly  with  the  heat  from  different  sources,  as  Melloni  made  evident 
from  the  following  table,  in  which  the  numbers  express  what  proportion  of 
every  100  rays  from  the  different  sources  of  heat  incident  on  the  plates  is 
transmitted  : — 


Locatelli's 
lamp 

Incandescent 
platinum  wire 

Copper  at  400° 

Copper  at  ioo°| 

i 

Rock  salt  . 

92 

92 

92 

92 

Fluor  spar 

78 

69 

42 

33 

Plate  glass 

39 

24 

6 

0 

Black  glass 

26 

55 

12 

0 

Selenite    .... 

14 

5 

0 

0 

Alum         .... 

9 

2                          0 

o 

Ice    

6 

0'5 

0 

0 

These  different  sources  of  heat  correspond  to  light  from  different  sources. 
Rock  salt  is  here  stated  to  transmit  all  kinds  of  heat  with  equal  facility,  and 
to  be  the  only  substance  which  does  so.  It  is  analogous  to  white  glass, 
which  is  transparent  for  light  from  all  sources.  Fluor  spar  transmits  78  per 
cent,  of  the  rays  from  a  lamp,  but  only  33  of  those  from  a  blackened  surface 
at  100°.  A  piece  of  plate  glass  only  one-tenth  of  an  inch  thick,  and  perfectly 
transparent  to  light,  is  opaque  to  all  the  radiation  from  a  source  of  100°, 
transmits  only  6  per  cent,  of  the  heat  from  a  source  at  400°,  and  but  39  of 
the  radiation  from  the  .lamp.  Black  glass,  on  the  contrary,  though  it  cuts 
off  all  heat  from  a  source  at  100°,  allows  12  per  cent,  of  the  heat  at  400°  to 
pass,  and  is  equally  transparent  to  the  heat  from  the  spiral,  but  on  account 
of  its  blackness  is  more  opaque  to  the  heat  from  the  lamp.  As  we  have 
already  seen,  every  luminous  ray  is  a  heat  ray  ;  now  as  several  of  the  sub- 


-435] 


Influence  of  the  Nature  of  the  Heat. 


stances  in  this  table  are  pervious  to  all  the  luminous  rays,  and  yet,  as  in  the 
case  of  ice,  transmit  about  6  per  cent,  of  luminous  heat,  we  have  an  apparent 
anomaly  ;  which,  however,  is  only  a  confirmation  of  the  remarkably  small 
proportion  which  the  luminous  rays  of  a  lamp  bear  to  the  obscure. 

From  these  experiments  Melloni  concluded  that  as  the  temperature  of 
the  source  rose,  more  heat  was  transmitted.  This  general  law  has  been 
confirmed  by  some  experiments  of  Tyndall.  The  platinum  lamp,  previously 
described,  was  used  as  the  source,  the  temperature  of  which  could  be  varied 
from  a  dark  to  a  brilliant  white  heat,  without  disturbing  in  any  way  the 
position  of  the  apparatus  ;  the  gradations  of  temperature  being  obtained  by 
a  gradual  augmentation  of  the  strength  of  the  electric  current  which  heated 
the  platinum  spiral.  Instead  of  liquids,  vapours  were  examined  in  a  manner 
to  be  described  subsequently  ;  the  measurements  are  given  in  the  following 
table  :— 

Absorption  of  heat  by  vapours. 


Source,  platinum  spiral 

"W              f 

Barely  visible 

Bright  red 

White  hot 

Near  fusion 

Bisulphide  of  carbon 

6-5 

47 

2'9 

2'5 

Chloroform 

9-1 

6'3 

5-6 

3'9 

Iodide  of  methyl 

12-5 

9-6 

7'8 

Benzole     .         .         .         .          26*4 

20'6 

16-5 

Ether        .         .         .         .         43*4 

31-4 

25-9 

237 

Formic  ether    . 

45-2 

31-9 

25-1 

21-3 

Acetic  ether 

49-6 

34-6 

27-2 

The  percentage  of  rays  absorbed  is  here  seen  to  diminish  in  each  case 
as  the  temperature  of  the  source  rises.  Mere  elevation  of  temperature  does 
not,  however,  invariably  produce  a  high  penetrative  power  in  the  rays 
emitted ;  the  rays  from  sources  of  far  higher  temperature  than  any  of  the 
foregoing  are  more  largely  absorbed  by  certain  substances  than  are  the  rays 
emitted  from  any  one  of  the  sources  as  yet  mentioned.  Thus  Tyndall  found 
that  the  radiation  from  a  hydrogen  flame  was  completely  intercepted  by  a 
layer  of  water  only  0*27  of  an  inch  thick,  the  same  layer  transmitting  9  per 
cent,  of  the  radiation  from  the  red-hot  spiral,  a  source  of  much  lower  tem- 
perature. The  explanation  of  this  is,  that  those  rays  which  heated  water 
emits  (and  water,  the  product  of  combustion,  is  the  main  radiant  in  a 
hydrogen  flame)  are  the  very  ones  which  this  substance  most  largely  absorbs. 
This  statement,  which  will  become  clearer  after  reading  the  analogous 
phenomena  in  the  case  of  light,  was  strikingly  exemplified  by  the  powerful 
absorption  of  the  heat  from  a  carbonic  oxide  flame  by  carbonic  acid  gas. 
It  will  be  seen  presently  (438)  that  of  the  rays  from  a  heated  plate  of  copper, 
defiant  gas  absorbs  10  times  the  quantity  intercepted  by  carbonic  acid, 
whilst  of  the  rays  from  a  carbonic  oxide  flame  Tyndall  found  carbonic  acid 
absorbed  twice  as  much  as  olefiant  gas.  A  tenth  of  an  atmosphere  of  carbonic 
acid,  inclosed  in  a  tube  4  feet  long,  absorbs  60  per  cent,  of  the  radiation  from 
a  carbonic  oxide  flame.  Radiant  heat  of  this  character  can  thus  be  used  as 
a  delicate  test  for  the  presence  of  carbonic  acid,  the  amount  of  which  in 


372  On  Heal.  [435- 

even  be  accurately  measured  by  the  same  means.  This  has  been  done  by 
Prof.  Barrett,  who,  in  this  way,  has  made  a  physical  analysis  of  the  human 
breath.  In  one  experiment  the  quantity  of  carbonic  acid  contained  in  breath 
physically  analysed  was  found  to  be  4*65  per  cent.,  whilst  the  same  breath 
chemically  analysed  gave  4-66  per  cent. 

436.  Influence  of  the  thickness  and  nature  of  screens. — It  will  be 
seen  from  the  table  (435)  that  of  every  100  rays  rock  salt  transmits  92.  The 
other  8  may  either  have  been  absorbed  or  reflected  from  the  surface  of  the 
plate.  According  to  Melloni,  the  latter  is  the  case  ;  for  if,  instead  of  on  one 
plate,  heat  be  allowed  to  fall  on  two  or  more  plates  whose  total  thickness 
does  not  exceed  that  of  the  one,  the  quantity  of  heat  arrested  will  be  propor- 
tional to  the  number  of  reflecting  surfaces.  He  therefore  concluded  rock 
salt  to  be  quite  diathermanous. 

The  experiments  of  later  observers  show  that  this  conclusion  is  not  strictly 
correct  ;  rock  salt  does  absorb  a  very  small  proportion  of  obscure  rays. 

The  quantity  of  heat  transmitted  through  rock  salt  is  practically  the 
same,  whether  the  plate  be  I,  2,  or  4  millimetres  thick.  But  with  other  bodies 
absorption  increases  with  the  thickness,  although  by  no  means  in  direct 
proportion.  This  is  seen  to  be  the  case  in  the  table  of  absorption  by  liquids 
at  different  thicknesses.  The  following  table  tells  what  proportion  of 
1,000  rays  from  a  Locatelli's  lamp  pass  through  a  glass  plate  of  the  given 
thickness  : — 

Thickness  in  millimetres     .0-512345678 
Rays  transmitted         .         -775  733  682  653  634  620  609  600  592 

The  absorption  takes  place  in  the  first  layers  ;  the  rays  which  have  passed 
these  possess  the  property  of  passing  through  other  layers  in  a  higher  degree, 
so  that  beyond  the  first  layers  the  heat  transmitted  approaches  a  certain 
constant  value.  If  a  thin  glass  plate  be  placed  behind  another  glass  plate 
a  centimetre  thick,  the  former  diminishes  the  transmission  by  little  more 
than  the  reflection  from  its  surface.  But  if  a  plate  of  alum  were  placed  be- 
hind the  glass  plate,  the  result  would  be  different,  for  the  latter  is  opaque  for 
much  of  the  heat  transmitted  by  glass. 

Heat,  therefore,  which  has  traversed  a  glass  plate  traverses  another  plate 
of  the  same  material  with  very  slight  loss,  but  is  very  greatly  diminished  by 
a  plate  of  alum.  Of  100  rays  which  had  passed  through  green  glass  or  tour- 
maline, only  5  and  7  were  respectively  transmitted  by  the  same  plate  of 
alum.  A  plate  of  blackened  rock  salt  only  transmits  obscure  rays,  while 
alum  extinguishes  them.  Consequently,  when  these  two  substances  are 
superposed,  a  system  impervious  to  light  and  heat  is  obtained. 

These  phenomena  find  their  exact  analogies  in  the  case  of  light.  The 
different  sources  of  heat  correspond  to  flames  of  different  colours,  and  the 
various  screens  to  glasses  of  different  colours.  A  red  flame  looked  at  through 
a  red  glass  appears  quite  bright,  but  through  a  green  glass  it  appears  dim  or 
is  scarcely  visible.  So  in  like  manner  heat  which  has  traversed  a  red  glass 
passes  through  another  red  glass  with  little  diminution,  but  it  is  almost 
completely  stopped  by  a  green  glass.  Rock  salt  at  1 50°  emits  only  one  kind 
of  heat ;  it  is  monothermal,  just  as  sodium  vapour  is  monochromatic. 

Different  luminous  rays  being  distinguished  by  their  colours ;  to  these 


-437]  Diffusion  of  Heat.  373 

different  obscure  calorific  rays  Melloni  gives  the  name  of  thermocrose  or  heat 
coloration.  The  invisible  portion  of  the  spectrum  is  accordingly  mapped 
out  into  a  series  of  spaces,  each  possessing  its  own  peculiar  feature  corre- 
sponding to  the  col6ured  spaces  which  are  seen  in  that  portion  of  the  spec- 
trum visible  to  our  eyes.  . 

Besides  thickness  and  colour,  the  polish  of  a  substance  influences  the 
transmission.  Glass  'plates  of  the  same  size  and  thickness  transmit  more 
heat  as  their  surface  is  more  polished.  Bodies  which  transmit  heat  of  any 
kind  very  readily  are  not  heated.  Thus  a  window  pane  is  not  much  heated 
by  the  strongest  sun's  heat ;  but  a  glass  screen  held  before  a  common  fire 
stops  most  of  the  heat,  and  is  itself  heated  thereby.  The  reason  of  this  is 
that  by  far  the  greater  part  of  the  heat  from  a  fire  is  obscure,  and  to  this  kind 
of  heat  glass  is  opaque. 

437.  Diffusion  of  heat. — When  a  ray  of  light  falls  upon  an  unpolished 
surface  in  a  definite  direction,  it  is  decomposed  into  a  variety  of  rays  which 
are  reflected  from  the  surface  in  all  directions.  This  irregular  reflection  is 
called  diffusion^  and  it  is  in  virtue  of  it  that  bodies  are  visible  when  light 
falls  upon  them.  A  further  peculiarity  is,  that  all  solar  rays  are  not  equally 
diffused  from  the  surface  of  bodies.  Certain  bodies  diffuse  certain  rays  and 
absorb  others,  and  accordingly  appear  coloured.  The  red  colour  of  a  gera- 
nium is  caused  by  its  absorbing  all  the  rays,  excepting  the  red,  which  are 
irregularly  reflected.  Just  as  is  the  case  with  transmitted  light  in  transparent 
bodies,  so  with  diffused  light  in  opaque  ones  ;  for  if  a  red  body  is  illuminated 
by  red  light  it  appears  of  a  bright  red  colour,  but  if  green  light  fall  upon  it 
it  is  almost  black.  We  shall  now  see  that  here  again  analogous  phenomena 
prevail  with  heat. 

Various  substances  diffuse  different  thermal  rays  to  a  different  extent ; 
each  possesses  a  peculiar  thermocrose.  Melloni  placed  a  number  of  strips 
of  brass  foil  between  the  source  of  heat  and  the  thermo-pile.  They  were 
coated  on  the  side  opposite  to  the  pile  with  lampblack,  and  on  the  other 
side  with  the  substances  to  be  investigated.  Representing  the  quantity  of 
heat  absorbed  by  the  lampblack  by  100,  the  absorption  of  the  other  bodies 
was  as  follows  : — 

Incandescent  Copper  Copper 

platinum  at  400°  at  100° 

Lampblack ....     100  100  100 

White  lead  ....       56  89  100 

Isinglass      ....       54  64  91 

Indian  ink  .         .         .         -95  87  85 

Shellac         ....       47  70  72 

Polished  metal                      .    13*5  13  13 

Hence,  white  lead  absorbs  far  less  of  the  heat  radiated  from  incandescent 
platinum  than  lampblack,  but  it  absorbs  the  obscure  rays  from  copper  at 
100°  as  completely  as  lampblack.  Indian  ink  is  the  reverse  of  this  ;  it 
absorbs  obscure  rays  less  completely  than  luminous  rays.  Lampblack 
absorbs  the  heat  from  all  sources  in  equal  quantities,  and  very  nearly  com- 
pletely. In  consequence  of  this  property  all  thermoscopes  which  are  used 
for  investigating  radiant  heat  are  covered  with  lampblack,  as  it  is  the  best- 
known  absorbent  of  heat.  The  behaviour  of  metals  is  the  reverse  of  that  of 


71R 


374  On  Heat.  [437- 

lampblack.  They  reflect  the  heat  of  different  sources  in  the  same  degree. 
They  are  to  heat  what  'white  bodies  are  to  light. 

As  coloured  light  is  altered  by  diffusion  from  several  bodies,  so  Knoblauch 
has  shown  that  the  different  kinds  of  heat  are  altered  by  reflection  from  dif- 
ferent surfaces.  The  heat  of  an  Argand  lamp  diffused  from  white  paper 
passes  more  easily  through  calcspar  than  when  it  has  been  diffused  from 
black  paper. 

The  rays  of  heat,  like  the  rays  of  light,  are  susceptible  of  polarisation 
and  double  refraction.  These  properties  will  be  better  understood  after 
treating  of  light. 

438.  Relation  of  gases  and  vapours  to  radiant  heat.— For  a  long  time 
it  was  believed  that  gaseous  bodies  were  as  permeable  to  heat  as  a  vacuum  ; 
and  though  subsequently  this  was  disproved,  yet  down  to  a  recent  period  it 
was  thought  that  whatever  absorption  such  bodies  might  exercise  was  slight 
and  similar  in  degree.  The  whole  subject  has,  however,  been  investigated 
by  Tyndall ;  the  apparatus  he  used  is  represented  in  the  adjacent  figure, 
the  arrangement  being  looked  upon  from  above. 

A  (fig.  359)  is  a  cylinder  about  4  feet  in  length  and  2i  inches  in  diameter, 
placed  horizontally,  the  ends  of  which  can  be  closed,  with  rock-salt  plates  : 

by  means  of  a 

lateral  tube  at  r 

it  can  k£  con" 
nected  with  an 
air-pump  and  ex- 
hausted ;  while 
at  /is  another 
tube  which 
serves  for  the 

introduction  of  gases  and  vapours.  T  is  a  sensitive  thermo-pile  connected 
with  an  extremely  delicate  galvanometer,  M. 

The  deflections  of  this  galvanometer  were  proportional  to  the  degrees  of 
heat  up  to  about  30°  ;  beyond  this  point  the  proportionality  no  longer  held 
good,  and  accordingly,  for  the  higher  degrees,  a  table  was  empirically  con- 
structed, in  which  the  value  of  the  higher  deflections  was  expressed  in  units  ; 
the  unit  being  the  amount  of  heat  necessary  to  move  the  needle  through  one 
of  the  lower  degrees. 

C  is  a  source  of  heat,  which  usually  was  either  a  Leslie's  cube  filled  with 
boiling  water,  or  else  a  sheet  of  blackened  copper  heated  by  gas.  Now, 
when  the  source  of  heat  was  permitted  to  radiate  through  the  exhausted 
tube,  the  needle  made  a  great  deflection  ;  and  in  this  position  a  very  con- 
siderable degree  of  absorption  would  have  been  needed  to  produce  an 
alteration  of  I  °  of  the  galvanometer.  And  if  to  lessen  this  deflection  a  lower 
source  of  heat  had  been  used,  the  fraction  absorbed  would  be  correspondingly 
less,  and  might  well  have  been  insensible.  Hence  Tyndall  adopted  the  fol- 
lowing device,  by  which  he  was  enabled  to  use  a  powerful  flux  of  heat,  and  at 
the  same  time  to  discover  small  variations  in  the  quantity  falling  on  the  pile. 
The  source  of  heat  at  C  was  allowed  to  radiate  through  the  tube  at  the 
end  of  which  the  pile  was  placed  ;  a  deflection  was  produced  of,  say,  70°  ; 
a  second  source  of  heat,  D,  was  then  placed  near  the  other  face  of  the  pile 


-439]       Relation  of  Gases  and  Vapours  to  Radiant  Heat.       375 

the  amount  of  heat  falling  on  the  pile  from  this  compensating  cube  being 
regulated  by  means  of  a  movable  screen  S.  When  both  faces  of  the  pile 
are  warmed,  two  currents  are  produced,  which  are  in  opposite  directions, 
and  tend,  therefore,  to  neutralise  each  other  :  when  the  heat  on  both  faces 
is  precisely  equal,  the  neutralisation  is  perfect,  and  no  current  at  all  is  pro- 
duced, however  high  may  be  the  temperature  on  both  sides.  In  the  arrange- 
ment just  described,  by  means  of  the  screen  S,  the  radiation  from  the  com- 
pensating cube  was  caused  to  neutralise  exactly  the  radiation  from  the  source 
C  ;  the  needle  consequently  was  brought  down  from  70°  to  zero,  and  re- 
mained there  so  long  as  both  sources  were  equal.  If  now  a  gas  or  vapour 
be  admitted  into  the  exhausted  tube,  any  power  of  absorption  it  may  possess 
will  be  indicated  by  the  destruction  of  this  equilibrium,  and  preponderance 
of  the  radiation  from  the  compensating  cube,  by  an  amount  corresponding 
to  the  heat  cut  off  by  the  gas.  Examined  in  this  way,  air,  hydrogen,  and 
nitrogen,  when  dried  by  passing  through  sulphuric  acid,  were  found  to  exert 
an  almost  inappreciable  effect ;  their  presence  as  regards  radiant  heat  being 
but  little  different  to  a  vacuum.  But  with  olefiant  and  other  complex  gases 
the  case  was  entirely  different.  Representing  by  the  number  i  the  quantity 
of  radiant  heat  absorbed  by  air,  olefiant  gas  absorbs  970  times,  and  am- 
moniacal  gas  1,195  times,  this  amount.  In  the  following  table  is  given  the 
absorption  of  obscure  heat  by  various  gases,  referred  to  air  as  unity  : — 

Absorption  under        mjr  Absorption  under 

Name  of  gas  30  inches  of  pressure  ^/»      Name  of  gas  30  inches  of  pressure 

Air •  Oi  ,'      Carbonic  acid ...         90 

Oxygen    ....  i  Nitrous  oxide  .         .         .335 

Nitrogen          ...  I  Marsh  gas       ...       403 

Hydrogen        ...  i  Sulphurous  acid       .         .       710 

Chlorine .         .         .         .  39  Olefiant  .         .         .         -97° 

Hydrochloric  acid  .         .  62  Ammonia         .         .         .1195 

If,  instead  of  comparing  the  gases  at  a  common  pressure  of  one  atmo- 
sphere, they  are  compared  at  a  common  pressure  of  an  inch,  their  differences 
in  absorption  are  still  more  strikingly  seen.  Thus,  assuming  the  absorption 
by  i  inch  of  dry  air  to  be  i,  the  absorption  by  i  inch  of  olefiant  gas  is  7,950, 
and  by  the  same  amount  of  sulphurous  acid  8,800. 

459.  Influence  of  pressure  and  thickness  on  the  absorption  of  heat 
by  gases. — The  absorption  of  heat  by  gases  varies  with  the  pressure  ;  this 
vibration  cannot  be  seen  in  the  case  of  air,  as  the  total  absorption  is  so  small, 
but  in  the  case  of  those  gases  which  have  considerable  absorptive  power  it  is 
easily  shown.  Taking  the  total  absorption  by  atmospheric  air  under  ordinary 
pressure  at  unity,  the  numbers  of  olefiant  gas  under  a  pressure  of  1,3,  5,  7, 
and  10  inches  of  mercury7  are  respectively  90,  142,  168,  182,  and  193.  Thus 
one-thirtieth  of  an  atmosphere  of  olefiant  gas  exerts  90  times  the  absorption 
of  an  entire  atmosphere  of  air.  And  the  absorption,  it  is  seen,  increases 
with  the  density,  though  not  in  a  direct  ratio.  Tyndall  showed,  however,  by 
special  experiments,  that  for  very  low  pressures  the  absorption  does  increase 
with  the  density.  Employing  as  a  unit  volume  of  the  gas  a  quantity  which 
measured  only  i  of  a  cubic  inch,  and  admitting  successive  measures  of 


376  On  Heat.  [439- 

olefiant  gas  into  the  experimental  tube,  it  was  found  that  up  to  15  measures 
the  absorption  was  directly  proportionate  to  the  density  in  each  case. 

In  these  experiments  the  length  of  the  experimental  tube  remained  the 
same  whilst  the  pressure  of  the  gas  within  it  was  caused  to  vary ;  in  other 
subsequent  experiments  the  pressure  of  the  gas  was  kept  constant,  whilst  the 
length  of  the  tube  was,  by  suitable  means,  varied  from  croi  of  an  inch  up  to 
50  inches.  The  source  was  a  heated  plate  of  copper  ;  of  the  total  radiation 
from  this  nearly  2  per  cent,  was  absorbed  by  a  film  of  defiant  gas  *oi  of  an 
inch  thick,  upwards  of  9  per  cent,  by  a  layer  of  the  same  gas  o-i  of  an  inch 
thick,  33  per  cent,  by  a  layer  2  inches  thick,  68  per  cent,  by  a  column  20 
inches  long,  and  77  per  cent,  by  a  column  rather  more  than  4  feet  long. 

440.  Absorptive  power  of  vapours. — The  absorptive  power  of  defiant 
gas  is  exceeded  by  that  of  several  vapours.  The  mode  of  experimenting 
was  analogous  to  that  with  the  gases.  The  liquid  from  which  the  vapours 
were  to  be  produced  was  inclosed  in  a  small  flask,  which  could  be  attached 
with  a  stopcock  to  the  exhausted  experimental  tube.  The  absorption  was 
then  determined  after  admitting  the  vapours  into  the  tube  in  quantities 
measured  by  the  pressure  of  the  barometer  gauge  attached  to  the  air-pump. 

The  following  table  shows  the  absorption  of  vapours  under  pressures 
varying  from  cri  to  ro  inch  of  mercury  : — 

Absorption  under  pressure 
Name  of  vapours  in  inches  of  mercury 

o'i  o's  i'o 

Bisulphide  of  carbon          ....  15  47  62 

Benzole 66  182  267 

Chloroform 85  182  236 

Ether/ 300  710  870 

Alcohol 325  622 

Acetic  ether        ......  590  980  1195 

These  numbers  refer  to  the  absorption  of  a  whole  atmosphere  of  dry  air 
as  their  unit,  and  it  is  thus  seen  that  a  quantity  of  bisulphide  of  carbon 
vapour,  the  feeblest  absorbent  yet  examined,  which  only  exerts  a  pressure  of 
^  of  an  inch  of  mercury,  or  the  3^  of  an  atmosphere,  gave  15  times  the 
absorption  of  an  entire  atmosphere  of  air ;  and  ^  of  an  inch  of  acetic 
ether  590  times  as  much.  Comparing  air  at  a  pressure  of  o-i  with  acetic 
ether  of  the  same  pressure,  the  absorption  of  the  latter  would  be  more  than 
17,500  times  as  great  as  that  of  the  former. 

The  absorption  by  the  infinitesimally  small  quantity  of  matter  constituting 
a  perfume  can  never  be  measured  ;  though  Tyndall  found  that  the  odours 
from  the  essential  oils  exercised  a  marked  influence  on  radiant  heat.  Per- 
fectly dry  air  was  allowed  to  pass  through  a  tube  containing  dried  paper 
impregnated  with  various  essential  oils,  and  then  admitted  into  the  experi- 
mental tube.  Taking  the  absorption  of  dry  air  as  unity,  the  following  were 
the  numbers  respectively  obtained  for  air  scented  with  various  oils  : — 
Patchouli  31,  otto  of  roses  37,  lavender  60,  thyme  68,  rosemary  74,  cassia 
109,  aniseed  372.  Thus  the  perfume  of  a  flower-bed  absorbs  a  large  per- 
centage of  the  heat  of  low  refrangibility  emitted  from  it. 

Ozone  prepared  by  electrolysing  water  was  also  found  to  have  a  remark- 
able absorptive  effect.  The  small  quantity  of  ozone  present  in  electrolytic 


-442]  Absorptive  Power  of  Vapours.  377 

oxygen  was  found  in  one  experiment  to  exercise  136  times  the  absorption  of 
the  entire  mass  of  the  oxygen  itself. 

But  the  most  important  results  which  Tyndall  has  obtained  are  those 
which  follow  from  his  experiments  on  the  behaviour  of  aqueous  vapour  to 
radiant  heat.  The  experimental  tube  was  filled  with  air,  dried  as  perfectly 
as  possible,  and  the  absorption  it  exercised  was  found  to  be  one  unit.  Ex- 
hausting the  tube,  and  admitting  the  ordinary  undried,  but  not  specially 
moist,  air  from  the  laboratory,  the  absorption  now  rose  to  72  units.  The 
difference  between  dried  and  undried  air  can  only  be  ascribed  to  the  aqueous 
vapour  the  latter  contains.  Thus  on  a  day  of  average  humidity  the  absorp- 
tive effect  due  to  the  transparent  aqueous  vapour  present  in  the  atmosphere 
is  72  times  as  great  as  that  of  the  air  itself,  though  in  quantity  the  latter  is 
about  200  times  greater  than  the  former.  Analogous  results  were  obtained 
on  different  days,  and  with  specimens  of  air  taken  from  various  localities. 
When  air  which  had  been  specially  purified  was  allowed  to  pass  through  a 
tube  filled  with  fragments  of  moistened  glass  and  examined,  it  was  found  to 
exert  an  absorption  90  times  that  of  pure  air. 

In  some  other  experiments  Tyndall  suppressed  the  use  of  rock-salt  plates 
in  his  experimental  tube,  and  even  the  tube  itself,  and  yet  in  every  case  the 
results  were  such  as  to  show  the  great  power  which  aqueous  vapour  possesses 
as  an  absorbent  of  radiant  heat. 

The  absorptive  action  which  the  aqueous  vapour  in  the  atmosphere  exerts 
on  the  sun's  heat  has  been  established  by  a  series  of  actinometrical  observa- 
tions made  by  Soret  at  Geneva  and  on  the  summit  of  Mont  Blanc ;  he  finds 
that  the  intensity  of  the  solar  heat  on  the  top  of  Mont  Blanc  is  f  of  that 
at  Geneva  ;  in  other  words,  that  of  the  heat  which  is  radiated  at  the  height 
of  Mont  Blanc,  about  \  is  absorbed  in  passing  through  a  vertical  layer  of 
the  atmosphere  14,436  feet  in  thickness.  The  same  observer  has  found  that 
with  virtually  equal  solar  heights  there  is  the  smallest  transmission  of  heat 
on  those  days  on  which  the  tension  of  aqueous  vapour  is  greatest ;  that  is, 
when  there  is  most  moisture  in  the  atmosphere. 

441.  Radiating:  power  of  gases. — Tyndall  also  examined  the  radiating 
power  of  gases.     A  red-hot  copper  ball  was  placed  so  that  the  current  of 
heated  air  which  rose  from  it  acted  on  one  face  of  a  thermo-pile  ;  this  action 
was  compensated  by  a  cube  of  hot  water  placed  in  front  of  the  opposite  face. 
On  then  allowing  a  current  of  dry  olefiant  gas  from  a  gasholder  to  stream 
through  a  ring  burner  over  the  heated  ball  and  thus  supplant  the  ascending 
current  of  hot  air,  it  was  found  that  the  gas  radiated  energetically.     By  com- 
paring in  this  manner  the  action  of  many  gases  it  was  discovered  that,  as  is 
the  case  with  solids,  those  gases  which  are  the  best  absorbers  are  also  those 
which  radiate  most  freely. 

442.  Dynamic  radiation  and  absorption. — A  gas  when  permitted  to 
enter  an  exhausted  tube  is  heated  in  consequence  of  the  collision  of  its  par- 
ticles against  the  sides  of  the  vessel ;  it  thus  becomes  a  source  of  heat,  which 
is  perfectly  capable  of  being  measured.     Tyndall  calls  this  dynamic  heating. 
In  like  manner,  when  a  tube  full  of  gas  or  vapour  is  rapidly  exhausted,  a 
chilling  takes  place  owing  to  the  loss  of  heat  in  the  production  of  motion  ; 
this  he  calls  dynamic  chilling  or  absorption. 

He  could  thus  determine  the  radiation  or  absorption  of  a  gas  without 


3;8  On  Heal.  [442- 

any  source  of  heat  external  to  the  gas  itself.  An  experimental  tube  was 
taken,  one  end  of  which  was  closed  with  a  polished  metal  plate,  and  the 
other  with  a  plate  of  rock  salt ;  in  front  of  the  latter  was  the  face  of  the  pile. 
The  needle  being  at  zero,  and  the  tube  exhausted,  a  gas  was  allowed  quickly 
to  enter  until  the  tube  was  full,  the  effect  on  the  galvanometer  being  noted. 
This  being  only  a  transitory  effect,  the  needle  soon  returned  to  zero  ;  the 
tube  was  then  rapidly  pumped  out,  by  which  a  sudden  chilling  was  produced, 
and  the  needle  exhibited  a  deflection  in  the  opposite  direction.  Comparing 
in  this  way  the  dynamic  heating  and  chilling  of  various  gases,  those  gases 
which  are  the  best  absorbers  were  also  found  to  be  the  best  radiators. 

Polished  metallic  surfaces  are,  as  we  have  seen  (427),  bad  radiators, 
but  radiate  freely  when  covered  with  varnish.  Tyndall  made  the  curious 
experiment  of  varnishing  a  metallic  surface  by  a  film  of  gas.  A  Leslie's 
cube  was  placed  with  its  polished  metal  side  in  front  of  the  pile,  and  its  effect 
neutralised  by  a  second  cube  placed  before  the  other  face  of  the  pile.  On 
allowing  a  stream  of  olefiant  or  coal  gas  to  flow  from  a  gasholder  over  the 
metallic  face  of  the  first  cube,  a  copious  radiation  from  that  side  was  pro- 
duced as  long  as  the  flow  of  gas  continued.  Acting  on  the  principle  indi- 
cated in  the  foregoing  experiment,  Tyndall  determined  the  dynamic  radiation 
and  absorption  of  vapours.  The  experimental  tube  containing  a  vapour 
under  a  small  known  pressure,  air  was  allowed  to  enter  until  the  pressure 
inside  the  tube  was  the  same  as  that  of  the  atmosphere.  In  this  way  the 
entering  air,  by  its  impact  against  the  tube,  became  heated  ;  and  its  particles 
mixing  with  those  of  the  minute  quantity  of  vapour  present,  each  of  them 
became,  so  to  speak,  coated  with  a  layer  of  the  vapour.  The  entering  air 
was  in  this  case  a  source  of  heat,  just  as  in  the  above  experiments  the  Leslie's 
cube  was.  Here,  however,  one  gas  varnished  another ;  the  radiation  and 
subsequently  the  absorption  of  various  vapours  could  thus  be  determined. 

It  was  found  that  vapours  differed  very  materially  in  their  power  of 
radiating  under  these  circumstances  :  of  those  which  were  tried  bisulphide 
of  carbon  vapour  was  the  worst  and  boracic  ether  the  best  radiator.  And 
in  all  cases  those  which  were  the  best  absorbents  were  also  the  best  radiators. 
By  this  method  Tyndall  was  able  to  observe  a  definite  radiative  power  with 
the  more  powerful  vapours  when  the  quantity  present  was  immeasurably  small. 

443.  Relation  of  absorption  to  molecular  state. — Up  to  a  recent  period 
it  was  considered  that  the  absorption  of  heat  was  mainly  dependent  upon  the 
physical  condition  of  the  body  examined.  This  led  to  the  belief  that  it  was 
impossible  for  substances  of  such  tenuity  as  gases  and  vapours  to  absorb  any 
sensible  amount  of  heat ;  and  that  the  absorption  by  bodies  when  in  a  liquid 
state  would  be  unlike  the  same  bodies  when  solid  ;  moreover,  that  if  all 
solid  bodies  were  reduced  to  an  equally  fine  state  of  division,  the  present 
differences  in  their  absorbent  and  radiative  powers  would  disappear.  A  few 
experiments  made  by  Melloni  on  atmospheric  air  supported  the  first  idea, 
and  a  series  of  experiments  by  Masson  and  Courtepe'e  established  the  belief 
in  the  last.  But  TyndalPs  researches  revealed  the  powerful  absorption  of 
heat  by  various  gases  and  vapours,  and  his  researches  have  overthrown  the 
last  two  conclusions. 

After  the  examination  of  the  absorption  of  heat  by  vapours,  Tyndall  tried 
the  same  substances  in  a  liquid  form.  The  conditions  of  the  experiments 


-443]  Relation  of  Absorption  to  Molecular  State.  379 

were  in  both  cases  the  same;  the  source  of  heat  was  always  a  spiral  of 
platinum  heated  to  redness  by  an  electric  current  of  known  strength  ;  and 
plates  of  rock  salt  were  invariably  employed  to  contain  both  vapours  and 
liquids.  Finally,  the  absorption  by  the  vapours  was  remeasured ;  in  this 
case  introducing  into  the  experimental  tube,  not,  as  Before,  equal  quantities 
of  vapour,  but  amounts  proportional  to  the  density  of  the  liquid.  When  this 
last  condition  had  been  attained,  it  was  found  that  the  order  of  absorption 
by  a  series  of  liquids,  and  by  the  same  series  when  turned  into  vapour,  was 
precisely  the  same.  Thus  the  substances  tried  stood  in  the  following  order 
as  liquid  and  as  vapour,  beginning  with  the  feeblest  absorbent,  and  ending 
with  the  most  powerful  : — 

Liquids.  Vapours. 

Bisulphide  of  carbon Bisulphide  of  carbon. 

Chloroform Chloroform. 

Iodide  of  ethyl Iodide  of  ethyL 

Benzole Benzole. 

Ether Ether. 

Alcohol Alcohol. 

Water. 

A  direct  determination  of  the  proportional  amount  of  the  vapour  of  water 
could  not  be  made,  on  account  of  the  lowness  of  its  tension,  and  the  hygro- 
scopic nature  of  the  plates  of  the  rock  salt.  But  the  remarkable  and  unde- 
viating  regularity  of  the  absorption  by  all  the  other  substances  in  the  list, 
when  as  liquid  and  vapour,  establishes  the  fact,  which  is  corroborated  by 
the  experiments  already  mentioned,  that  aqueous  vapour  is  one  of  the  most 
energetic  absorbents  of  heat. 

In  this  table  it  will  be  noticed  that  those  substances  which  have  the 
simplest  chemical  constitution  stand  first  in  the  list,  with  one  anomalous 
exception,  namely  that  of  water.  In  the  absorption  of  heat  by  gases,  Tyndall 
found  that  the  elementary  gases  were  the  feeblest  absorbents,  while  the 
gases  of  most  complex  constitution  were  the  most  powerful  absorbents.  Thus 
it  may  be  inferred  that  absorption  is  mainly  dependent  on  chemical  consti- 
tution ;  that  is  to  say,  that  absorption  and  radiation  are  molecular  acts 
independent  of  the  physical  condition  of  the  body. 

But  this  conclusion  appeared  to  be  contradicted  by  the  experiments  of 
Masson  and  Courtepe'e  on  powders.  Tyndall  repeated  these  experiments, 
avoiding  certain  sources  of  error  into  which  the  French  experimenters  had 
fallen,  and  discovered  that  the  radiation  of  powders  is  similar  to  that  of  the 
solids  from  which  they  were  derived,  and  therefore  differs  greatly  inter  se. 
The  absorbent  power  of  powders  was  also  found  to  correspond  with  their 
radiative  power — as  we  have  shown  to  be  the  case  with  solids  and  gases,  and, 
though  as  yet  we  have  no  experiments  on  the  subject,  is  doubtless  also  true 
for  liquids.  The  powders  were  attached  to  the  tin  surfaces  of  a  Leslie's  cube, 
in  such  a  manner  that  radiation  took  place  from  the  surface  of  the  powder 
alone.  The  following  table  gives  the  radiation  in  units  from  some  of  the 
powders  examined  by  Tyndall ;  the  metal  surface  of  the  cube  giving  a 
deflection  of  15  units  : — 


380  On  Heat.  [443- 

Radiation  from  powders. 

Rock  salt 35-3  Sulphate  of  calcium        .  .     777 

Biniodide  of  mercury         .         .  397  Red  oxide  of  iron   .         .  .     78-4 

Sulphur      .....  4O'6  Hydrated  oxide  of  zinc  .  .     80^4 

Carbonate  of  calcium         .         .  70-2  Sulphide  of  iron      .         .  .817 

Red  oxide  of  lead       .         .         .  74-0  Lampblack     .         .         .  .84-0 

These  substances  are  of  various  colours.  Some  are  white,  such  as  rock 
salt,  carbonate  and  sulphate  of  calcium,  and  hydrated  oxide  of  zinc  ;  some 
are  red,  such  as  biniodide  of  mercury  and  oxide  of  lead  ;  whilst  others  are 
black,  as  sulphide  of  iron  and  lampblack  :  we  have  besides  other  colours. 
The  colours,  therefore,  have  no  influence  on  the  radiating  power  :  rock  salt, 
for  example,  is  the  feeblest  radiator,  and  hydrated  oxide  of  zinc  one  of  the 
most  powerful  radiators. 

Nearly  a  century  ago  Franklin  made  experiments  on  coloured  pieces  of 
cloth,  and  found  their  absorption,  indicated  by  their  sinking  into  snow  on 
which  they  were  placed,  to  increase  with  the  darkness  of  the  Colour.  But 
all  the  clothes  were  equally  powerful  absorbents  of  obscure  heat,  and  the 
effects  noticed  were  only  produced  by  their  relative  absorptions  of  light.  In 
fact,  the  conclusions  to  be  drawn  from  Franklin's  experiment  only  hold  good 
for  luminous  heat,  especially  sunlight,  such  as  he  employed. 

444.  Applications. — The  properties  which  bodies  possess  of  absorbing, 
emitting,  and  reflecting  heat  meet  with  numerous  applications  in  domestic 
economy  and  in  the  arts.  Leslie  stated  in  a  general  manner  that  white 
bodies  reflect  heat  very  well,  and  absorb  very  little,  and  that  the  contrary  is 
the  case  with  black  substances.  As  we  have  seen,  this  principle  is  not 
generally  true,  as  Leslie  supposed  ;  for  example,  for  non-luminous  rays  white 
lead  has  as  great  an  absorbing  power  as  lampblack  (437).  Leslie's  principle 
applies  to  powerful  absorbents  like  cloth,  cotton,  wool,  and  other  organic 
substances  when  exposed  to  luminous  heat.  Accordingly,  the  most  suitable 
coloured  clothing  for  summer  is  just  that  which  experience  has  taught  us  to 
use,  namely,  white,  for  it  absorbs  less  of  the  sun's  rays  than  black  clothing, 
and  hence  feels  cooler. 

The  polished  fire-irons  "before  a  fire  are  cold,  whilst  the  black  fender  is 
often  unbearably  hot.  If,  on  the  contrary,  a  liquid  is  to  be  kept  hot  as  long 
as  possible,  it  must  be  placed  in  a  brightly  polished  metallic  vessel,  for 
then,  the  emissive  power  being  less,  the  cooling  is  slower.  Hence  it  is 
advantageous  that  the  steam  pipes,  &c.,  of  locomotives  should  be  kept 
bright.  In  the  Alps,  the  mountaineers  accelerate  the  fusion  of  the  snow  by 
covering  it  with  earth,  which  increases  the  absorbing  power. 

In  our  dwellings,  the  outsides  of  the  stoves  and  of  hot-water  apparatus 
ought  to  be  black,  and  the  insides  of  fire-places  ought  to  be  lined  with  fire- 
brick, in  order  to  increase  the  radiating  power  towards  the  apartment. 

It  is  in  consequence  of  the  great  diathermaneity  of  dry  atmospheric  air 
that  the  higher  regions  of  the  atmosphere  are  so  cold,  notwithstanding  the 
great  heat  which  traverses  them  :  whilst  the  intense  heat  of  the  sun's  direct 
rays  on  high  mountains  is  probably  due  to  the  comparative  absence  of  aqueous 
vapour  at  those  high  elevations. 


-445]  Radiation  from  Powders.  381 

As  nearly  all  the  luminous  rays  of  the  sun  pass  through  water,  and  the 
sun's  radiation  as  we  receive  it  on  the  surface  of  the  earth  consisting  of  a 
large  proportion  of  luminous  rays,  accidents  have  often  arisen  from  the 
convergence  of  these  luminous  rays  by  bottles  of  water  which  act  as  lenses. 
In  this  way  gunpowder  could  be  fired  by  the  heat  of  the  sun's  rays  con- 
centrated by  a  water  lens  ;  and  the  drops  of  water  on  leaves  in  greenhouses 
have,  it  is  said,  been  found  to  act  as  lenses,  and  burn  the  leaves  on  which 
they  rest. 

Certain  bodies  can  be  used  (436)  to  separate  the  heat  and  light  radiated 
from  the  same  source.  Rock  salt  covered  with  lampblack,  or  still  better 
with  iodine,  transmits  heat,  but  completely  stops  light.  On  the  other  hand, 
alum,  either  as  a  plate  or  in  solution,  or  a  thin  layer  of  water,  is  permeable 
to  light,  but  stops  all  the  heat  from  obscure  sources.  This  property  is  made 
use  of  in  apparatus  which  are  illuminated  by  the  sun's  rays,  in  order  to  sift 
the  rays  of  their  heating  power ;  and  a  vessel  full  of  water,  or  a  solution  of 
alum,  is  used  with  the  electric  light  when  it  is  desirable  to  avoid  too  intense 
a  heat. 

In  gardens,  the  use  of  shades  to  protect  plants  depends  partly  on  the 
diathermancy  of  glass  for  heat  from  luminous  rays  and  its  athermancy  for 
obscure  rays.  The  heat  which  radiates  from  the  sun  is  largely  of  the  former 
quality,  but  by  contact  with  the  earth  it  is  changed  into  obscure  heat,  which, 
as  such,  cannot  retraverse  the  glass.  This  explains  the  manner  in  which 
greenhouses  accumulate  their  warmth,  and  also  the  great  heat  experienced 
in  summer  in  rooms  having  glass  roofs,  for  the  glass  in  both  cases  acts,  as  it 
were,  as  a  valve  which  effectually  entraps  the  solar  rays.  On  the  same 
principle  plates  of  glass  are  frequently  used  as  screens  to  protect  us  from  the 
heat  of  a  fire ;  the  glass  allows  us  to  see  the  cheerful  light  of  the  fire,  but 
intercepts  the  larger  part  of  the  heat  radiated  from  the  fire.  Though  the 
screens  thus  become  warm  by  the  heat  they  have  absorbed,  yet,  as  they 
radiate  this  heat  in  all  directions  towards  the  fire  as  well  as  towards  us,  we 
finally  receive  less  heat  when  they  are  interposed. 

445.  Attraction  and  repulsion  arising:  from  radiation. — Crookes  has 
discovered  a  highly  remarkable  class  of  phenomena  which  are  due  to  the 
radiant  action  of  heated  and  of  luminous  bodies.  These  phenomena  are 
most  conveniently  illustrated  by  means  of  an  instrument  which  he  has  de- 
vised and  which  is  called  the  radiometer,  the  construction  of  which  is  as 
follows  : — A  glass  tube  (fig.  360),  with  a  bulb  blown  on  it,  is  fused  at  the 
bottom  to  a  glass  tube  which  at  one  end  serves  to  rest  the  whole  apparatus 
in  a  wooden  support.  In  the  other  end  is  fused  a  fine  steel  point.  On  this 
rests  a  small  vane  or  fly  consisting  of  four  arms  of  aluminium  wire  fixed  at 
one  end  to  a  small  cap,  while  at  the  others  are  fixed  small  discs  or  lozenges 
of  thin  mica,  coated  on  one  side  with  lampblack.  The  weight  of  the  fly  is 
not  more  than  two  grains. 

In  order  to  keep  the  fly  on  the  pivot  a  tube  is  fused  in  the  upper  part  of 
the  bulb  which  reaches  down  to  and  just  surrounds  the  top  of  the  cap,  with- 
out, however,  touching  it ;  the  other  end  of  this  tube  is  drawn  out  and  con- 
nected with  an  arrangement  for  exhausting  the  air  by  the  Sprengel  pump 
or  by  chemical  means ;  when  the  desired  degree  of  exhaustion  has  been 
attained  this  can  be  sealed.  By  keeping  the  apparatus  during  exhaustion 


382 


On  Heat. 


[445- 


in  a  hot-air  bath  at  a  temperature  of  300°,  the  gases  occluded  on  the  inner 
surface  of  the  glass  and  by  the  vanes  are  got  rid  of. 

If  a  source  of  light  or  of  heat,  a  candle  for  instance,  is  brought  near  the 
fly,  it  is  attracted,  and  the  fly  rotates  slowly  in  a  direction  showing  that  the 

blackened  side  moves  towards  the  light ; 
this  movement,  indicating  an  attraction, 
depends  on  a  certain  state  of  rarefaction. 
If,  however,  the  apparatus  be  connected 
with  an  arrangement  which  allows  the 
pressure  to  be  varied,  as  the  air  within  is 
further  rarefied,  this  rotation  gradually 
diminishes  in  rapidity,  until  a  certain 
point  is  reached  at  which  it  ceases.  If 
now  the  rarefaction  is  pushed  further,  the 
highly  remarkable  phenomenon  is  ob- 
served that  repulsion  succeeds  to  attrac- 
tion, and  that  the  fly  now  rotates  in  the 
direction  of  the  blackened  sides  away 
from  the  source  of  heat.  In  a  double 
radiometer,  in  which  two  flys  are  pivoted 
independently  one  over  the  other,  having 
their  blackened  sides  opposite  each  other, 
on  the  approach  of  a  lighted  candle  the 
flys  rotate  in  opposite  directions.  When 
a  cold  body  is  brought  near  instead  of  a 
hot  one — a  piece  of  ice,  for  instance — 
exactly  the  opposite  effects  are  observed  ; 
when  the  vessel  contains  air  the  pith  ball 
is  repelled,  the  neutral  point  is  observed, 
and  at  high  degrees  of  rarefaction  at- 
traction ensues. 

One  of  the  most  important  facts 
brought  to  light  by  these  experiments  is, 
that  what  has  hitherto  been  looked  upon 
as  a  complete  vacuum  is  not  so  in  reality  ; 
the  most  perfect  vacuum  obtainable  still 
contains  a  certain  residue  of  gas,  as  has 
been  proved  by  the  experiments  of 
Crookes  and  others,  among  whom  that  of 
The  latter  placed  on  the  vanes  a  light  disc 
of  mica,  and  at  a  little  distance  above  it  a  similar  disc  was  arranged  so  as 
to  rotate  freely  in  a  horizontal  plane  independently  of  the  first.  When  the 
lower  vane  was  made  to  rotate  by  bringing  a  light  near,  it  was  found 
that  the  upper  disc  was  also  put  in  rotation  in  the  same  direction,  being 
dragged  by  the  viscosity  of  the  residual  air.  Accordingly  the  explanation  of 
the  phenomena  of  the  radiometer  must  take  into  account  the  existence  of 
this  gaseous  residue. 

The  nature  of  the  gas  seems  to  have  no  special  influence  on  the  pheno- 
mena ;  whether  the  vacuum'  be  one  of  hydrogen,  of  aqueous  vapour,  or  of 


Fig.  360. 

Kundt  may  be  mentioned. 


-445]      Attraction  and  Repulsion  arising  from  Radiation.       383 

iodine  vapour,  seems  immaterial ;  though  with  hydrogen  the  exhaustion  need 
not  be  pushed  so  far  as  with  air.  The  repulsion  takes  place  with  all  the  rays 
of  the  spectrum,  the  intensity  diminishing  from  the  ultra  red  to  the  ultra 
violet.  When  the  chemical  rays  act,  the  interposition  of  a  plate  of  alum  has 
no  effect,  while  a  solution  of  iodine  in  bisulphide  of  carbon  diminishes  the 
repulsion.  The  rate  at  which  the  vane  rotates  depends  on  the  intensity  of 
the  source  of  light.  With  a  strong  light  the  rotation  is  so  rapid  that  its  rate 
cannot  be  determined.  With  two  candles  at  the  same  distance  the  rotation 
is  twice  as  rapid  as  with  one.  Two  sources  of  light  which,  successively  placed 
at  the  same  distance,  produce  the  same  rate  of  rotation,  are  equal  in  inten- 
sity. If,  when  placed  at  different  distances,  they  produce  the  same  speed 
of  rotation,  their  intensities  are  directly  as  the  squares  of  these  distances  from 
the  radiometer.  On  this  is  based  the  use  of  the  instrument  as  a  photometer 
(509)  for  comparing  together  various  sources  of  artificial  light.  It  may  also 
be  used  for  making  comparative  measurements  of  the  intensity  of  sunlight, 
and  the  distribution  of  heat  in  the  solar  spectrum  may  be  investigated  by  its 
means. 

It  is  not  difficult  to  understand  that  the  attraction  observed  in  the  experi- 
ments, as  long  as  the  apparatus  still  contains  air,  may  be  explained  by  the 
action  of  convection  currents.  For  heat  falling  upon  this  blackened  disc 
would  raise  its  temperature,  and  the  temperature  of  a  layer  of  air  in  im- 
mediate contact  with  the  disc  would  be  raised  too  ;  it  would  expand  and 
rise,  flowing  over  into  the  space  behind  the  disc,  and  would  thus  increase 
the  pressure  there. 

On  the  other  hand  the  repulsion  observed  at  the  higher  degrees  of  ex- 
haustion, approaching  a  vacuum,  is  explained  by  reference  to  the  modern 
views  as  to  the  constitution  of  gases,  of  which  it  is  at  once  an  illustration 
and  a  proof. 

The  general  nature  of  this  theory  is  that  a  gas  is  an  assemblage  of  in- 
dependent molecules,  which  are  perfectly  elastic,  and  which  move  with  great 
rapidity  ;  their  impacts  against  the  sides  of  the  vessel  in  which  the  gas  is 
contained  are  the  cause  of  the  pressure.  The  impact  of  the  molecules 
against  each  other  is  the  mechanism  by  which  the  equal  transmission  of 
pressure  in  gases  is  effected  (294). 

Crookes  has  calculated  that  the  mechanical  effect  of  the  force  of  repulsion 
is  equal  to  about  the  -^~  of  a  millogramme  on  a  square  centimetre,  and 
Stoney  has  shown  that  this  force  is  sufficient  to  account  for  the  effects 
observed  by  reference  to  admitted  principles  of  the  mechanical  theory  of  gases. 

The  rays  of  heat  pass  through  the  thin  glass  without  raising  its  tempera- 
ture, and,  falling  on  the  blackened  side  of  the  vane,  are  absorbed  by  it  ;  the 
consequence  of  this  is,  that  it  will  become  slightly  hotter.  The  layer  of  ex- 
tremely rarefied  air  in  immediate  contact  with  the  blackened  disc  will  also 
become  somewhat  hotter,  and  the  molecules  will  fly  from  the  disc  with 
greater  velocity.  Under  ordinary  pressures  or  even  at  moderate  degrees  of 
rarefaction  these  more  rapid  motions  would  be  equalised  by  their  impacts 
against  other  molecules,  and  a  uniformity  of  pressure — that  is,  of  temperature 
— would  be  established.  But  the  frequency  of  these  intramolecular  shocks 
diminishes  rapidly  with  the  increase  of  rarefaction  ;  and  the  consequence  is, 
that  a  great  number  of  molecules,  after  having  been  heated  by  contact  with 


384  On  Heat.  [445- 

the  blackened  side  of  the  palette,  will  strike  against  the  cold  glass.  The  effect 
of  this  will  be  to  cool  these  molecules — that  is,  to  diminish  their  velocity  ;  it 
will  be  chiefly  molecules  of  this  kind  which  fall  on  the  back  of  the  disc,  and 
on  the  regions  behind  it.  An  excess  of  force  equal  and  opposite  to  that  on 
the  glass  acts  against  the  front  of  the  disc,  and  is  sufficient  to  account  for 
the  phenomena  exhibited  by  Crookes. 

It  follows  from  this  explanation  that,  other  things  being  equal,  a  fly  will 
rotate  more  rapidly  in  a  small  than  in  a  large  bulb.  This  has  been  con- 
clusively proved  by  Crookes,  who  constructed  a  double-bulb  radiometer,  the 
two  bulbs  being  very  different  in  size,  and  so  connected  that,  by  dexterous 
manipulation,  the  fly  could  be  transferred  from  the  pivot  of  the  one  to  that 
of  the  other  bulb. 

446.  Internal  friction  or  viscosity  of  gases. — In  some  recent  experi- 
ments in  connection  with  the  radiometer,  Crookes  used  an  arrangement  con- 
sisting of  a  long  but  light  arm  of  straw  suspended  by  a  delicate  glass  fibre  in 
a  sort  of  T  tube  turned  upside  down  ;  in  this  way  even  a  greater  degree 
of  delicacy  was  obtained  than  with  the  radiometer.  Thus  he  was  able  to 
get  a  deflection  by  moonlight,  which  does  not  move  the  fly  of  the  radiometer. 
He  examined  the  internal  friction  or  viscosity  of  the  residual  gas  by  causing 
the  arm  to  oscillate,  and  then  observing  the  rate  at  which  the  oscillations 
diminish  under  various  pressures.  He  thus  found  that  from  ordinary  pres- 
sures down  to  a  pressure  of  o-i9mm>,  or  what  may  be  called  a  Torricellian 
vacuum,  the  viscosity  is  practically  constant,  only  diminishing  from  0-126  to 
O'ii2.  It  now  begins  to  fall  off,  and  at  a  pressure  of  O'oooo76mm>  it  has 
diminished  to  O-QI,  or  about  i.  Simultaneously  with  this  decrease  in 
viscosity  the  force  of  repulsion  excited  by  a  standard  light  on  a  blackened 
surface  varies.  It  incr-eases  as  the  pressure  diminishes  until  the  exhaus- 
tion is  about  0'05mm',  and  attains  its  maximum  at  about  cro3ram-.  It  then 
sinks  very  rapidly  until  it  is  at  O'oooo76mm>,  when  it  is  less  than  ~  of  its 
maximum. 

The  viscosity  varies  in  different  gases  ;  it  is  considerably  less  in  hydrogen 
than  in  air  ;  and  hence  it  is  not  necessary  to  drive  the  exhaustion  so  far  to 
produce  a  considerable  degree  of  repulsion. 

The  researches  of  Crookes  have  opened  the  way  to  an  entirely  new  field 
of  experimental  inquiry  into  the  phenomena  which  occur  in  what  is  called  the 
ultra-gaseous  state  of  matter,  or  that  in  which  the  rarefaction  of  gases  is 
pushed  to  its  utmost  limits.  This  state  in  which  molecular,  as  distinguished 
from  molar,  actions  come  into  play,  has  been  aptly  termed  Crooked  s  vacuum 
A  further  account  of  the  researches  requires  too  great  an  amount  of  detail 
for  the  purposes  of  this  work  ;  and  it  must  also  be  added  that  the  explana- 
tions which  have  been  given  are  still  not  beyond  the  range  of  controversy. 


-448]  Specific  Heat.  385 


CHAPTER   IX. 

CALORIMETRV. 

447.  Calorimetry.      Thermal   unit. — The   object  of  calorimetry  is  to 
measure  the  quantity  of  heat  which  a  body  parts  with  or  absorbs,  when  its 
temperature  sinks  or  rises  through  a  certain  number  of  degrees,  or  when  it 
changes  its  condition. 

Quantities  of  heat  may  be  expressed  by  any  of  its  directly  measurable 
effects,  but  the  most  convenient  is  the  alteration  of  temperature,  and  quan- 
tities of  heat  are  usually  defined  by  stating  the  extent  to  which  they  are 
capable  of  raising  a  known  weight  of  a  known  substance,  such  as  water. 
The  unit  chosen  for  comparison,  and  called  the  thermal  unit,  is  not  every- 
where the  same.  In  France  it  is  the  quantity  of  heat  necessary  to  raise  the 
temperature  of  one  kilogramme  of  water  through  one  degree  Centigrade  ;  this 
is  called  a  calorie.  In  this  book  we  shall  adopt,  as  a  thermal  unit,  the 
quantity  of  heat  necessary  to  raise  one  pound  of  water  through  one  degree 
Centigrade  :  I  calorie  =  2'2  thermal  units,  and  I  thermal  unit  =0*45  calorie. 

On  the  centimetre-gramme-second  system  of  units  the  heat  required  to 
raise  one  gramme  of  water  through  one  degree  is  taken  as  the  unit.  This  is 
called  the  gramme  degree. 

448.  Specific  beat. — When  equal  weights  of  two  different  substances,  at 
the  same  temperature,  placed  in  similar  vessels,  are  subjected  for  the  same 
length  of  time  to  the  heat  of  the  same  lamp,  or  are  placed  at  the  same 
distance  in  front  of  the  same  fire,  it  is  found  that  their  temperatures  will  vary 
considerably  ;  thus  mercury  will  be  much  hotter  than  water.     But  as,  from 
the  conditions  of  the  experiment,  they  have  each  been  receiving  the  same 
amount  of  heat,  it  is  clear  that  the  quantity  of  heat  which  is  sufficient  to 
raise  the  temperature  of  mercury  through  a  certain  number  of  degrees,  will 
only  raise  the  temperature  of  the  same  quantity  of  water  through  a  less 
number  of  degrees  ;  in  other  words,  that  it  requires  more  heat  to  raise  the 
temperature  of  water  through  one  degree  than  it  does  to  raise  the  temperature 
of  mercury  by  the  same  extent.    Conversely,  if  the  same  quantities  of  water 
and  of  mercury  at  100°  C.,be  allowed  to  cool  down  to  the  temperature  of  the 
atmosphere,  the  water  will  require  a  much  longer  time  for  the  purpose  than 
the  mercury  :  hence,  in  cooling  through  the  same  number  of  degrees,  water 
gives  out  more  heat  than  does  mercury. 

It  is  readily  seen  that  all  bodies  have  not  the  same  specific  heat.  If  a 
pound  of  mercury  at  100°  is  mixed  with  a  pound  of  water  at  zero,  the  tem- 
perature of  the  mixture  will  only  be  about  3° ;  that  is  to  say,  that  while  the 
mercury  has  cooled  through  97°,  the  temperature  of  the  water  has  only  been 
raised  3°.  Consequently  the  same  weight  of  water  requires  about  32  times  as 
much  heat  as  mercury  does  to  produce  the  same  elevation  of  temperature. 

S 


386  On  Heat.  [449- 

If  similar  experiments  are  made  with  other  substances  it  will  be  found 
that  the  quantity  of  heat  required  to  effect  a  certain  change  of  temperature 
is  different  for  almost  every  substance,  and  we  speak  of  the  specific  heat,  or 
calorific  capacity,  of  a  body  as  the  quantity  of  heat  which  it  absorbs  when  its 
temperature  rises  through  a  given  range  of  temperature,  from  zero  to  i°  for 
example,  compared  with  the  quantity  of  heat  which  would  be  absorbed, 
under  the  same  circumstances,  by  the  same  weight  of  water  ;  that  is,  water 
is  taken  as  the  standard  for  the  comparison  of  specific  heats.  Thus,  to  say 
that  the  specific  heat  of  lead  is  0-0314,  means  that  the  quantity  of  heat 
which  would  raise  the  temperature  of  any  given  weight  of  lead  through  i° 
C.  would  only  raise  the  temperature  of  the  same  weight  of  water  through 
0-0314°  C. 

Temperature  is  the  ins  viva  of  the  smallest  particles  of  a  body  ;  in 
bodies  of  the  same  temperature  the  atoms  have  the  same  vis  viva,  the 
smaller  mass  of  the  lighter  atoms  being  compensated  by  their  greater 
velocity.  The  heat  absorbed  by  a  body  not  only  raises  its  temperature — that 
is,  increases  the  vis  viva  of  the  progressive  motion  of  the  atoms — but  in  over- 
coming the  attraction  of  the  atoms  it  moves  them  further  apart,  and,  along 
with  the  expansion  which  this  represents,  some  external  pressure  is  overcome. 
In  the  conception  of  specific  heat  is  included,  not  merely  that  amount  of  heat 
which  goes  to  raise  the  temperature,  but  also  that  necessary  for  the  internal 
work  of  expansion,  and  that  required  for  the  external  work.  If  these  latter 
could  be  separated  we  should  get  the  true  heat  of  temperature,  that  which  is 
used  solely  in  increasing  the  vis  viva  of  the  atoms.  This  is  sometimes 
called  the  true  specific  heat. 

Three  methods  have  been  employed  for  determining  the  specific  heats  of 
bodies  :  (i.)  the  method  of  the  melting  of  ice,  (ii.)  the  method  of  mixtures, 
and  (iii.)  that  of  cooling.  In  the  latter,  the  specific  heat  of  a  body  is  deter- 
mined by  the  time  which  it  takes  to  cool  through  a  certain  temperature. 
Previous  to  describing  these  methods,  it  will  be  convenient  to  explain  the 
expression  for  the  quantity  of  heat  absorbed  or  given  out  by  a  body  of  known 
weight  and  specific  heat,  when  its  temperature  rises  or  falls  through  a  certain 
number  of  degrees. 

449.  Measure  of  tbe  sensible  heat  absorbed  by  a  body. —  Let  m  be 
the  weight  of  a  body  in  pounds,  c  its  specific  heat,  and  /  its  temperature. 
The  quantity  of  heat  necessary  to  raise  a  pound  of  water  through  one  degree 
being  taken  as  unity,  m  of  these  units  would  be  required  to  raise  m  pounds 
of  water  through  one  degree,  and  to  raise  it  through  t  degrees,  /  times  as 
much,  or  mt.  As  this  is  the  quantity  of  heat  necessary  to  raise  through  / 
degrees  m  pounds  of  water,  whose  specific  heat  is  unity,  a  body  of  the  same 
weight,  only  of  different  specific  heat,  would  require  mtc.  Consequently, 
when  a  body  is  heated  through  /  degrees,  the  quantity  of  heat  which  it 
absorbs  is  the  product  of  its  weight,  into  the  range  of  temperature,  into  its 
specific  heat.  This  principle  is  the  basis  of  all  the  formulae  for  calculating 
specific  heats. 

If  a  body  is  heated  or  cooled  from  t  to  f  degrees,  the  heat  absorbed  or 
disengaged  will  be  represented  by  the  formula 

m(t'  -f}c,  or  jn(t-f)c. 


-450] 


MetJiod  of  the  Fusion  of  Ice. 


387 


=  %Q  P  we  have 


450.  Method  of  the  fusion  of  ice. — This  method  of  determining  specific 
heats  is  based  on  the  fact  that  to  melt  a  pound  of  ice  80  thermal  units  are 
necessary,  or  more  exactly  79*25.  Black's  calorimeter  (fig.  361)  consists  of 
a  block  of  ice  in  which  a  cavity  is  made, 
and  which  is  provided  with  a  cover  of  ice. 
The  substance  whose  specific  heat  is  to  be 
determined  is  heated  to  a  certain  tempera- 
ture, and  is  then  placed  in  the  cavity,  which 
is  covered.  After  some  time  the  body  be- 
comes cooled  to  zero.  It  is  then  opened,  and 
both  the  substance  and  the  cavity  wiped  dry 
with  a  sponge  which  has  been  previously 
weighed.  The  increase  of  weight  of  this 
sponge  obviously  represents  the  ice  which  Fig  361. 

has  been  converted  into  water. 

Now,  since  one  pound  of  ice  at  o°  in  melting  to  water  at  o°  absorbs  80 
thermal  units,  P  pounds  absorbs  80  P  units.  On  the  other  hand  this  quan- 
tity of  heat  is  equal  to  the  heat  given  out  by  the  body  in  cooling  from  /°  to 
zero,  which  is  ;;//r,  for  it  may  be  taken  for  granted  that  in  cooling  from  /°  to 
zero  a  body  gives  out  as  much  heat  as  it  absorbs  in  being  heated  from  zero 
to  /°.  Consequently  from 

8oP 
;///' 

It  is  difficult  to  obtain  blocks  of  ice  as  large  and  pure  as  those  used 
by  Black  in  his  experiments,  and  Lavoisier  and  Laplace  replaced  the  block 
of  ice  by  a  more  complicated 
apparatus  which  is  called  the 
ice  calorimeter.  Fig.  362 
gives  a  perspective  view  of  it, 
and  fig.  363  represents  a  sec- 
tion. It  consists  of  three 
concentric  tin  vessels  ;  in  the 
central  one  is  placed  the  body 
M,  whose  specific  heat  is  to 
be  determined,  while  the  two 
others  are  filled  with  pounded- 
ice.  The  ice  in  the  com- 
partment A,  is  melted  by  the 
heated  body,  while  the  ice  in 
the  compartment  B  cuts  off 
the  heating  influence  of  the 
surrounding  atmosphere. 
The  two  stopcocks  E  and  D  Fig.  362.  Fig.  363. 

give  issue  to  the  water  which 
arises  from  the  liquefaction  of  the  ice. 

In  order  to  find  the  specific  heat  of  a  body  by  this  apparatus,  its  weight, 
;;/,  is  first  determined  ;  it  is  then  raised  to  a  given  temperature,  /,  by  keeping 
it  for  some  time  in  an  oil  or  water  bath,  or  in  a  current  of  steam.  Having 
been  quickly  brought  into  the  central  compartment,  the  lids  are  replaced 

S  2 


388 


On  Heat. 


[450- 


and  covered  with  ice,  as  represented  in  the  figure.  The  water  which  flows 
out  by  the  stopcock  D  is  collected.  Its  weight,  P,  is  manifestly  that  of  the 
melted  ice.  The  calculation  is  then  made  as  in  the  preceding 
case. 

There  are  many  objections  to  the  use  of  this  apparatus. 
From  its  size  it  requires  some  quantity  of  ice,  and  a  body,  M, 
of  large  mass  ;  while  the  experiment  lasts  a  considerable  time. 
A  certain  weight  of  the  melted  water  remains  adhering  to  the 
ice,  so  that  the  water  which  flows  out  from  D  does  not  exactly 
represent  the  weight  of  the  melted  ice. 

451.  Bunsen's  ice  calorimeter. — On  the  very  considerable 
diminution  of  volume  which   ice   experiences  on  passing  into 
water  (347),  Bunsen  has  based  a  calorimeter  which  is  particu- 
larly suitable  when  only  small    quantities  of  a  substance  can 
be   used   in   determinations.     A   small   test   tube   a   (fig.   364) 
intended  to  receive  the  substance  experimented  upon  is  fused 
in    the   wider   tube    B.      The    part    ab   contains    pure   freshly 
boiled-out   distilled   water,  and  the  prolongation  of  this  tube 
BC,  together  with  the  capillary  tube  d,  contains  pure  mercury. 
This  tube  d  is  firmly  fixed  to  the   end  of  the  tube  C  ;    it  is 
|B  graduated,  and  the  value  of  each  division  of  the  graduation  is 
specially  determined  by  calibration.      When  the  apparatus  is 
immersed  'in    a    freezing   mixture,    the   water   in    the   part   ab 
Fig.  364.       freezes.     Hence,  if  afterwards,  while  the  apparatus  is  protected 
against  the  access  of  heat  from  without,  a  weighed  quantity  of 
a  substance  at  a  given  temperature  is  introduced  into  the  tube,  it  imparts 
its  heat  to  this  in  sinking  to  zero.     In  doing  so  it  melts  a  certain  quantity 

of  ice,  which  is  evidenced  by  a  cor- 
responding depression  of  the  mercury 
in  the  tube  d.  Thus  the  weight  of 
ice  melted,  together  with  the  weight 
and  original  temperature  of  the  sub- 
stance experimented  upon,  furnish  all 
the  data  for  calculating  the  specific 
heat. 

For  heating  the  substance  in  this, 
and  also  in  other  calorimetrical  ex- 
periments, the  apparatus  fig.  365  is 
well  adapted.  The  cylindrical  metal 
vessel  G  is  narrower  at  the  top,  and 
a  glass  test  tube  R  is  fitted  into  a 
cork  which  closes  G.  In  this  glass  tube, 
which  is  also  closed  by  a  cork  K,  the 
substance  is  placed  which  is  to  be 
heated.  The  greater  part  of  the  vessel 
is  covered  by  a  thick  mantle  of  felt,  B. 
The  water  in  the  vessel  is  boiled,  the 

steam  emerging  at  d,  until  the  substance  has  acquired  the  temperature  of 
boiling  water,  for  which  about  twenty  minutes  is  required.     The  mantle  and 


Fig.  365- 


-453]  Corrections.  389 

the  lamp  having  been  taken  away,  the  tube  R  is  rapidly  removed,  and  its 
contents  tipped  into  the  tube  d  of  the  calorimeter  (fig.  364). 

For  this  mode  of  determining  the  specific  heat  a  new  determination  of 
the  latent  heat  of  ice  was  made,  and  was  found  to  be  80-025.  It  was  also 
in  connection  with  these  experiments  that  Bunsen  made  his  determination 
of  the  specific  gravity  of  ice,  which  he  found  to  be  in  the  mean  0*91  674. 

By  the  above  method  Bunsen  determined  the  specific  heat  of  several  of 
the  rare  metals  for  which  a  weight  of  only  a  few  grains  could  be  used. 

452.  Method  of  mixtures.  —  In  determining  the  specific  heat  of  a  solid 
body  by  this  method,  it  is  weighed  and  raised  to  a  known  temperature,  by 
keeping  it,  for  instance,  for  some  time  in  a  closed  place  heated  by  steam  ; 
it  is  then  immersed  in  a  mass  of  cold  water,  the  weight  and  temperature  of 
which  are  known.  From  the  temperature  of  the  water  after  mixture  the 
specific  heat  of  the  body  is  determined. 

Let  M  be  the  weight  of  the  body,  T  its  temperature,  c  its  specific  heat  ; 
and  let  m  be  the  weight  of  the  cold  water,  and  /  its  temperature. 

As  soon  as  the  heated  body  is  plunged  into  the  water,  the  temperature  of 
the  latter  rises  until  both  are  at  the  same  temperature.  Let  this  temperature 
be  9.  The  heated  body  has  been  copied  by  T  -  6  ;  it  has,  therefore,  lost  a 
quantity  of  heat,  M(T  —  6}c.  The  cooling  water  has,  on  the  contrary,  ab- 
sorbed a  quantity  of  heat  equal  to  m  (6  -  /),  for  the  specific  heat  of  water  is 
unity.  Now  the  quantity  of  heat  given  out  by  the  body  is  manifestly  equal 
to  the  quantity  of  heat  absorbed  by  the  water;  that  is,  M(T  —  &]c  =  m(6  —  /), 
from  which 


An  example  will  illustrate  the  application  of  this  formula.  A  piece  of 
iron  weighing  60  ounces,  and  at  a  temperature  of  100°  C.,  is  immersed  in 
1  80  ounces  of  water,  whose  temperature  is  19°  C.  After  the  temperatures 
have  become  uniform,  that  of  the  cooling  water  is  found  to  be  22°  C.  What 
is  the  specific  heat  of  the  iron  ? 

Here  the  weight  of  the  heated  body,  M,  is  60,  the  temperature,  T,  is  100°, 
c  is  to  be  determined  ;  the  temperature  of  mixture,  0,  is  22°,  the  weight  of 
the  cooling  water  is  180,  and  its  temperature  19°.     Therefore 
_  180(22-  19)  _  9  __.ITC- 

'-60(100-22)  -T8-01153' 

453.  Corrections.  —  The  vessel  containing  the  cooling  water  is  usually 
a  small  cylinder  of  silver  or  brass,  with  thin  polished  sides,  and  is  supported 
by  some  badly  conducting  arrangement.  It  is  obvious  that  this  vessel,  which 
is  originally  at  the  temperature  of  the  cooling  water,  shares  its  increase  of 
temperature,  and  in  accurate  experiments  this  must  be  allowed  for.  The 
decrease  of  temperature  of  the  heated  body  is  equal  to  the  increase  of 
temperature  of  the  cooling  water,  and  of  the  vessel  in  which  it  is  contained. 
If  the  weight  of  this  latter  be  ;«',  and  its  specific  heat  c',  its  temperature,  like 
that  of  the  water,  is  /  :  consequently  the  previous  equation  becomes 

M<r(T  -  6}  =  m(B  -  /)  +  m  'c\Q  -  /)  ; 
from  which,  by  obvious  transformations, 


M  T-0) 


390  On  Heat.  [453- 

Generally  speaking,  the  value  me'  is  put  =  /n  ;  that  is  to  say,  p.  is  the 
weight  of  water  which  would  absorb  the  same  quantity  of  heat  as  the  vessel. 
This  is  said  to  be  the  reduced  value  in  water  of  the  vessel,  or  the  water  equi- 
valent. The  expression  accordingly  becomes 

(m  +  ii)  (6-f] 


M(T-0) 

In  accurate  experiments  it  is  necessary  also  to  allow  for  the  heat  absorbed 
by  the  glass  and  mercury  of  the  thermometer,  by  introducing  into  the  equa- 
tion their  values  reduced  on  the  same  principle. 

In  order  to  allow  for  the  loss  of  heat  due  to  radiation,  a  preliminary  experi- 
ment is  made  with  the  body  whose  specific  heat  is  sought,  the  only  object  of 
which  is  to  ascertain  approximately  the  increase  of  temperature  of  the 
cooling  water.  If  this  increase  be  10°,  for  example,  the  temperature  of  the 
water  is  reduced  by  half  this  number  —  that  is  to  say  5°  below  the  tempera- 
ture of  the  atmosphere  —  and  the  experiment  is  then  carried  out  in  the 
ordinary  manner. 

By  this  method  of  compensation,  first  introduced  by  Rumford,  the  water 
receives  as  much  heat  from  the  atmosphere  during  the  first  part  of  the  ex- 
periment as  it  Ios3s  by  radiation  during  the  second  part. 

454.  Regnault  s  apparatus  for  determining  specific  heats.  —  Fig.  366 
represents  one  of  the  forms  of  apparatus  used  by  Regnault  in  determining 
specific  heats  by  the  method  of  mixtures. 

The  principal  part  is  a  water  bath,  AA,  of  which  fig.  367  represents  a 
section.  It  consists  of  three  concentric  compartments  ;  in  the  central  one 
there  is  a  small  basket  of  brass  wire,  c,  containing  fragments  of  the  substance 
whose  specific  heat  is  to  be  determined,  in  the  middle  of  which  is  placed  a 
thermometer,  T.  The  second  compartment  is  heated  by  a  current  of  steam 
coming  through  the  tube,  *,  from  a  boiler,  B,  and  passing  into  a  worm,  a, 
where  it  is  condensed.  The  third  compartment,  z'z,  is  an  air  chamber,  to 
hinder  the  loss  of  heat.  The  water  bath  A  A  rests  on  a  chamber,  K,  with 
double  sides,  E  E,  forming  a  jacket,  which  is  kept  full  of  cold  water,  in  order 
to  exclude  the  heat  from  A  A  and  from  the  boiler,  B.  The  central  compart- 
ment of  the  water  bath  is  closed  by  a  damper,  r,  which  can  be  opened  at 
pleasure,  so  that  the  basket,  <:,  can  be  lowered  into  the  chamber,  K. 

On  the  left  of  the  figure  is  represented  a  small  and  very  thin  brass  vessel, 
D,  suspended  by  silk  threads  on  a  small  carriage,  which  can  be  moved  out 
of,  or  into,  the  chamber,  K.  This  vessel,  which  serves  as  a  calorimeter,  con- 
tains water,  in  which  is  immersed  a  thermometer,  /.  Another  thermometer 
at  the  side,  t\  gives  the  temperature  of  the  air. 

When  the  thermometer,  T,  shows  that  the  temperature  of  the  substance 
in  the  bath  is  stationary,  the  screen,  ^,  is  raised,  and  the  vessel,  D,  moved  to 
just  below  the  central  compartment  of  the  water  bath.  The  damper,  r,  is 
then  withdrawn,  and  the  basket,  c,  and  its  contents  are  lowered  into  the  water 
of  the  vessel,  D,  the  thermometer,  T,  remaining  fixed  in  the  cork.  The 
carriage  and  the  vessel,  D,  are  then  moved  out,  and  the  water  agitated  until 
the  thermometer,  T,  becomes  stationary.  The  temperature  which  it  indicates 
is  6.  This  temperature  known,  the  rest  of  the  calculation  is  made  in  the 


-455] 


Method  of  Cooling: 


391 


manner  described  in  art.  449,  care  being  taken  to  make  all  the  necessary 
corrections. 

In  determining  the  specific  heat  of  substances — phosphorus,  for  instance 
— which  could  not  be  heated  without  causing  them  to  melt,  or  undergo  some 
change  which  would  interfere  with  the  accuracy  of  the  result,  Regnault 
adopted  an  inverse  process  :  he  cooled  them  down  to  a  temperature  con- 
siderably below  that  of  the  water  in  the  calorimeter,  and  then  observed  the 
diminution  in  the  temperature  of  the  latter,  which  resulted  from  immersing 
the  cooled  substance  in  it. 

In  determining  the  specific  heat  of  substances,  which,  like  potassium, 
would  decompose  water,  some  other  liquid,  such  as  turpentine  or  benzole, 


W 

must  be  used.  These  liquids  have  the  additional  advantage  of  having  a 
lower  specific  heat  than  water,  which  has  the  highest  of  any  liquid,  so  that 
any  error  in  determining  the  temperature  of  the  cooling  liquid  has  a  less 
influence  on  the  value  of  the  specific  heat.  With  this  view  use  has  been 
made  of  mercury,  the  specific  heat  of  which  is  only  one-thirtieth  that  of 
water. 

455.  Method  of  cooling-. — Equal  weights  of  different  bodies  whose 
specific  heats  are  different,  will  occupy  different  times  in  cooling  through 
the  same  number  of  degrees.  Dulong  and  Petit  applied  this  principle  in 


392  On  Heal.  [455- 

determining  the  specific  heats  of  bodies  in  the  following  manner  : — A  small 
polished  silver  vessel  is  filled  with  the  substance  in  a  state  of  fine  powder, 
and  a  thermometer  placed  in  the  powder,  which  is  pressed  down.  This 
vessel  is  heated  to  a  certain  temperature,  and  is  then  introduced  into  a 
copper  vessel,  in  which  it  fits  hermetically.  This  copper  vessel  is  exhausted, 
and  maintained  at  the  constant  temperature  of  melting  ice,  and  the  time 
noted  which  the  substance  takes  in  falling  through  a  given  range  of  tem- 
perature, from  1 5°  to  5°  for  example.  The  times  which  equal  weights  of  dif- 
ferent bodies  require  for  cooling  through  the  same  range  of  temperature  are 
directly  as  their  specific  heats. 

Regnault  has  proved  that  with  solids  this  method  does  not  give  trust- 
worthy results  ;  it  assumes,  which  is  not  quite  the  case,  that  the  cooling  in 
all  parts  is  equal,  and  that  all  substances  part  with  their  heat  to  the  silver 
case  with  equal  facility.  The  method  may,  however,  be  employed  with 
success  in  the  determination  of  the  specific  heat  of  liquids. 

In  an  investigation  of  the  specific  heats  of  various  soils,  Pfaundler  found 
that  a  soil  of  low  specific  heat  heats  and  cools  rapidly,  while  earth  of  higher 
specific  heat  undergoes  slow  heating  and  slow  cooling  ;  that  moist  earths 
rich  in  humus  have  a  high  specific  heat,  amounting  in  the  case  of  turf  to  as 
much  as  0*5  •  while  dry  soils  free  from  humus,  such  as  lime  and  sand,  have 
a  low  specific  heat,  not  more  than  about  0-2. 

456.  Specific   heat   of  liquids. — The  specific  heat  of  liquids  may  be 
determined  either  by  the  method  of  cooling,  by  that  of  mixtures,  or  by  that 
of  the  ice  calorimeter.     In  the  latter  case  they  are  contained  in  a  small 
metal  vessel,  or  a  glass  tube,  which  is  placed  in  the  central  compartment 
(fig.  366),  and  the  experiment  then  made  in  the  usual  manner. 

It  will  be  seen  from  the  following  table  that  water  and  oil  of  turpentine 
have  a  much  greater  specific  heat  than  other  substances,  and  more 
especially  than  the  metals.  It  is  from  its  great  specific  heat  that  water  re- 
quires a  long  time  in  being  heated  or  cooled,  and  that  for  the  same  weight 
and  temperature  it  absorbs  or  gives  out  far  more  heat  than  other  substances. 
This  double  property  is  applied  in  the  hot-water  apparatus,  of  which  we 
shall  presently  speak,  and  it  plays  a  most  important  part  in  the  economy  of 
nature. 

457.  Specific  heats  of  bodies. — The  list  contained  in  the  next  article 
(458)  gives  the  specific  heats  of  a  great  number  of  elementary  substances. 
We  give  here  the  specific  heats  of  a  few  substances,  mostly  liquids  : — 

Specific  heat  Specific  heat 

Turpentine       .         .         .  0-426  Bisulphide  of  carbon       .  0*245 

Alcohol    ....  0^62  Thermometer  glass          .  0-198 

Ether      ....  0-516  Steel         .         .  .  0-118 

Glycerine        .         .         .  0-555  Brass        ....  0*094 

The  specific  heat  of  water  is  commonly  taken  at  unity,  which  is  not 
strictly  correct.  According  to  the  most  recent  determinations  it  is  expressed 
by  the  formula  I  +0-0001 5/. 

These  numbers,  as  well  as  the  numbers  in  458,  represent  the  mean  specific 
heats  between  o°  and  100°.  It  was,  however,  shown  by  Dulong  and  Petit 
that  the  specific  heats  increase  with  the  temperature.  Those  of  the  metals 


-457]  Specific  Heats  of  Bodies.  393 

for  instance,  are  greater  between  100°  and  200°  than  between  o°  and  100°, 
and  are  still  greater  between  200°  and  300°  ;  that  is  to  say,  a  greater  amount 
of  heat  is  required  to  raise  a  body  from  200°  to  250°,  than  from  100°  to  150°, 
and  still  more  than-  from  o°  to  50°.  For  silver,  the  mean  specific  heat  be- 
tween o°  and  100°  is  0-057,  while  between  o°  and  200°  it  is  0-0611.  The  fol- 
lowing table  gives  the  specific  heats  at  various  temperatures  :  — 

Copper  0-0910 +  0-000046/ 

Zinc 0-0865  +  o-oooo88/ 

Lead 0-0286  +  o-oooo3S/ 

Platinum 0-0317 +  o-ooooo62/ 

Water i+o-oooi5/ 

The  increase  of  specific  heat  with  the  temperature  is  greater  as  bodies 
are  nearer  their  fusing  point.  Any  action  which  increases  the  density  and 
molecular  aggregation  of  a  body,  diminishes  its  specific  heat.  The  specific 
heat  of  copper  is  diminished  by  its  being  hammered,  but  it  regains  its  original 
value  after  the  metal  has  been  again  heated. 

The  specific  heat  of  a  liquid  increases  with  the  temperature  much  more 
rapidly  than  that  of  a  solid.  Water  is,  however,  an  exception  ;  its  specific 
heat  increases  less  rapidly  than  does  that  of  solids. 

The  most  remarkable  examples  of  the  influence  of  temperature  on  the 
specific  heat  are  afforded  by  carbon,  boron,  and  silicon.  Weber  has  found 
that  at  600°  the  specific  heat  of  carbon  is  7  times,  and  that  of  boron  2£  times, 
as  great  as  their  respective  specific  heats  at  —  50°.  The  specific  heat  of 
diamond  is  0*0635  at  —  5°°>  0-1318  at  33°,  0*2218  at  140°,  and  0-3026  at  247°. 
Although  the  specific  heat  increases  thus  rapidly  between  —50°  and  2  50°, 
beyond  that  point  the  rate  of  increase  is  slower ;  and  beyond  600°,  or  at  an 
incipient  red  heat,  it  seems  to  be  pretty  constant,  or  at  any  rate  to  exhibit 
no  greater  variations  with  the  temperature  than  are  afforded  by  other  sub- 
stances. Thus,  while  at  600°  the  specific  heat  is  0-441,  at  985°  it  is  0-459. 
Graphite  also  has  at  22°  the  specific  heat  0-168  ;  this  increases,  but  at  a 
gradually  diminishing  rate,  to  642°,  where  its  specific  heat  is  0-445.  Like 
diamond,  an  incipient  red  heat  seems  to  be  a  limiting  temperature  beyond 
which  graphite  exhibits  only  the  ordinary  variation  with  the  temperature. 
Weber  has  also  found  that,  in  their  thermal  deportment,  there  are  only  two 
essentially  different  modifications  of  carbon — the  transparent  one  (diamond), 
and  the  opaque  ones  (graphite,  dense  amorphous  carbon,  and  porous  amor- 
phous carbon). 

Crystallised  boron  is  similar  in  its  deportment  to  carbon  ;  its  specific  heat 
increases  from  0-1915  at  —40°  to  0*2382  at  27°,  and  to  0-3663  at  233°.  The 
rate  of  increase  is  very  rapid  up  to  80°  ;  it  increases  beyond  that  temperature, 
but  at  a  gradually  diminished  rate,  and,  no  doubt,  tends  to  an  almost  constant 
value  of  0-5. 

The  specific  heat  of  silicon  also  varies  with  the  temperature  ;  between 
—  40°  and  200°  it  increases  from  0-136  to  0-203  '•>  t^e  rate  °f  increase  is  less 
rapid  with  higher  temperatures,  being  at  200°  only  £  what  it  is  at  10°.  At 
200°  it  reaches  its  limiting  value. 

The  specific  heat  of  substances  is  greater  in  the  liquid  than  in  the  solid 
state,  as  will  be  seen  by  the  following  table  : — 

S3 


394  On  Heat.  [457- 

Solid  Liquid 

Water           .......  0-489  rooo 

Bromine       .......  0-084  o-iio 

Mercury        .......  0*031  0-033 

Phosphorus           ......  0-190  0*202 

Tin        ........  0-056  0-064 

Lead     ........  0*031  0*040 

It  also  differs  with  the  allotropic  modification  ;  thus  the  specific  heat  of 
red  phosphorus  is  0*19,  and  that  of  white  0*17;  of  crystallised  arsenic 
0*083,  and  of  amorphous  0*058  ;  of  crystallised  selenium  0-084,  and  of 
amorphous  0-0953*  of  wood  charcoal  0*241  *  of  graphite  0*202;  and  of 
diamond  0*147. 

Pouillet  used  the  specific  heat  of  platinum  for  measuring  high  degrees  of 
heat.  Supposing  200  ounces  of  platinum  had  been  heated  in  a  furnace,  and 
had  then  been  placed  in  1000  ounces  of  water,  the  temperature  of  which  it 
had  raised  from  13°  to  20°.  From  the  formula  we  have  M  =200,  m  =  1000  ; 
6  is  20,  and  /is  13.  The  specific  heat  of  platinum  is  0*033,  and  we  have, 
therefore,  from  the  equation  — 


T  =  ^(-0  +  M      =  7000+  I32  =  7£33  =  Tnono 
M^  6-6  6*6  " 

It  is  found,  however,  that  the  mean  specific  heat  of  platinum  at  tempera- 
tures up  to  about  1200  is  0*0377  ;  if  this  value,  therefore,  be  substituted  for 
c  in  the  above  equation,  we  have  — 


7'54 

By  this  method,  which  requires  great  skill  in  the  experimenter,  Pouillet 
determined  a  series  of  high  temperatures.  He  found,  for  example,  the  tem- 
perature of  melting  iron  to  be  1500°  to  1600°  C. 

458.  Dillon?  and  Petit's  law.  —  A  knowledge  of  the  specific  heat  of 
bodies  has  become  of  great  importance,  in  consequence  of  Dulong  and  Petit's 
discovery  of  the  remarkable  law,  that  the  product  of  the  specific  heat  of  any 
solid  element  into  its  atomic  weight  is  approximately  a  constant  number,  as 
will  be  seen  from  the  following  table  :  — 


Aluminium 

Specific 
heat 
.       0-2143 
O*O  r;  I  T, 

Atomic 
weight 
27-4 
122 

Atomic 
heat 

5*87 
6*26 

Arsenic 
Bismuth     . 
Bromine     . 

.      0-0822 
.      0-0308 
.      0-0843 
O-Oi;67 

75 

210 
80 
I  12 

6-17 
6-47 
674 
6'35 

Cobalt 
Copper 
Gold  . 
Iodine 

.      0-1067 
•      0-0939 
.      0-0324 
0-0541 

58*7 

63-5 
197 

127 

6*26 

5'99 
6*38 
6*87 

Iron  . 

.      0*1138 

56 

6-37 

-458]  Dnlong  and  Petit' s  Law.  395 

Specific  Atomic  Atomic 

neat  weight  heat 

Lead 0-0314  207  6-50 

Magnesium        ....  0-2475  24  5 '94 

Mercury 0-0332  200  6-64 

Nickel 0-1092  587  6-41 

Phosphorus        ....  0-1740  31*0  5-39 

Platinum    .         .         .         .    •     .  0-0524  I97'5  6-40 

Potassium          .         .         .         .0-1655  39' *  6-47 

Silver 0-0570  108-0  6- 1 6 

Sulphur 0-178  32  570 

Tin    ". 0-0555  1'8  6-55 

Zinc 0-0956  65-2  6-23 

It  will  be  seen  that  the  number  is  not  a  constant,  varying  as  it  does 
between  5-39  and  6-87.  These  variations  may  depend  partly  on  the  difficulty 
of  getting  the  elements  in  a  state  of  perfect  purity,  and  partly  on  errors  in- 
cidental to  the  determination  of  the  specific  heats,  and  of  the  atomic  weights. 
Again,  the  specific  heats  of  bodies  vary  with  the  state  of  aggregation  of  the 
bodies,  and  also  with  the  temperatures  at  which  they  are  determined  ;  some, 
such  as  potassium,  have  been  determined  at  temperatures  very  near  their 
fusing  points  ;  others,  like  platinum,  at  temperatures  much  removed  from 
them.  A  main  cause,  therefore,  of  the  discrepancies  is  doubtless  to  be  found 
in  the  fact  that  all  the  determinations  have  not  been  made  under  corre- 
sponding physical  conditions. 

According  to  modern  views,  the  heat  imparted  to  a  body  is  partly  ex- 
pended in  external  work,  which  in  the  case  of  a  solid  would  be  extremely 
small,  being  only  that  required  for  the  pressure  of  the  atmosphere  raised 
through  a  distance  representing  the  expansion  ;  secondly,  the  internal  work, 
or  the  heat  used  in  overcoming  the  attraction  of  the  atoms,  and  forcing 
them  apart  ;  and  thirdly,  there  is  the  true  specific  heat,  or  the  heat  applied  in 
increasing  the  temperature — that  is,  in  increasing  the  vis  viva  of  the  molecules 
(448).  By  far  the  most  considerable  of  these  is  the  latter  ;  the  amount  of 
heat  consumed  in  the  two  former  operations  is  small,  and  the  variations 
with  different  bodies  must  be  inconsiderable.  Until,  however,  the  relation 
between  the  various  factors  is  made  out,  absolute  identity  in  the  numbers 
for  the  atomic  specific  heat  cannot  be  expected.  Weber  holds  that  even 
when  due  allowance  has  been  made  for  these  circumstances,  the  variations 
are  too  great  to  be  accounted  for,  and  he  considers  that  they  point  for  their 
explanation  to  an  alteration  in  the  constitution  of  the  atom,  and  render 
probable  a  changing  valency  of  the  atom  of  carbon. 

The  atomic  weights  of  the  elements  represent  the  relative  weights  of  equal 
numbers  of  atoms  of  these  bodies,  and  the  product, /<:,  of  the  specific  heat, 
c,  into  the  atomic  weight,  p,  is  the  atomic  heat,  or  the  quantity  of  heat 
necessary  to  raise  the  temperature  of  the  same  number  of  atoms  of  different 
substances  by  one  degree  ;  and  Dulong  and  Petit's  law  may  be  thus  ex- 
pressed :  the  same  quantity  of  heat  is  needed  to  heat  an  atom  of  all  simple 
bodies  to  the  same  extent. 

The  atomic  heat  of  a  body,  when  divided  by  its  specific  heat,  gives  the 
atomic  weight  of  a  body.  Regnault  has  even  proposed  to  use  this  relation 


396  On  Heat.  [458- 

as  a  means  of  determining  the  atomic  weight,  and  it  certainly  is  of  great 
service  in  deciding  on  the  atomic  weight  of  a  body  in  cases  where  the 
chemical  relations  permit  a  choice  between  two  or  more  numbers. 

In  compound  bodies  the  law  also  prevails  :  the  product  of  the  specific 
heat  into  the  equivalent  is  an  almost  constant  number,  which  varies,  how- 
ever, with  different  classes  of  bodies.  Thus,  for  the  class  of  oxides  of  the 
general  formula  RO,  it  is  ii'3o;  for  the  sesquioxides  R2O3,  it  is  27*15; 
for  the  sulphides  RS,  it  is  18-88  ;  and  for  the  carbonates  RCO3,  it  is  21-54. 
The  law,  which  is  known  as  Naumanrfs  /aw,  may  be  expressed  in  the 
following  general  manner  :  —  With  compounds  of  the  same  formula,  and  of  a 
similar  chemical  constitution,  the  product  of  the  atomic  weight  into  the 
specific  heat  is  a  constant  quantity.  This  includes  Dulong  and  Petit's  law  as 
a  particular  case. 

459.  Specific  heat  of  compound  bodies.  —  In  order  to  deduce  the  specific 
heat  of  the  compound  from  that  of  its  elements,  Wcestyn  has  made  the 
following  hypothesis  :  he  assumes  that  an  element,  in  entering  into  com- 
bination with  others  to  form  a  compound  body,  retains  its  own  specific  heat, 
so  that  if  p,  p'  ',  p"  ....  represent  the  atomic  weights  of  the  elements,  and 
P  that  of  the  compound  ;  c,  c',  c",  .  .  .  .  C,  the  corresponding  specific  heats, 
while  n,  n',  n",  ....  are  the  numbers  of  atoms  of  these  simple  bodies  which 
make  up  the  molecule  of  the  compound,  the  relation  obtains  :  — 


The  numbers  obtained  by  calculating,  on  this  hypothesis,  the  specific 
heats  of  the  sulphides,  iodides,  and  bromides,  agree  with  experimental 
results. 

460.  Specific  beat  of  gases.  —  The  specific  heat  of  a  gas  may  be  re- 
ferred either  to  that  of  water  or  to  that  of  air.  In  the  former  case,  it  repre- 
sents the  quantity  of  heat  necessary  to  raise  a  given  weight  of  the  gas  through 
one  degree,  as  compared  with  the  heat  necessary  to  raise  the  same  weight 
of  water  one  degree.  In  the  latter  case  it  represents  the  quantity  of  heat 
necessary  to  raise  a  given  volume  of  the  gas  through  one  degree,  compared 
with  the  quantity  necessary  for  the  same  volume  of  air  treated  in  the  same 
manner. 

De  la  Roche  and  Berard  determined  the  specific  heats  of  gases  in  re- 
ference' to  water  by  causing  known  volumes  of  a  given  gas  under  constant 
pressure,  and  at  a  given  temperature,  to  pass  through  a  spiral  glass  tube 
placed  in  water.  From  the  increase  in  temperature  of  this  water,  and  from 
the  other  data,  the  specific  heat  was  determined  by  a  calculation  analogous 
to  that  given  under  the  method  of  mixtures.  They  also  determined  the 
specific  heats  of  different  gases  relatively  to  that  of  air,  by  comparing  the 
quantities  of  heat  which  equal  volumes  of  a  given  gas,  and  of  air  at  the  same 
pressure  and  temperature,  imparted  to  equal  weights  of  water.  Subsequently 
to  these  researches,  De  la  Rive  and  Marcet  applied  the  method  of  cooling  to 
the  same  determination  ;  and  more  recently  Regnault  made  a  series  of  in- 
vestigations on  the  calorific  capacities  of  gases  and  vapours,  in  which  he 
adopted,  but  with  material  improvements,  the  method  of  De  la  Roche  and 
Berard.  He  thus  obtained  the  following  results  for  the  specific  heats  of  the 
various  gases  and  vapours,  compared  first  with  an  equal  weight  of  water 


Vapours 


-460]  Specific  Heat  of  Gases.  397 

taken  as  unity  ;  secondly,  with  that  of  an  equal  volume  of  air,  referred,  as 
before,  to  its  own  weight  of  water  taken  as  unity  : — 

Specific  weights 

Equal  Equal 

weights  volumes 

Air 0-2374  0-2374 

(Oxygen 0-2175  0-2405 

Simple        ]  Nitrogen 0-2438  0-2370 

gases        1  Hydrogen 3-4090  0-2359 

I  Chlorine 0-1210  0-2962 

/  Binoxide  of  nitrogen       .         .         .  0-2315  0-2406 

I  Carbonic  oxide        ....  0-2450  0*2370 

Compound      Carbonic  acid          ....  0-2163  0*3307 

gases        ~  Hydrochloric  acid  ....  0-1845  0-2333 

I  Ammonia        .....  0-5083  0*2966 

\Olefiantgas 0-4040  0-4106 

Water 0-4805  0-2984 

Ether 0-4810  1-2296 

Alcohol 0-4534  0-7171 

Turpentine 0-5061  2*3776 

Bisulphide  of  carbon       .         .         .  0-1570  0-4140 

Benzole 0-3754  1-0114 

In  making  these  determinations  the  gases  were  under  a  constant  pressure, 
but  variable  volume ;  that  is,  the  gas  as  it  was  heated  could  expand,  and 
this  is  called  the  specific  heat  under  constant  pressure.  But  if  the  gas  when 
being  heated  is  kept  at  a  constant  volume,  its  pressure  or  elastic  force  then 
necessarily  increasing,  it  has  a  different  capacity  for  heat  ;  this  latter  is 
spoken  of  as  the  specific  heat  under  constant  volume.  That  this  latter  is  less 
than  the  former  is  evident  from  the  following  considerations  : — 

Suppose  a  given  quantity  of  gas  to  have  had  its  temperature  raised  /°, 
while  the  pressure  remained  constant,  this  increase  of  temperature  will  have 
been  accompanied  by  a  certain  increase  in  volume.  Supposing  now  that 
the  gas  is  so  compressed  as  to  restore  it  to  its  original  volume,  the  result  of 
this  compression  will  be  to  raise  its  temperature  again  to  a  certain  extent, 
say  /'°.  The  gas  will  now  be  in  the  same  condition  as  if  it  had  been  heated 
and  not  been  allowed  to  expand.  Hence,  the  same  quantity  of  heat  which 
is  required  to  raise  the  temperature  of  a  given  weight  of  gas,  /°,  while  the 
pressure  remains  constant  and  the  volume  alters,  will  raise  the  temperature 
/  -r  /'  degrees  if  it  is  kept  at  a  constant  volume  but  variable  pressure.  The 
specific  heat,  therefore,  of  a  gas  at  constant  pressure,  c,  is  greater  than  the 
specific  heat  under  constant  volume,  c^  and  they  are  to  each  other  as  /  +  f  :  /, 


It  is  not  possible  to  determine  by  direct  means  the  specific  heat  of  gases 
under  constant  volume  with  much  approach  to  accuracy  ;  and  it  has  always 
been  determined  by  some  indirect  method,  of  which  the  most  accurate  is 
based  on  the  theory  of  the  propagation  of  sound  (229).  A  critical  comparison 
of  the  most  accurate  recent  determinations  gives  the  number  1-405  for  the 

value  of  c . 


398  On  Heat.  [461 

461.  Latent  heat  of  fusion.  —  Black  was  the  first  to  observe  that  during 
the  passage  of  a  body  from  the  solid  to  the  liquid  state,  a  quantity  of  heat 
disappears,  so  far  as  thermometric  effects  are  concerned,  and  which  is  ac- 
cordingly said  to  become  latent. 

In  one  experiment  he  suspended  in  a  room  at  the  temperature  8-5°  two 
thin  glass  flasks,  one  containing  water  at  o°,  and  'the  other  the  same  weight 
of  ice  at  o°.  At  the  end  of  half  an  hour  the  temperature  of  the  water  had 
risen  4°,  that  of  the  ice  being  unchanged,  and  it  was  io£  hours  before  the 
ice  had  melted  and  attained  the  same  temperature.  Now  the  temperature 
of  the  room  remained  constant,  and  it  must  be  concluded  that  both  vessels 
received  the  same  amount  of  heat  in  the  same  time.  Hence  21  times  as 
much  heat  was  required  to  melt  the  ice  and  raise  it  to  4°  as  was  sufficient  to 
raise  the  same  weight  of  water  through  4°.  So  that  the  total  quantity  of 
heat  imparted  to  the  ice  was  21  x4  =  84  ;  and  as  of  this  only  4  was  used 
in  raising  the  temperature,  the  remainder,  80,  was  used  in  simply  melting 
the  ice. 

He  also  determined  the  latent  heat  by  immersing  119  parts  of  ice  at  o° 
in  135  parts  -of  water  at  877°  C.  He  thus  obtained  254  parts  of  water  at 
11-6°  C.  Taking  into  account  the  heat  received  by  the  vessel  in  which  the 
liquid  was  placed,  he  obtained  the  number  79*44  as  the  latent  heat  of  liquidity 
of  ice. 

We  may  thus  say 

Water  at  o°  =  Ice  at  o°  +  latent  heat  of  liquefaction. 

The  method  which  Black  adopted  is  essentially  that  which  is  now  used 
for  the  determination  of  latent  heats  of  liquids  ;  it  consists  in  placing  the 
substance  under  examination  at  a  known  temperature  in  the  water  (or  other 
liquid)  of  a  calorimeter,  the  temperature  of  which  is  sufficient  to  melt  the 
substance  if  it  is  solid,  and  to  solidify  it  if  liquid  ;  and  when  uniformity  of 
temperature  is  established  in  the  calorimeter,  this  temperature  is  determined. 
Thus,  to  take  a  simple  case,  suppose  it  is  required  to  determine  the  latent 
heat  of  the  liquidity  of  ice.  Let  M  be  a  certain  weight  of  ice  at  zero,  and  m 
a  weight  of  water  at  t°  sufficient  to  melt  the  ice.  The  ice  is  immersed  in 
the  water,  and  as  soon  as  it  has  melted  the  final  temperature  6°  is  noted. 
The  water,  in  cooling  from  /°  to  0°,  has  parted  with  a  quantity  of  heat, 
m(t  —  6}.  If  .r  be  the  latent  heat  of  the  ice,  it  absorbs,  in  liquefying,  a  quantity 
of  heat,  MX-  ;  but,  besides  this,  the  water  which  it  forms  has  risen  to  the 
temperature  $°,  and  to  do  so  has  required  a  quantity  of  heat,  represented  by 
M#.  We  thus  get  the  equation 


from  which  the  value  of  x  is  deduced. 

By  this  method  Desains  and  De  la  Provostaye  found  that  the  latent  heat 
of  the  liquefaction  of  ice  is  79*25  ;  that  is,  a  pound  of  ice,  in  liquefying,. 
absorbs  the  quantity  of  heat  which  would  be  necessary  to  raise  79*25  pounds 
of  water  i°,  or,  what  is  the  same  thing,  one  pound  of  water  from  zero  to 
79-25°  (vide  451). 

This  method  is  thus  essentially  that  of  the  method  of  mixtures  ;  the  same 
apparatus  may  be  used,  and  the  same  precautions  are  required,  in  the  two 
cases.  In  determining  the  latent  heat  of  liquidity  of  most  solids,  the  differ- 


461] 


Latent  Heat  of  Fusion. 


399 


ent  specific  heats  of  the  substance  in  the  solid  and  in  the  liquid  state  require 
to  be  taken  into  account.  In  such  a  case,  let  ;;/  be  the  weight  of  the  water 
in  the  calorimeter  (the  water  equivalents  of  the  calorimeter  and  thermometer 
supposed  to  be  included)  ;  M  the  weight  of  the  substance  worked  with  ;  /  the 
original  and  6  the  final  temperature  of  the  calorimeter  ;  T  the  original  tem- 
perature of  the  substance  ;  C  its  melting  (or  freezing)  point  ;  C  the  specific 
heat  of  the  substance  in  the  solid  state  between  the  temperature  C  and  6  ;  c 
its  specific  heat  in  the  liquid  state  between  the  temperatures  T  and  C  ;  and 
let  L  be  the  latent  heat  sought. 

If  the  experiment  be  made  on  a  melted  substance  which  gives  out  heat 
to  the  calorimeter  and  is  thereby  solidified  (it  is  taken  for  granted  that  a 
body  gives  out  as  much  heat  in  solidifying  as  it  absorbs  in  liquefying),  it  is 
plain  that  the  quantity  of  heat  absorbed  by  the  calorimeter,  m(6  -  /),  is  made 
up  of  three  parts  :  first,  the  heat  lost  by  the  substance  in  cooling  from  its 
original  temperature  T  to  the  solidifying  point  C  ;  secondly,  the  heat  given 
out  in  solidification,  L  ;  and,  thirdly,  the  heat  it  loses  in  sinking  from  its 
solidifying  point  C  to  the  temperature  of  the  water  of  the  calorimeter. 


That  is 


whence, 


m(e  - 


L  +  <e  -  0)c] 


The  following  numbers  have  been  obtained  for  the  latent  heats  of  fusion  : — 


Water 

Nitrate  of  Sodium     . 
„         „  Potassium 
Zinc  ... 

Platinum  . 
Silver 
Tin 


79-24  Cadmium 

62-97  Bismuth 

47-37  Sulphur . 

28-13  Lead 

27*18  Phosphorus    . 

2 1  -07  D'Arcet's  alloy 

14-25  Mercury 


13-66 
12-64 
9*37 
5'37 
5-03 
4-50 
2-83 


These  numbers  represent  the  number  of  degrees  through  which  a  pound 
of  water  would  be  raised  by  a  pound  of  the  body  in  question  in  passing 
from  the  liquid  to  the  solid  state  ;  or, 
what  is  the  same  thing,  the  number  of 
pounds  of  water  that  would  be  raised 
i°  C.  by  one  of  the  bodies  in  solidifying. 

On  modern  views  the  heat  ex- 
pended in  melting  is  consumed  in 
moving  the  atoms  into  new  positions  ; 
the  work,  or  its  equivalent  in  heat 
required  for  this,  the  potential  energy 
they  thus  acquire,  is  strictly  compar- 
able to  the  expenditure  of  work  in  the 
process  of  raising  a  weight.  When 
the  liquid  solidifies,  it  reproduces  the 
heat  which  had  been  expended  in 
liquefying  the  solid  ;  just  as  when  a 


Fig.  368. 


stone  falls  it  produces  by  its  impact  against  the  ground  the  heat,  the  equiva- 


400  On  Heat.  [461- 

lent  of  which  in  work  had  been  expended  in  raising  it,  and  a  similar 
explanation  applies  to  the  latent  heat  of  gasification. 

462.  Determination  of  the  latent  heat  of  vapours.  —  Liquids,  as  we 
have  seen,  in  passing  into  the  state  of  vapour,  absorb  a  very  considerable 
quantity  of  heat,  which  is  termed  latent  heat  of  'vaporisation.  In  deter- 
mining the  heat  absorbed  in  liquids,  it  is  assumed  that  a  vapour,  in  liquefy- 
ing, gives  out  as  much  heat  as  it  had  absorbed  in  becoming  converted  into 
vapour. 

The  method  employed  is  essentially  the  same  as  that  for  determining 
the  specific  heat  of  gases.  Fig.  368  represents  the  apparatus  used  by 
Despretz.  The  vapour  is  produced  in  a  retort,  C,  where  its  temperature  is  in- 
dicated by  a  thermometer.  It  passes  into  a  worm  SS  immersed  in  cold  water, 
where  it  condenses,  imparting  its  latent  heat  to  the  condensing  water  in  the 
vessel  B.  The  condensed  vapour  is  collected  in  a  vessel,  A,  and  its  weight 
represents  the  quantity  of  vapour  which  has  passed  through  the  worm.  The 
thermometers  in  B  give  the  change  of  temperature. 

Let  M  be  the  weight  of  the  condensed  vapour,  T  its  temperature  on 
entering  the  worm,  which  is  that  of  its  boiling  point,  and  x  the  latent  heat  of 
vaporisation.  Similarly,  let  m  be  the  weight  of  the  condensing  water  (com- 
prising the  weight  of  the  vessel  B  and  of  the  worm  SS  reduced  \n  water),  let 
t°  be  the  temperature  of  the  water  at  the  beginning,  and  6°  its  temperature 
at  the  end  of  the  experiment. 

It  is  to  be  observed  that,  at  the  commencement  of  the  experiment,  the 
condensed  vapour  passes  out  at  the  temperature  /°,  while  at  the  conclusion 
its  temperature  is  6°  •  we  may,  however,  assume  that  its  mean  temperature 

during  the  experiment  is  (   +    '.     The  vapour  M   after   condensation   has 

therefore  parted  with  a  quantity  of  heat  M  (T  —  —  +    W  while   the   heat 

disengaged  in  liquefaction  is  represented  by  M.r.  The  quantity  of  heat 
absorbed  by  the  cold  water,  the  worm,  and  the  vessel,  is  m(B-t\  Therefore, 


from  which  x  is  obtained.  Despretz  found  that  the  latent  heat  of  aqueous 
vapour  at  100°  is  540  ;  that  is,  a  pound  of  water  at  100°  absorbs  in  vaporising 
as  much  heat  as  would  raise  540  pounds  of  water  through  i°.  Regnault 
found  the  number  537,  and  Favre  and  Silbermann  538-8. 

As  in  the  case  of  the  latent  heat  of  water  we  may  say, 

Steam  at  ioo°  =  Water  at  ioo°  +  latent  heat  of  gasification. 

In  the  conversion  of  a  body  from  the  liquid  into  the  gaseous  state,  as  in 
the  analogous  process  of  fusion,  one  part  of  the  heat  is  used  in  increasing 
the  temperature  and  another  in  internal  work.  For  vaporisation,  the 
greater  portion  is  consumed  in  the  internal  work  of  overcoming  the 
reciprocal  attraction  of  the  particles  of  liquid,  and  in  removing  them  to 
the  far  greater  distances  apart  in  which  they  exist  in  the  gaseous  state.  In 
addition  to  this  there  is  the  external  work—  namely,  that  required  to  over- 
come the  external  pressure,  usually  that  of  the  atmosphere  :  and  as  the  in- 
crease of  volume  in  vaporisation  is  considerable,  this  pressure  has  to  be 


-463] 


Favre  and  Silbermanrts  Calorimeter. 


401 


raised  through  a  greater  space.  Vaporisation  may  take  place  without 
having  external  work  to  perform,  as  when  it  is  effected  in  vacuo ;  but 
whether  the  evaporation  is  under  a  high  or  under  a  low  pressure,  on  the 
surface  of  a  liquid  or  in  the  interior,  there  is  always  a  great  consumption  of 
heat  in  internal  work. 

463.  Pavre  and  Silbermann's  Calorimeter. — The  apparatus  (fig.  369) 
furnishes  a  very  delicate  means  of  determining  the  calorific  capacity  of 
liquids,  latent  heats  of  evaporation,  and  the  heat  disengaged  in  chemical 
actions. 

The  principal  part  is  a  spherical  iron  reservoir,  A,  full  of  mercury,  of 
which  it  holds  about  50  pounds,  and  represents,  therefore,  a  volume  of  more 


Fig.  369- 

than  half  a  gallon.  On  the  left  there  are  two  tubulures,  B,  in  which  are 
fitted  two  sheet-iron  tubes  or  muffles,  projecting  into  the  interior  of  the  bulb. 
Each  can  be  fitted  with  a  glass  tube  for  containing  the  substance  experi- 
mented upon.  In  most  cases  one  muffle  and  one  glass  tube  are  enough  ; 
the  two  are  used  when  it  is  desired  to  compare  the  quantities  of  heat  pro- 
duced in  two  different  operations.  In  a  third  vertical  tubulure,  C,  there  is 
also  a  muffle,  which  can  be  used  for  determining  calorific  capacities  by 
Regnault's  method  (455),  in  which  case  it  is  placed  beneath  the  r  of  fig.  366. 
The  tubulure  d  contains  a  steel  piston  ;  a  rod,  turned  by  a  handle,  tn, 
and  which  is  provided  with  a  screw  thread,  transmits  a  vertical  motion  to 


402  On  Heat.  [463- 

the  piston  ;  but,  by  a  peculiar  mechanism,  gives  it  no  rotatory  motion.     In 
the  last  tubulure  is  a  glass  bulb,  a,  in  which  is  a  long  capillary  glass  tube,  bo, 
divided  into  parts  of  equal  capacity. 

It  will  be  seen  from  this  description  that   the  mercury  calorimeter  is 
essentially  a  thermometer  with  a  very  large  bulb  and  a  capillary  stem  :  it 
is  therefore  extremely  delicate.     It  differs,  however,  from  a  thermometer  in 
the  fact  that  the  divisions  do  not  indicate  the  temperature  of  the  mercury 
in  the  bulb,  but  the  number  of  thermal  units  imparted  to  it  by  the  substances 
placed  in  the  muffle. 

This   graduation   is   effected   as  follows  : — By  working  the  piston   the 
mercury  can  be  made  to  stop  at  any  point  of  the  tube,  bo,  at  which  it  is 
desired  the  graduation  should  commence.     Having  then  placed  in  the  iron 
tube  a  small  quantity  of  mercury,  which  is  not  afterwards  changed,  a  thin 

glass  tube,  *,  is  inserted, 
which  is  kept  fixed  against 
the  buoyancy  of  the  mer- 
cury by  a   small   wedge 
'%......-.,  ;//  not   represented    in    the 

figure.  The  tube  being 
thus  adjusted,  the  point 
of  a  bulb  tube  (see  fig. 
370)  is  introduced  con- 
taining water,  which  is 
raised  to  the  boiling 
point  :  turning  the  posi- 
tion of  the  pipette,  then, 
as  represented  in  n',  a 
quantity  of  the  liquid  flows 
into  the  test  tube. 

The  heat  which  is  thus 


Fig.  370. 


imparted  to  the  mercury  makes  it  expand  ;  the  column  of  mercury  in  bo  is 
lengthened  by  a  number  of  divisions,  which  we  shall  call  «.  If  the  water 
poured  into  the  test  glass  be  weighed,  and  if  its  temperature  be  taken  when 
the  column  bo  is  stationary,  the  product  of  the  weight  of  the  water  into  the 
number  of  degrees  through  which  it  has  fallen  indicates  the  number  of 
thermal  units  which  the  water  gives  up  to  the  entire  apparatus  (447). 
Dividing,  by  »,  this  number  of  thermal  units,  the  quotient  gives  the 
number,  a,  of  thermal  units  corresponding  to  a  single  division  of  the 
tube  bo. 

In  determining  the  specific  heat  of  liquids,  a  given  weight,  M,  of  the 
liquid  in  question  is  raised  to  the  temperature  T,  and  is  poured  into  the  tube 
C.  Calling  the  specific  heat  of  the  liquid  <:,  its  final  temperature  6,  and  n 
the  number  of  divisions  by  which  the  mercurial  column  bo  has  advanced, 
we  have 

M<r(T  -  &}  =  na,  from  which  c  = na 

M(T  -6) 

The  boards  represented  round  the  apparatus  are  hinged  so  as  to  form 
a  box,  which  is  lined  with  eiderdown  or  wadding  to  prevent  any  loss  of  heat. 
It  is  closed  at  the  top  by  a  board,  which  is  provided  with  a  suitable  case, 


-464]  Examples.  403 

also  lined,  which  fits  over  the  tubulures  d  and  a.     A  small  magnifying  glass 
which  slides  along  the  latter  enables  the  divisions  on  the  scale  to  be  read  off. 

464.  Examples. — I.  What  weight  of  ice  at  zero  must  be  mixed  with  9 
pounds  of  water  at  20°  in  order  to  cool  it  to  5°  ? 

Let  M  be  the  weight  of  ice  necessary  ;  in  passing  from  the  state  of  ice 
to  that  of  water  at  zero,  it  will  absorb  8oM  thermal  units  ;  and  in  order  to 
raise  it  from  zero  to  5°,  5>1  thermal  units  will  be  needed.  Hence  the  total 
heat  which  it  absorbs  is  8oM  +  5M  =  85M.  On  the  other  hand,  the  heat 
given  up  by  the  water  in  cooling  from  20°  to  5°  is  9  x  (20—5)  =  135.  Con- 
sequently, 

85 M  -  135  ;  from  which  M  =  1-588  pounds. 

II.  What  weight  of  steam  at  100°  is  necessary  to  raise  the  temperature 
of  208  pounds  of  water  from  14°  to  32°  ? 

Let  p  be  the  weight  of  the  steam.  The  latent  heat  of  steam  is  540°,  and 
consequently^  pounds  of  steam  in  condensing  into  water  give  up  a  quantity 
of  heat,  540^,  and  form  p  pounds  of  water  at  100°.  But  the  temperature 
of  the  mixture  is  32°,  and  therefore  p  gives  up  a  further  quantity  of  heat 
p(\oo  —  32)  =  68/,  for  in  this  case  c  is  unity.  The  208  pounds  of  water  in 
being  heated  from  14°  to  32°  absorb  208(32  -  14)  =  3744  units.  Therefore 

+  68/fr  -  3744  ',  from  which  p  =  6'i  58  pounds. 


404 


On  Heat. 


[465- 


CHAPTER   X. 

STEAM   ENGINES. 

465.  Steam  engines. — Steam  engines  are  machines  in  which  the  elastic 
force  of  aqueous  vapour  is  used  as  the  motive  power.     In  the  ordinary  engines 
the  alternate  expansion  and  condensation  of  steam  imparts  to  a  piston  ah 
alternating  rectilinear  motion,  which  is  changed  into   a  circular  motion  by 
means  of  various  mechanical  arrangements. 

Every  steam  engine  consists  essentially  of  two  distinct  parts  :  the  ap- 
paratus in  which  the  steam  is  produced,  and  the  engine  proper.  We  shall 
first  describe  the  former. 

466.  Steam  boiler. — The  boiler  is  the  apparatus  in  which  steam  is  gene- 
rated.    Fig.  371   represents  a  side  view,  and  fig.  372  a  cross  section  of  a 


Fig.  371. 

cylindrical  boiler,  such  as  are  used  for  fixed  engines  ;  those  of  locomotives 
and  of  steam  vessels  are  very  different. 


-466] 


Steam  Boiler. 


405 


It  is  a  long  wrought-iron  cylinder,  PQ,  with  curved  ends,  beneath  which 
there  are  two  smaller  cylinders,  BB,  of  the  same  material,  and  communicating 
with  the  boiler  by  two  tubes.  Only  one  of  these  cylinders  is  represented  in 
fig.  371.  They  are  called  heaters,  and  are  quite  full  of  water,  while  the 
boiler  is  only  about  half  full. 

In  order  to  multiply  the  heating  surface,  and  utilise  all  the  heat  carried 
off  by  the  products  of  combustion,  the  latter  are  made  to  circulate  through 
brick  conduits  which  surround  the  sides  of  the  heaters  and  of  the  boiler. 
These  conduits,  which  are  called  flues,  divide  the  furnace.into  two  horizontal 
compartments,  FF  and  DCD  (fig.  372).  The  upper  compartment  is  more- 
over divided  into  three  distinct  flues,  D,  C,  D,  by  two  vertical  divisions 
which  are  not  represented  in  the  drawing,  and  which  correspond  to  the  two 
sides  of  the  boiler.  The  flame  and  the  products  of  combustion,  which  first 
sweep  below  the  heaters  from  back  to  front,  return  in  the  opposite  direction 
by  the  central  flue  C  ;  then,  dividing,  they  pass  by  the  lateral  flues  into  the 
chimney  K,  where  they  are  lost  in  the  atmosphere. 

Explanation  of  Figitres  37 1  and  372. 

E.  Float  of  the  safety  whistle,  s. 
FF.  Furnace. 

F'.  Float,  to  show  the  level  of  the  water  in  the  boiler.  It  consists  of  a 
rectangular  piece  of  stone  partially  immersed  in  water,  as  seen  through  the 
space  which  is  represented  as  left  open. 
This  stone,  which  is  suspended  at  one 
end  of  a  lever,  is  kept  poised  by  the  loss  •»* 
of  weight  which  it  sustains  by  immersion 
in  the  water,  and  by  a  weight,  a,  at  the 
other  end  of  the  lever.  As  long  as  the 
water  is  at  the  desired  height,  the  lever 
which  sustains  the  float  remains  horizontal ; 
but  it  sinks  when  there  is  too  little  water, 
and  rises  in  the  contrary  direction  when 
there  is  too  much.  Guided  by  these  in- 
dications, the  stoker  can  regulate  the 
supply  of  water. 

K.  Chimney,  which  has  usually  a  great 
height,  so  as  to  increase  the  draught. 

S.  Safety  valve  described  under  Papin's 
digester  (373). 

T.  Man-hole,  an  aperture  by  which  -&*« 
the  boiler  can  be  repaired  and  cleansed. 
This  is  self-closing,  and  consists  of  a  cover 
fitting  against  the  inside  edges.  It  is  kept  in  position  by  a  screw,  which  also 
presses  it  strongly  against  the  sides.  Thus  the  greater  the  internal  pressure, 
the  more  firmly  is  the  cover  pressed  against  the  sides,  and  the  more  com- 
pletely does  it  close,  a.  Counterpoise  of  the  float. 

m.  Tube  which  leads  the  steam  to  the  tube  c  of  the  valve  chest  (fig.  372) 

n.  Tube  for  the  admission  of  feed  water  for  the  boiler. 


Fig.  372- 


406 


On  Heat. 


[466- 


s.  Safety  whistle — so  called  because  it  gives  a  whistle  when  there  is  not 
enough  water  in  the  boiler — a  circumstance  which  might  produce  an  accident. 
As  long  as  the  level  of  the  water  is  not  too  low  in  the  boiler,  the  steam  does 
not  pass  into  the  whistle  ;  but  if  the  level  sinks  below  a  certain  point,  a  small 
float,  E,  which  closes  the  bottom  of  the  whistle  sinks,  and  the  steam  escapes  ; 
in  so  doing  it  grazes  against  the  edge  of  a  thin  metal  plate,  which  it  sets  in 
vibration,  and  produces  a  sharp  and  loud  sound.  This  steam  whistle  is 
the  sound  frequently  heard  upon  railways  ;  it  is  used  as  a  signal  in  locomo- 
tives. 


467.  Double  action  or  Watt's  engine. — In  the  double-acting  steam  en- 
gine, the  steam  acts  alternately  above  and  below  the  piston.  It  is  also  known 
as  Watfs  engine,  from  its  illustrious  inventor. 

We  shall  first  give  a  general  idea  of  this  engine,  and  shall  then  describe 
each  part  separately.  On  the  left  of  the  fig.  373,  is  the  cylinder  which  receives 
the  steam  from  the  boiler.  A  part  of  its  side  is  represented  as  being  left 
open,  and  a  piston,  P,  can  be  seen,  which  is  moved  alternately  up  and  down 
by  the  pressure  of  the  steam  above  or  below  the  piston.  By  the  piston  rod 
A  this  motion  is  transmitted  to  a  huge  iron  lever,  L,  called  the  beam,  which 
is  supported  by  four  iron  columns.  The  beam  transmits  its  motion  to  a 


-467]  Double  Action  or  Watt's  Engine.  407 

connecting  rod,  I,  working  on  a  crank,  K,  to  which  it  imparts  a  continuous 
rotatory  motion.  The  crank  is  fixed  to  a  horizontal  shaft,  which  turns  with 
it,  and,  by  means  of  wheels  or  endless  bands,  this  shaft  sets  in  motion  various 
machines,  such  as  spinning  frames,  saw  mills,  lathes,  &c. 

On  the  left  of  the  cylinder  is  a  valve  chest,  where,  by  a  mechanism  which 
will  presently  be  described,  the  steam  passes  alternately  above  and  below 
the  piston.  Now,  after  its  action  on  either  face  of  the  piston,  it  must  dis- 
appear, for  otherwise  a  pressure  would  be  exerted  in  two  opposite  directions 
and  the  piston  would  remain  at  rest.  To  effect  this  the  steam,  after  it  has 
acted  on  one  side  of  the  piston,  passes  into  a  vessel,  O,  called  the  condenser, 
into  which  cold  water  is  injected.  It  is  almost  completely  condensed  there, 
and  consequently  the  pressure  ceases  in  that  part  of  the  cylinder  which  is 
in  communication  with  the  condenser,  and  as  there  is  now  pressure  on  only 
one  face  of  the  piston,  it  either  rises  or  sinks. 

The  use  of  the  condenser  depends  upon  Watt's  law  of  vapours  (360), 
that  when  two  vessels  communicating  with  each  other,  and  containing 
saturated  vapour,  are  at  different  temperatures,  the  tension  is  the  same 
in  both  vessels,  and  is  that  corresponding  to  the  temperature  of  the  colder 
vessel. 

The  injected  water  is  rapidly  heated  by  the  condensation  of  the  steam, 
and  must  be  constantly  renewed.  This  is  effected  by  means  of  two  pumps ; 
one  M,  is  called  the  air  pump,  and  draws,  from  the  condenser,  the  heated 
water  which  it  contains,  and  also  the  air  which  was  dissolved  in  the  water  of 
the  boiler,  and  which  passes  with  the  steam  into  the  cylinder  and  condenser ; 
the  other,  R,  is  called  the  cold  -water pump,  and  forces  cold  water  from  a 
well,  or  from  a  river,  into  the  condenser. 

A  third  pump,  Q,  which  is  called  \hzfeed  pump,  utilises  the  heated  water 
by  forcing  it  from  the  condenser  into  the  boiler. 

Double-acting  Steam  Engine. 

A.  Piston  rod  connected  with  a  parallel  motion,  and  serving  to  transmit 
to  the  beam  the  upward  and  downward  motion  of  the  piston. 

B.  Rod  fixed  to  the  cylinder,  or  elsewhere,  and  supporting  the  guiding 
arm  or  radius  rod,  C. 

DDDE.  Rods  forming  at  the  end  of  the  beam  a  parallel  motion,  to  which 
is  fixed  the  piston  rod,  and  the  object  of  which  is  to  guide  the  motion  of  this 
rod  in  a  straight  line.  F.  Rod  of  the  air  pump,  which  removes  from  the 
condenser  the  air  and  heated  water  which  it  contains. 

G.  Rod  of  the  feed  pump,  which  forces  into  the  boiler  through  the  tube  S 
the  heated  water  pumped  from  the  condenser.  H.  Rod  of  the  cold  water 
pump,  which  supplies  the  cold  water  necessary  for  condensation. 

I.  Connecting  rod,  which  transmits  the  motion  of  the  beam  to  the  crank. 

K.   Crank,  which  imparts  the  motion  of  the  rod  to  the  horizontal  shaft. 

L.  Beam,  which  moves  on  an  axle  in  its  middle,  and  transmits  the  motion 
of  the  piston  to  the  connecting  rod  I.  M.  Cylinder  of  the  air  pump,  in 
connection  with  the  condenser  O.  N.  Reservoir  for  the  hot  water  pumped 
by  the  air  pump  from  the  condenser.  O.  Condenser  into  which  cold  water 
is  injected  to  condense  the  steam  after  it  has  acted  on  the  piston. 


408 


On  Heat. 


[467- 


P.  Metal  piston,  moving  in  a  cast-iron  cylinder ;  this  piston  receives 
the  direct  pressure  of  the  steam,  and  transmits  the  motion  to  all  parts  of  the 
machine.  Q.  Feeding  force  pump,  which  sends  the  water  into  the  boiler. 
R.  Cold  water  pump.  S.  Pipe  by  which  the  hot  water  from  the  feed  pump 
passes  into  the  boiler.  T.  Pipe  by  which  cold  water  from  the  reservoir  of 
the  pump,  R,  passes  into  the  condenser.  U.  Pipe  by  which  the  steam  from 
the  cylinder  passes  into  the  condenser  after  acting  on  the  piston. 

V.  Large  iron  wheel,  called  the_/?y  wheel,  which,  by  its  inertia,  serves  to 
regulate  the  motion,  especially  when  the  piston  is  at  the  top  or  bottom  of  its 
course,  and  the  crank  K  at  its  dead  points.  Y.  Bent  lever  which  imparts  the 
motion  of  the  eccentric  e  to  the  slide  valve  b.  Z.  Eccentric  rod. 

a.  Aperture  which  communicates  both  with  the  upper  and  lower  part  of 
the  cylinder,  according  to  the  position  of  the  slide  valve,  and  by  which  steam 
passes  into  the  condenser  through  the  tube  U.  b.  Rod  transmitting  the 
motion  of  the  slide  'valve,  by  which  steam  is  alternately  admitted  above 
and  below  the  piston,  c.  Aperture  by  which  steam  reaches  the  valve  chest. 
d.  Stuffing  box,  in  which  the  piston  rod  works  without  giving  exit  to  the 
steam,  e.  Eccentric,  fixed  to  the  horizontal  shaft,  and  rotating  in  a  collar, 
to  which  the  rod  Z  is  attached,  m.  Rod  which  connects  the  rod  of  the  slide 
valve  b  to  the  bent  lever  Y,  and  to  the  eccentric. 

The  lower  part  of  the  figure  does  not  exactly  represent  the  usual  arrange- 
ment of  the  pumps.  The  drawing  has  been  modified  in  order  more  clearly 
to  show  how  these  parts  work,  and  their  connection  with  each  other. 


374- 


468.  Distribution  of  the  steam.     Eccentric.—  Fig.  374  represents  the 
details  of  the  valve  chest  or  arrangement  for  the  distribution  of  steam.     The 


-469]  Single-acting  Engine.  409 

steam  from  the  boiler  passes  by  a  pipe,  c,  into  a  cast-iron  box  on  the  side  of 
the  cylinder.  In  the  sides  of  the  cylinder  there  are  three  openings  or  ports 
u,  n,  and  a,  of  which  u  communicates  by  an  internal  conduit  with  the  upper 
part  of  the  cylinder,  and  n  with  the  lower  part.  A  slide,  /,  works  over  these 
three  orifices.  It  is  fixed  to  a  vertical  rod,  £,  which  is  jointed  at ;;/  to  a  larger 
rod,  d,  and  receives  an  upward  and  downward  motion  from  the  bent  lever 
yoS,  attached  to  the  eccentric  rod.  When  the  slide  is  at  the  top  of  its  course, 
as  shown  in  the  figune,  the  steam  passes  through  n  into  the  lower  part  of  the 
cylinder,  while  the  steam  cannot  pass  through  the  orifice  u,  for  it  is  covered 
by  the  slide.  But  the  steam  which  is  above  the  piston  passes  through  u  and 
through  a  into  the  hole  r,  from  which  it  enters  the  condenser.  The  piston 
is  then  only  pressed  upwards,  and  therefore  ascends.  When  the  slide  is  at 
the  bottom  of  its  course,  the  steam  enters  the  cylinder  by  the  aperture  u,  and 
passes  from  the  lower  part  of  the  cylinder  into  the  condenser  by  n  and  a. 
The  piston  consequently  descends,  and  this  motion  goes  on  for  each  dis- 
placement of  the  slide. 

The  upward  and  downward  motion  of  the  slide  is  effected  by  means  of 
the  eccentric.  This  is  a  circular  piece,  E,  fixed  to  the  horizontal  shaft,  A,  but 
in  such  a  manner  that  its  centre  does  not  coincide  with  the  axis  of  this  shaft. 
The  eccentric  works  with  gentle  friction  in  a  collar,  C,  to  which  the  rod  ZZ 
is  fixed.  The  collar,  without  rotating,  follows  the  motion  of  the  eccentric, 
and  receives  an  alternating  motion  in  a  horizontal  direction,  which  it  com- 
municates to  the  lever  S0y,  and  from  thence  to  the  slide. 

469.  Single-acting  engine. — In  a  single-acting  engine  the  steam  only 
acts  on  the  upper  face  of  the  piston  ;  a  counterpoise  fixed  to  the  other  end 
of  the  beam  makes  the  piston  rise.  These  engines  were  first  constructed  by 
Watt  for  pumping  water  from  mines,  and  are  still  used  for  this  purpose  in 
Cornwall,  and  also  for  the  supply  of  water  to  towns.  They  are  preferred  for 
these  purposes  from  their  simplicity,  but  for  other  applications  they  have 
been  superseded  by  the  double-acting  engine. 

Fig.  375  represents  a  section.  The  beam  B  B  is  of  wood,  with  wooden 
segments  at  each  end,  to  which  chains  are  attached.  One  of  these  chains  is 
connected  with  the  piston  P,  and  the  other  with  the  pump  Q.  On  the  right 
of  the  cylinder  A  is  a  valve  chest,  C,  into  which  steam  passes  from  the  boiler 
by  the  tube  T.  There  are  three  valves,  m,  n,  and  o,  on  a  vertical  rod.  The 
valves  m  and  o  open  upwards,  the  valve  n  downwards. 

When  m  and  o  are  open,  as  shown  in  the  drawing,  the  steam  passes 
through  the  tube  T,  over  the  piston,  while  the  steam  which  is  below  is  forced 
into  the  condenser  through  the  tube  M.  The  piston  therefore  descends. 
The  rod,  on  which  are  the  valves  m,  n,  and  o,  is  connected  with  a  bent  lever, 
dck,  moving  on  a  joint  c.  This  bent  lever  closes  and  opens  the  valves.  For 
this  purpose  there  are  two  catches,  b  and  a,  on  a  rod,  F,  connected  with  the 
beam,  by  means  of  which  the  rod  works  against  the  end  of  the  bent  lever. 
From  the  arrangement  of  the  valves,  as  represented  in  the  drawing,  the  piston 
sinks  and  carries  with  it  the  rod  F,  and,  consequently,  the  catch  strikes 
against  the  lever,  and  makes  it  sink  at  the  same  time  as  the  rod  dmo  ;  the 
valves  m  and  o  then  close,  while  n  opens. 

The  communication  with  the  boiler  as  well  as  with  the  condenser  is  now 
cut  off,  and  the  steam  which  has  made  the  piston  sink,  passes  below  by  the 

T 


4io 


On  Heat. 


[469- 


pipe  C.  As  it  presses  equally  on  both  faces,  the  piston  would  remain  at 
rest,  but  it  rises  in  consequence  of  the  traction  of  the  weight  Q.  Very  little 
force  is  necessary  for  this  ;  for  the  pump,  the  rod  of  which  is  fixed  to  the 
weight  Q,  only  requires  power  when  its  piston  rises.  When  the  piston  P  is 
at  the  top  of  its  course,  the  catch  a  strikes  in  turn  against  the  lever  k,  raises 
the  rod  dmo,  the  steam  again  passes  to  the  top  of  the  piston,  which  again 
descends,  and  so  on. 

470.    locomotives. — Locomotive    engines,   or    simply   locomotives,   are 
steam-engines  which,  mounted  on  a  carriage,  propel  themselves  by  trans- 


Fig-  375- 

mitting  their  motion  to  wheels.  The  principal  parts  are  \heframework,  the 
fire  box,  \htcasing  of  the  boiler,  the  smoke  box,  the  steam  cylinders,  the  driving 
wheels,  and  \^&  feed  pump. 

The  framework  is  of  oak,  and  rests  on  the  axles  of  the  wheels.  Fig.  376 
represents  the  driver  of  the  locomotive  in  the  act  of  opening  the  regulator 
valve  I,  placed  in  the  upper  part  of  the  steam  dome.  In  the  lower  part  of 
this  is  the  fire  box,  from  whence  the  flame  and  the  products  of  combustion 
pass  into  the  smoke  box,  Y,  and  then  into  the  chimney  Q,  after  having  pre- 
viously traversed  i2$brassjire  tubes  which  pass  through  the  boiler.  The 
boiler,  which  connects  the  fire  box  with  the  smoke  box,  is  made  of  iron,  and 
is  cylindrical.  It  is  cased  with  staves  of  mahogany,  which,  being  a  bad  con- 
ductor, prevents  its  cooling  too  rapidly.  The  steam  passes  from  the  boiler 


-470]  Locomotives.  4 1 1 

into  two  cylinders,  placed  on  either  side  of  the  smoke  box.  There,  by 
means  of  a  steam  chest  similar  to  that  already  described,  it  acts  alternately 
on  the  two  faces  of  the  piston,  the  motion  of  which  is  transmitted  to  the 


axle  of  the  large  driving  wheels.  This  arrangement  of  the  slide  valve  is  not 
seen  in  the  drawing,  because  it  is  placed  under  the  frame  between  the  two 
cylinders.  After  having  acted  on  the  pistons,  the  steam  is  forced  through 
the  blast  pipe  E  into  the  chimney,  thus  increasing  the  draught. 


T  2 


4I2  On  Heat.  [470- 

The  motion  of  the  pistons  is  transmitted  to  the  two  large  driving  wheels 
by  two  connecting  rods,  which,  by  means  of  cranks,  connect  the  piston 
rods  with  the  axles  of  the  wheels.  The  alternating  motion  of  the  slide 
valve  is  effected  by  means  of  eccentrics  placed  on  the  axles  of  the  large 
wheels.  The  feeding  or  supply  of  water  to  the  boiler  is  obtained  by  means 
of  two  pumps,  placed  under  the  frame,  and  moved  by  eccentrics.  These 
pumps  suck  the  water  from  a  reservoir  placed  on  the  tender,  which  is  a 
carriage  attached  to  the  locomotive  for  carrying  the  necessary  water  and 
coal. 

Explariation  of  Figure  376. 

A.  Copper  tube,  into  which  steam  passes  by  the  extremity  I,  and  which, 
dividing  at  the  other  end  into  two  branches,  conveys  the  steam  to  the  two 
cylinders  which  contain  the  pistons.  B.  Handle  of  the  lever  by  which  the 
motion  is  reversed.  It  imparts  motion  to  a  rod,  C,  which  communicates 
with  the  steam  chest.  C.  Rod  by  which  the  motion  is  reversed.  D.  Lower 
part  of  the  fire  box  and  ash  pan.  E.  Escape  pipe  for  the  steam  after  acting 
on  the  pistons.  F.  Iron  cylinder  containing  a  piston,  P.  There  is  one  of 
these  on  each  side  of  the  engine,  and  the  one  in  front  is  represented  as  being 
left  open  in  order  that  the  piston  may  be  seen. 

G.  Rod  which  opens  the  regulator  valve  I,  in  order  to  allow  the  steam  to 
pass  into  the  tube  A.  In  the  drawing  the  driver  holds  in  his  hand  the  lever 
which  moves  this  rod.  H.  Cock  for  blowing  off  water  from  the  boiler. 

I.  Regulator  valve,  which  is  opened  and  closed  by  hand,  so  as  to  regulate 
the  quantity  of  steam  passing  into  the  cylinders. 

K.  Large  rod  connecting  the  head  of  the  piston  rod  with  the  crank  M  of 
the  driving  wheel.  L.  Lamp.  M.  Crank,  which  transmits  the  motion  of 
the  piston  to  the  axle  of  the  large  wheel.  N.  Coupling  iron,  by  which  the 
tender  is  attached.  O.  Fire  door.  P.  Metallic  piston,  the  rod  of  which  is 
connected  with  the  rod  K.  Q.  Chimney.  R,  R.  Feed  pipes,  through  which 
the  water  in  the  tender  passes  to  two  force  pumps,  which  are  not  shown  in 
the  drawing.  S.  Guard  for  removing  obstructions  on  the  rails.  T,  T. 
Springs  on  which  the  engine  rests.  U,  U.  Iron  rails  fixed  in  chairs  on  wooden 
sleepers.  V.  Frame  of  the  stuffing  box  of  the  cylinder.  X,  X.  Cylindrical 
boiler,  covered  with  mahogany  staves,  which,  from  their  bad  conductivity, 
hinder  the  loss  of  heat.  The  level  of  the  water  is  just  below  the  tube  A. 
In  the  water  are  the  tubes  #,  through  which  the  smoke  and  flames  pass 
into  the  smoke  box.  Y.  Smoke  box  in  which  the  fire  tubes  a  terminate. 
Z,  Z.  Fire  box,  with  dome,  into  which  the  steam  passes. 

a.  Brass  tubes,  of  which  there  are  125,  open  at  both  ends,  and  terminating 
at  one  end  in  the  fire  box,  and  at  the  other  in  the  smoke  box.  .  These  tubes 
transmit  to  the  water  the  heat  of  the  fire. 

bb.  Toothed  segment,  placed  on  the  side  of  the  fire  box,  and  in  which 
the  arm  of  the  lever  B  works.  When  the  handle  is  pushed  forward  or  pulled 
back  as  far  as  it  can  go,  the  engine  is  in  full  forward  or  backward  gear  re- 
spectively ;  the  intermediate  teeth  give  various  rates  of  expansion  in  back- 
ward and  forward  motion,  the  middle  tooth  being  a  dead  point,  e.  Cases 
containing  springs  by  which  the  safety  valves  i  are  regulated,  g.  Signal 
whistle,  i.  Safety  valves,  m,  m.  Steps,  n.  Glass  tube,  showing  the  height 


-472] 


Reaction  Mac/lines.     Eolipyle. 


413 


of  water  in  the  boiler.  ?,  r.  Guiding  rods,  for  keeping  the  motion  of  the 
pistons  in  a  straight  line.  /,  /.  Blowing-off  taps,  for  use  when  the  pistons 
are  in  motion.  i>.  Rod  by  which  motion  is  transmitted  to  these  taps. 

471.  Reaction  machines.  Eolipyle. — In  reaction  machines  steam  acts 
by  a  reactive  force  like  water  in  a  hydraulic  tourniquet  (217).  The  idea  of 
these  machines  is  by  no  means  new  ;  Hero  of  Alexandria,  who  invented  the 
fountain  which  bears  his  name,  described  the  apparatus  which  is  represented 
in  fig.  377,  known  as  the  reaction  machine. 

It  consists  of  a  hollow  metal  sphere  which  rotates  on  two  pivots.  At 
the  ends  of  a  diameter  are  two  tubulures,  pierced  laterally  in  opposite 
directions  by  ori- 
fices through  which 
vapour  escapes. 
Water  is  introduced 
into  this  apparatus 
by  heating  it,  and 
then  allowing  it  to 
cool  in  cold  water. 
If  the  apparatus  be 
then  heated  to  boil- 
ing, the  vapour  dis- 
engaged imparts  to 
it  a  rotatory  motion, 
which  is  due  to  the 
pressure  of  the  va- 
pour on  the  side 
opposite  to  that 
from  which  it  es- 


Fig.  377- 

ISumerous  at- 
tempts have  been  made  to  use  this  reactive  force  of  the  vapour  on  a  large 
scale  as  a  motive  force,  and  endeavours  have  also  been  made  to  cause 
steam  to  act  by  impulse  by  directing  a  jet  of  steam  on  the  float  board  of 
a  paddle-wheel ;  but  in  both  cases  the  steam  exerts  by  no  means  so  great 
an  effect  as  is  obtained  when  it  acts  by  expansion  on  a  piston. 

472.  Various  kinds  of  steam  engines. — A  low-pressure  engine  is  one  in 
which  the  pressure  of  the  vapour  does  not  much  exceed  an  atmosphere ;  and 
a  high-pressure  engine  is  one  in  which  the  pressure  of  the  steam  usually 
exceeds  this  amount  considerably.  Low-pressure  engines  .  are  mostly  con- 
densing engines ;  in  other  words,  they  generally  have  a  condenser  where  the 
steam  becomes  condensed  after  having  acted  on  the  piston  ;  on  the  other 
hand,  high-pressure  engines  are  frequently  without  a  condenser ;  the  loco- 
motive is  an  example. 

If  the  communication  between  the  cylinder  and  boiler  remains  open 
during  the  whole  motion  of  the  piston,  the  steam  retains  essentially  the  same 
elastic  force,  and  is  said  to  act  without  expansion  ;  but  if,  by  a  suitable 
arrangement  of  the  slide  valve,  the  steam  ceases  to  pass  into  the  cylinder 
when  the  piston  is  at  \  or  f  of  its  course,  then  the  vapour  expands  ;  that  is 
to  say,  in  virtue  of  its  elastic  force,  which  is  due  to  the  high  temperature,  it 


On  Heat.  [472- 

still  acts  on  the  piston  and  causes  it  to  finish  its  course.  Hence  a  distinction 
is  made  between  expanding  and  non-expanding  engines. 

473.  Work  of  an  engine.     Horse-power. — The  work  of  an  engine  is 
measured  in  practice  by  the 

Mean  pressure  on  piston  x  area  of  piston  x  length  of  stroke. 

In  England  the  unit  of  work  is  the  foot-pound ';  that  is,  the  work  performed 
in  raising  a  weight  of  one  pound  through  a  height  of  a  foot.  Thus,  to  raise 
a  weight  of  14  pounds  through  a  height  of  20  feet  would  require  280  foot- 
pounds. On  the  Continent  the  kilogrammetre  is  used  ;  that  is,  the  work 
performed  in  raising  a  kilogramme  through  a  metre.  This  unit  corresponds 
to  7*233  foot-pounds. 

The  rate  of  work  in  machines  is  the  amount  of  work  performed  in  a  given 
time  ;  a  second  or  an  hour,  for  example.  In  England  the  rates  of  work  are 
compared  by  means  of  horse-power,  which  is  a  conventional  unit,  and  repre- 
sents 550  foot-pounds  in  a  second.  In  France  a  similar  unit  is  used  called 
the  cheval  vapeur,  which  represents  the  work  performed  in  raising  75  kilo- 
grammes through  one  metre  in  a  second.  It  is  equal  to  about  542  foot- 
pounds per  second.  Suppose,  for  instance,  that  a  steam-engine  works  under 
a  pressure  of  i|  atmospheres,  the  pressure  in  the  condenser  being  f  an  at- 
mosphere. If  the  area  of  the  piston  is  50  square  inches,  the  length  of  the 
stroke  2 1  inches,  and  the  number  of  up  and  down  strokes  60  in  a  minute  ; 
then,  taking  an  atmosphere  as  representing  14  pounds  on  a  square  inch, 
we  shall  have  14  x  50  x  175  x  120=  147,000  foot-pounds  in  a  minute. 

The  useful  effect  of  a  machine  is  only  about  o-5  to  07  of  the  theoretical 
effect  as  thus  calculated,  the  rest  is  consumed  in  the  unavoidable  friction 
of  the  machine,  in  working  the  pumps,  &c.  If  in  our  case  we  allow  ~  for 
this  loss  we  shall  have  88,200  foot-pounds  in  a  minute  as  the  available  useful 
effect  =  1, 470 foot-pounds  in  a  second,  or  nearly  2|  horse-power.  If  the  work 
of  a  steam-engine  be  calculated  from  the  heat  known  to  be  produced  from 
a  given  weight  of  fuel  (484),  the  discrepancy  is  far  greater.  The  best  Cornish 
engines  do  not  give  more  than  14  per  cent,  of  the  theoretical  yield  of  the 
combustible. 

474.  Kirn's  experiments. — Hirn  made  an  important  series  of  experiments 
in  order  to  determine  the  mechanical  equivalent  of  heat  by  means  of  the 
steam-engine  (497).     On  the  one  hand,  steam  of  known  temperature  and 
pressure  was  allowed  to  act  upon  the  steam-engine,  which  was  one  of  100 
horse-power.     The  amount  of  heat  contained  in  the  steam  could  be  readily 
calculated.     The  amount  of  work  which  the  engine  performed  was  also  de- 
termined by  means  of  a  dynamometer.    The  steam  was  ultimately  condensed 
in  the  condenser,  and  the  amount  of  heat  produced  there  could  readily  be 
measured  by  known  calorimetrical  methods.     It  was  found  in  all  cases  to  be 
less  than  that  which  originally  passed  into  the  engine,  and  the  difference  re- 
presented the  amount  of  heat  \\hich  had  been  converted  into  work  in  the 
engine  ;  in  Hirn's  experiments,  for  every  unit  of  heat  which  had  disappeared, 
1,354  units  of  work  had  been  performed — a  result,  considering  the  difficulty 
of  the  experiments,  closely  agreeing  with  the  best  determinations  (497). 

475.  Hot  air  and  gras  engines. — Numerous  attempts  have  been  made 
to  replace  the  expansive  force  of  steam  by  that  of  heated  air.     Yet  they 


-476] 


TJiermomotive  Wheel. 


415 


have  hitherto  not  been  completely  successful,  owing  to  practical  difficulties  ; 
for  either  the  temperature  had  to  be  so  high  that  it  was  impossible  to  keep 
the  valves  and  the  stuffing-boxes  tight,  or  else  it  was  necessary  greatly  to 
increase  the  dimensions  of  the  cylinder,  in  comparison  with  those  of  steam- 
engines  of  the  same  power. 

In  some  forms  of  gas-engines  a  mixture  of  coal  gas  and  of  atmospheric 
air  contained  in  a  cylinder  is  ignited  by  the  electrical  spark,  and  the 
expansive  force  of  the  heated  gas  thus  produced  moves  the  piston.  As  the 
combustion  of  the  gaseous  mixture  takes  place  within  the  cylinder  itself, 
the  loss  of  heat  is  the  smallest.  They  have,  moreover,  the  advantage  of 
requiring  no  special  fire,  but  can  be  set  up  and  worked  in  any  space  pro- 
vided with  gas.  Yet  these  engines  have  hitherto  only  succeeded  on  a  small 
scale. 

It  is  shown  by  mathematical  analysis  that  the  greatest  theoretical  effi- 
ciency of  any  heat-engine  may  be  expressed  by  the  formula 

t, 

Q 

where  q  is  the  quantity  of  heat  actually  utilised,  and  Q  that  brought  into  play, 
while  T  and  Tj  are  the  temperatures  of  the  source  and  of  the  condenser, 
these  temperatures  being  what  are  called  absohtte.  It  will  thus  be  seen  that 
it  is  desirable  to  extend  the  limit  between  the  two  temperatures ;  and  it  is 
probably  in  the  extension  of  the  use  of  superheated  steam  that  most  pro- 
gress in  the  perfectionment  of  steam-engines  is  to  be  anticipated.  This 
behaves  as  a  gas,  and  has  not  the  disadvantage  of  oxidising  the  metals. 

476.  Thermomotive  wheel. — This  is  an  interesting  example  of  the  con- 
version of  heat  into  motion.  It  consists  (fig.  378)  of  a  series  of  tubes  aa,  bb, 
cc,  bent  at  the  ends,  on 
which  bulbs  are  blown, 
which  are  covered  with 
muslin.  The  bulbs 
themselves  contain 
ether.  The  tubes  pass 
through  a  nave,  which 
has  an  axis  d,  resting 
on  a  support  on  the 
top  of  a  reservoir  e 
containing  water.  All 
the  bulbs  having  been 
wetted,  three  of  them 
will  be  in  the  air  and 
the  others  in  water. 
From  those  in  air  the 
water  in  the  muslin  will 
evaporate,  and  the  ether  inside  will  condense,  and  fresh  vapour  be  formed 
from  the  immersed  bulb.  This  will  continue  to  collect  and  condense 
in  the  upper  bulb,  which  will  sink,  and  the  other  bulb  rise,  and  so  on  with 
the  other  tubes,  and  this  continues  with  such  regularity  that  Bernardi,  the 
inventor,  has  been  able  to  drive  a  small  clock  by  its  means. 


Fig-  378. 


4i 6  On  Heat.  [477- 


CHAPTER   XI. 

SOURCES  OF  HEAT  AND  COLD. 

477.  Different  sources  of  heat. — The  following  different  sources  of  heat 
may  be  distinguished  :  i.  the  mechanical  sources,  comprising  friction,  percus- 
sion, and  pressure  ;  ii.  the  physical  sources — that  is,  solar  radiation,  terres- 
trial heat,  molecular  actions,  changes  of  condition,  and  electricity ;  iii.  the 
chemical  sources^  or  molecular  combinations,  and  more  especially  combus- 
tion. 

In  what  follows  it  will  be  S9en  that  heat  may  be  produced  by  reversing 
its  effects  ;  as,  for  instance,  when  a  liquid  is  solidified  or  a  gas  compressed 
(479) ;  though  it  does  not  necessarily  follow  that  in  all  cases  the  reversal  of 
its  effects  causes  heat  to  be  produced — instead  of  it,  an  equivalent  of  some 
other  form  of  energy  may  be  generated. 

In  like  manner  heat  may  be  forced  to  disappear,  or  cold  be  produced 
when  a  change  such  as  heat  can  produce  is  brought  about  by  other  means, 
as  when  a  liquid  is  vaporised  or  a  solid  liquefied  by  solution  ;  though  here 
also  the  disappearance  of  heat  is  not  always  a  necessary  consequence  of 
the  production,  by  other  means,  of  changes  such  as  might  be  effected  by 
heat. 

MECHANICAL  SOURCES. 

478.  Heat  due  to  friction. — The  friction  of  two  bodies,  one  against  the 
other,  produces  heat,  which  is  greater  the  greater  the  pressure  and  the  more 
rapid  the  motion.     For  example,  the  axles  of  carriage  wheels,  by  their  fric- 
tion against  the  boxes,  often  become  so  strongly  heated  as  to  take  fire.     By 
rubbing  together  two  pieces  of  ice  in  a  vacuum  below  zero,  Sir  H.  Davy 
partially  melted  them.     In  boring  a  brass  cannon  Rumford  found  that  the 
heat  developed  in  the  course  of  2|  hours  was  sufficient  to  raise  26|  pounds 
of  water  from  zero  to  100°,  which  represents  2,650  thermal  units  (447).  .Mayer 
raised  water  from  12°  to  13°  by  shaking  it.   At  the  Paris  Exhibition,  in  1855, 
Beaumont  and  Mayer  exhibited  an  apparatus,  which  consisted  of  a  wooden 
cone  covered  with  hemp,  and  moving  with  a  velocity  of  400  revolutions  in  a 
minute,  in  a  hollow  copper  cone,  which  was  fixed  and  immersed  in  the  water 
of  an  hermetically-closed  boiler.     The  surfaces  were  kept  covered  with  oil. 
By  means  of  this  apparatus  88  gallons  of  water  were  raised  from  10  to  130 
degrees  in  the  course  of  a  few  hours. 

In  the  case  of  flint  and  steel,  the  friction  of  the  flint  against  the  steel 
raises  the  temperature  of  the  metallic  particles,  which  fly  off,  heated  to  such 
an  extent,  that  they  take  fire  in  the  air. 

The  luminosity  of  aerolites  is  considered  to  be  due  to  their  friction  against 


-479]  Heat  due  to  Pressure  and  Percussion.  417 

the  air,  and  to  their  condensation  of  the  air  in  front  of  them  (479),  their 
velocity  attaining  as  much  as  1 50  miles  in  a  second. 

Tyndall  has  devised  an  experiment  by  which  the  great  heat  developed  by 
friction  is  illustrated  in  a  striking  manner.  A  brass  tube  (fig.  379),  about 
7  inches  in  length  and  \  of  "an  inch  in  diameter,  is  fixed  on  a  small  wheel. 
By  means  of  a  cord  passing  round  a  much  larger  wheeJ,  this  tube  can  be 
rotated  with  any  desired  velocity.  The  tube  is  three  parts  full  of  water,  and 
is  closed  by  a  cork.  In  making  the  experiment,  the  tube  is  pressed  between 
a  wooden  clamp,  while  the  wheel  is  rotated  with  some  rapidity.  The  water 
rapidly  becomes  heated  by  the  friction,  and  its  temperature  soon  exceeding 
the  boiling-point,  the  cork  is  projected  to  a  height  of  several  yards  by  the 
elastic  force  of  the  steam. 

479.  Heat  due  to  pressure  and  percussion. — If  a  body  be  so  com- 
pressed that  its  density  is  increased,  its  temperature  rises  according  as  the 


Fig-  379- 

volume  diminishes.  Joule  has  verified  this  in  the  case  of  water  an'd  of  oil, 
which  were  exposed  to  pressures  of  15  to  25  atmospheres.  In  the  case  of 
water  at  1-2°  C.,  increase  of  pressure  caused  lowering  of  temperature— a  result 
which  agrees  with  the  fact  that  water  contracts  by  heat  at-this  temperature. 
Similarly,  when  weights  are  laid  on  metallic  pillars,  heat  is  evolved,  and 
absorbed  when  they  are  removed.  So  in  like  manner  the  stretching  of  a 
metallic  wire  is  attended  with  a  diminution  of  temperature. 

The  production  of  heat  by  the  compression  of  gases  is  easily  shown  by 
means  of  the  pneumatic  syringe  (fig.  380).  This  consists  of  a  glass  tube 
with  thick  sides,  closed  hermetically  by  a  leather  piston.  At  the  bottom  of 
this  there  is  a  cavity  in  which  a  small  piece  of  cotton,  moistened  witk 
ether  or  bisulphide  of  carbon,  is  placed.  The  tube  being  full  of  air,  the 
piston  is  suddenly  plunged  downwards  ;  the  air  thus  compressed  disengages 
so  much  heat  as  to  ignite  the  cotton,  which  is  seen  to  burn  when  the  piston 
is  rapidly  withdrawn.  The  inflammation  of  the  cotton  in  this  experiment 
indicates  a  temperature  of  at  least  300°. 

A  curious  application  of  the  pneumatic  syringe  is  met  with  in  the  American 


4i 8  On  Heat.  [479- 

poivder  ram  for  pile  driving.  On  the  pile  to  be  driven  is  fixed  a  powder 
mortar,  above  which  is  suspended  at  a  suitable  distance  an  iron  rammer, 
shaped  like  a  gigantic  stopper,  which  just  fits  in  the  mortar.  Gunpowder  is 
placed  in  the  mortar,  and  when  the  rammer  is  detached  it  falls  into  the 
mortar,  condenses  the  air,  producing  so  much  heat  that  the  powder  is  ex- 
ploded. The  force  of  the  gases  projects  the  rammer  into  its  original  posi- 
tion where  it  is  caught  by  a  suitable  arrangement  ;  at  the  same  time  the 
reaction  of  the  mortar  on  the  pile  drives  this  in  with  far  greater  force  than 
the  fall  of  the  rammer.  After  adding  a  fresh  charge  of  powder,  the  rammer 


is  again  allowed  to  fall,  again  produces  heat,  explosion,  and  so  forth,  so  that 
the  driving  is  effected  in  a  surprisingly  short  time. 

The  elevation  of  temperature  produced  by  the  compression  in  the  above 
experiment  is  sufficient  to  effect  the  combination,  and  therefore  the  detona- 
tion, of  a  mixture  of  hydrogen  and  oxygen. 

Percussion  is  also  a  source  of  heat.  In  firing  shot  at  an  iron  target,  a 
sheet  of  flame  is  frequently  seen  at  the  moment  of  impact  ;  and  Sir  J.  Whit- 
worth  has  used  iron  shells  which  are  exploded  by  the  concussion  on  striking 
an  iron  target.  A  small  piece  of  iron  hammered  on  the  anvil  becomes  very 
hot.  The  heat  is  not  simply  due  to  an  approximation  of  the  molecules— 
that  is,  to  an  increase  in  density — but  arises  from  a  vibratory  motion  im- 
parted to  them  ;  for  lead,  which  does  not  increase  in  density  by  hammering, 
nevertheless  becomes  heated. 

The  heat  due  to  the  impact  of  bodies  is  not  difficult  to  calculate.  When- 
ever a  body  moving  with  a  velocity  v  is  suddenly  arrested  in  its  motion, 
its  vis  viva  is  converted  into  heat.  This  holds  equally  whatever  be  the 
cause  to  which  the  motion  is  due  :  whether  it  be  that  acquired  by  a  stone 
falling  from  a  height,  by  a  bullet  fired  from  a  gun,  or  the  rotation  of  a 
copper  disc  by  means  of  a  turning  table.  The  vis  viva  of  any  moving  body 


mv 


is  expressed  by——  or  in  foot-pounds 


—  ,  where  p   is 


the   weight    in 


pounds,  v  the  velocity  in  feet  per  second,  and  g  is  about  32  (29) ;  and  if  the 
whole  of  this  be  converted  into  heat,  its  equivalent  in  thermal  units  will 

be  .     ^ — .     Suppose,  for  instance,  a  lead  ball  weighing  a  pound  be  fired 
2£-x  1390 

from  a  gun,  and  strike  against  a  target,  what  amount  of  heat  will  it  produce  ? 
We  may  assume  that  its  velocity  will  be  about  1,600  feet  per  second  ;  then 

0  =  40,000  foot-pounds.     Some  of  this  will  have 


its  vis  viva  will  be 


2x32 


-480]  Solar  Radiation.  419 

been  consumed  in  producing  the  vibrations  which  represent  the  sound  of  the 
shock,  some  of  it  also  in  its  change  of  shape  ;  but  neglecting  these  two,  as 
being  small,  and  assuming  that  the  heat  is  equally  divided  between  the  ball 
and  the  target,  then,  since  40,000  foot-pounds  is  the  equivalent  of  287 
thermal  units,  the  share  of  the  ball  will  be  14-3  thermal  units  ;  and  if,  for 
simplicity's  sake,  we  assume  that  its  initial  temperature  is  zero,  then,  taking 
its  specific  heat  at  0*0314,  we  shall  have 

i  xo-o3i4x/=  14-3  or /  =  457°, 

which  is  a  temperature  considerably  above  that  of  the  melting  point  of  lead 
(338). 

By  allowing  a  lead  ball  to  fall  from  various  heights  on  an  iron  plate,  both 
experience  an  increase  of  temperature  which  may  be  measured  by  the 
thermopile  ;  and  from  these  increases  it  may  be  easily  shown  that  the  heat 
is  directly  proportional  to  the  height  of  fall,  and  therefore  to  the  square  of 
the  velocity. 

By  similar  methods  Mayer  has  calculated  that  if  the  motion  of  the  earth 
were  suddenly  arrested  the  temperature  produced  would  be  sufficient  to  melt 
and  even  volatilise  it ;  while,  if  it  fell  into  the  sun,  as  much  heat  would  be 
produced  as  results  from  the  combustion  of  5,000  spheres  of  carbon  the  size 
of  our  globe. 

PHYSICAL  SOURCES. 

480,  Solar  radiation. — The  most  intense  of  all  sources  of  heat  is  the  sun. 
Different  attempts  have  been  made  to  determine  the  quantity  of  heat  which 
it  emits.  Pouillet,  from  experiments  made  by  means  of  an  apparatus  which 
he  calls  a  pyroheliometcr,  calculated  that  if  the  total  quantity  of  heat  which 
the  earth  receives  from  the  sun  in  the  course  of  a  year  were  employed  to 
melt  ice,  it  would  be  capable  of  melting  a  layer  of  ice  all  round  the  earth  of 
35  yards  in  thickness.  The  heat  emitted  by  the  sun  is  equal  to  that  pro- 
duced by  the  combustion  of  1,500  pounds  of  coal  in  an  hour  on  each  square 
foot  of  its  surface.  But  from  the  surface  which  the  earth  exposes  to  the 
solar  radiation,  and  from  the  distance  which  separates  the  earth  from  the 
sun,  the  quantity  of  heat  which  the  earth  receives  can  only  be  1|38I|JUO|000  of  the 
heat  emitted  by  the  sun. 

Faraday  calculated  that  the  average  amount  of  heat  radiated  in  a  day  on 
each  acre  of  ground  in  the  latitude  of  London  is  equal  to  that  which  would 
be  produced  by  the  combustion  of  sixty  sacks  of  coal. 

The  heat  of  the  sun  cannot  be  due  to  a  combustion,  for  even  if  the  sun 
consisted  of  hydrogen,  which  of  all  substances  gives  the  most  heat  in  com- 
bining with  oxygen,  it  can  be  calculated  that  the  heat  thus  produced  would 
not  last  more  than  3,000  years.  Another  supposition  is  that  originally  put 
forth  by  Mayer,  according  to  which  the  heat  which  the  sun  loses  by  radiation 
is  replaced  by  the  fall  of  aerolites  against  its  surface.  One  class  of  these  is 
what  we  know  as  shooting  stars,  which  often  appear  in  the  heavens  with  great 
brilliancy,  especially  on  August  14  and  November  15  ;  the  term  meteoric  stone 
r>r  aerolite  being  properly  restricted  to  the  bodies  which  fall  on  the  earth. 
They  are  often  of  considerable  size,  and  are  even  met  with  in  the  form  of 


420  On  Heat.  [480- 

dust.  Although  some  of  the  sun's  heat  may  be  restored  by  the  impact  of 
such  bodies  against  the  sun,  the  amount  must  be  very  small,  for  Sir  W. 
Thomson  has  proved  that  a  fall  of  0-3  gramme  of  matter  in  a  second  on  each 
square  metre  of  surface  would  be  necessary  for  this  purpose.  The  effect  of 
this  would  be  that  the  mass  of  the  sun  would  increase,  and  the  velocity  of 
the  earth's  rotation  about  the  sun  would  be  accelerated  to  an  extent  which 
would  be  detected  by  astronomical  observations. 

Helmholtz  considers  that  the  heat  of  the  sun  was  produced  originally  by 
the  condensation  of  a  nebulous  mass,  and  is  kept  up  by  a  continuance  of 
this  contraction.  A  sudden  contraction  of  the  primitive  nebular  mass  of  the 
sun  to  its  present  volume  would  produce  a  temperature  of  28  millions  of 
degrees  Centigrade  ;  and  a  contraction  of  ^Q~  of  its  mass  would  be  sufficient 
to  supply  the  heat  radiated  by  the  sun  in  2,000  years.  This  amount  of  con- 
traction could  not  be  detected  even  by  the  most  refined  astronomical 
methods. 

481.  Terrestrial  beat. — Our  globe  possesses  a  heat  peculiar  to  it,  which 
is  called  the  terrestrial  heat.     The  variations  of  temperature  which  occur  at 
the  surface  gradually  penetrate  to  a  certain  depth,  at  which  their  influence 
becomes  too  slight  to  be  sensible.     It  is  hence  concluded  that  the  solar  heat 
does  not  penetrate  below  a  certain  internal  layer,  which  is  called  the  layer  of 
constant  temperature  :  its  depth  below  the  earth's  external  surface  varies,  of 
course,  in  different  parts  of  the  globe  ;  at  Paris  it  is  about  30  yards,  and  the 
temperature  is  constant  at  ir8°  C. 

Below  the  layer  of  constant  temperature,  the  temperature  is  observed  to 
increase,  on  the  average,  i°  C.  for  every  90  feet.  The  most  rapid  increase 
is  at  Irkutsk  in  Siberia,  where  it  is  i°  for  20  feet,  and  the  slowest  in  the  mines 
at  Mansfield,  where  it  is  about  i°  C.  for  330  feet.  This  increase  has  been 
verified  in  mines  and  artesian  wells.  According  to  this,  at  a  depth  of  3,000 
yards,  the  temperature  of  a  corresponding  layer  would  be  100°,  and  at  a 
depth  of  20  to  30  miles  there  would  be  a  temperature  sufficient  to  melt  all 
substances  which  exist  on  the  surface.  Hot  springs  and  volcanoes  confirm 
the  existence  of  this  central  heat. 

Various  hypotheses  have  been  proposed  to  account  for  the  existence  of 
this  central  heat.  The  one  usually  admitted  by  physicists  is  that  the  earth 
was  originally  in  a  liquid  state  in  consequence  of  the  high  temperature,  and 
that  by  radiation  the  surface  has  gradually  solidified,  so  as  to  form  a  solid 
crust.  The  thickness  of  this  crust  is  not  believed  to  be  more  than  40  to  50 
miles,  and  the  interior  is  probably  still  in  a  liquid  state.  The  cooling  must 
be  very  slow,  in  consequence  of  the  imperfect  conductivity  of  the  crust.  For 
the  same  reason  the  central  heat  does  not  appear  to  raise  the  temperature 
of  the  surface  more  than  ^  of  a  degree. 

482.  Heat  produced  by  absorption  and  Imbibition. — Molecular  phe- 
nomena, such  as  imbibition,  absorption,  capillary  actions,  are  usually  accom- 
panied by  disengagement  of  heat.     Pouillet  found  that  whenever  a  liquid  is 
poured  on  a  finely-divided  solid,  an  increase  of  temperature  is  produced 
which  varies  with  the  nature  of  the  substances.     With  inorganic  substances, 
such  as  metals,  the  oxides,  the  earths,  the  increase  is  T45  of  a  degree  ;  but 
with  organic  substances,  such  as  sponge,  flour,  starch,  roots,  dried  mem- 
branes, the  increase  varies  from  I  to  10  degrees. 


-483] 


Chemical  Combination.     Combustion. 


421 


The  absorption  of  gases  by  solid  bodies  presents  the  same  phenomena. 
Diibereiner  found  that  when  platinum,  in  the  fine  state  of  division  known  as 
platinum   black,  is   placed  in   oxygen,  it  absorbs 
many  hundred  times  its  volume,  and  that  the  gas 
is  then  in  such  a  state  of  density,  and  the  tempera- 
ture so  high,  as  to  give  rise  to  intense  combustions. 
Spongy  platinum  produces  the  same  effect.     A  jet 
of  hydrogen  directed  on  it  takes  fire. 

The  apparatus  known  as  Dobereiner's  Lamp 
depends  on  this  property  of  finely -divided  platinum. 
It  consists  of  two  glass  vessels  (fig.  381).  The 
first,  A,  fits  in  the  lower  vessel  by  means  of  a 
tubulure  which  closes  it  hermetically.  At  the  end 
of  the  tubulure  is  a  lump  of  zinc,  Z,  immersed  in 
dilute  sulphuric  acid.  By  the  chemical  action  of 
the  zinc  on  the  dilute  acid  hydrogen  gas  is  gene- 
rated, which,  finding  no  issue,  forces  the  liquid  out 
of  the  vessel  B  into  the  vessel  A,  so  that  the  zinc 
is  not  in  contact  with  the  liquid.  The  stopper  of 
the  upper  vessel  is  raised  to  give  exit  to  the  air  in 
proportion  as  the  water  rises.  On  a  copper  tube, 
H,  fixed  in  the  side  of  the  vessel  B,  there  is  a  small 

cone,  #,  perforated  by  an  orifice ;  above  this  there  is  some  spongy  platinum 
in  the  capsule  c.  As  soon  now  as  the  cock,  which  closes  the  tube,  H,  is 
opened,  the  hydrogen  escapes,  and,  coming  in  contact  with  the  spongy 
platinum,  is  ignited. 

The  condensation  of  vapours  by  solids  often  produces  an  appreciable 
increase  of  temperature.  This  is  particularly  the  case  with  humus,  which,  to 
the  benefit  of  plants,  is  warmer  in  moist  air  than  the  air  itself. 

Favre  has  found  that  when  a  gas  is  absorbed  by  charcoal  the  amount  of 
heat  produced  by  the  absorption  of  a  given  weight  of  sulphurous  acid,  or  of 
protoxide  of  nitrogen,  greatly  exceeds  that  which  is  disengaged  in  the  lique- 
faction of  the  same  weight  of  gas  ;  for  carbonic  acid,  the  heat  produced  by 
absorption  exceeds  even  the  heat  which  would  be  disengaged  by  the  solidifi- 
cation of  the  gas.  The  heat  produced  by  the  absorption  of  these  gases 
cannot,  therefore,  be  explained  by  assuming  that  the  gas  is  liquefied,  or  even 
solidified  in  the  pores  of  the  charcoal.  It  is  probable  that  it  is  due  to  that 
produced  by  the  liquefaction  of  the  gas,  and  to  the  heat  due  to  the  imbibition 
in  the  charcoal  of  the  liquid  so  produced. 

The  heat  produced  by  the  changes  of  condition  has  been  already  treated 
of  in  the  articles  Solidification  and  Liquefaction  ;  the  heat  produced  by  elec- 
trical action  will  be  discussed  under  the  head  of  Electi  icity. 


Fig.  381. 


CHEMICAL  SOURCES. 

483.  Chemical  combination.  Combustion. — Chemical  combinations 
are  usually  accompanied  by  a  certain  elevation  of  temperature.  When  these 
combinations  take  place  slowly,  as  when  iron  oxidises  in  the  air,  the  heat 
produced  is  imperceptible  ;  but  if  they  take  place  rapidly,  the  disengagement 


422  On  Heat.  [483- 

of  heat  is  very  intense.  The  same  quantity  of  heat  is  produced  in  both  cases, 
but  when  evolved  slowly  it  is  dissipated  as  fast  as  formed. 

Combustion  is  chemical  combination  attended  with  the  evolution  of  light 
and  heat.  In  ordinary  combustion  in  lamps,  fires,  candles,  the  carbon  and 
hydrogen  of  the  coal,  or  of  the  oil,  &c.,  combine  with  the  oxygen  of  the  air. 
But  combustion  does  not  necessarily  involve  the  presence  of  oxygen.  If 
either  powdered  antimony  or  a  fragment  of  phosphorus  be  placed  in  a  vessel 
of  chlorine,  it  unites  with  chlorine,  producing  thereby  heat  and  flame. 

Many  combustibles  burn  with  flame.  A  flame  is  a  gas  or  vapour  raised 
to  a  high  temperature  by  combustion.  Its  illuminating  power  varies  with 
the  nature  of  the  product  formed.  The  presence  of  a  solid  body  in  the  flame 
increases  the  illuminating  power.  The  flames  of  hydrogen,  carbonic  oxide, 
and  alcohol  are  pale,  because  they  only  contain  gaseous  products  of  com- 
bustion. But  the  flames  of  candles,  lamps,  coal  gas,  have  a  high  illuminating 
power.  They  owe  this  to  the  fact  that  the  high  temperature  produced  de- 
composes certain  of  the  gases  with  the  production  of  carbon,  which,  not 
being  perfectly  burnt,  becomes  incandescent  in  the  flame.  Coal  gas,  when 
burnt  in  an  arrangement  by  which  it  obtains  an  adequate  supply  of  air,  such 
as  a  Bunsen's  burner,  is  almost  entirely  devoid  of  luminosity.  A  non-lumi- 
nous flame  may  be  made  luminous  by  placing  in  it  platinum  wire  or  asbestos. 
The  temperature  of  a  flame  does  not  depend  on  its  illuminating  power.  A 
hydrogen  flame,  which  is  the  palest  of  all  flames,  gives  the  greatest  heat. 

Chemical  decomposition  in  which  the  attraction  of  heterogeneous  mole- 
cules for  each  other  is  overcome,  and  they  are  moved  further  apart,  is  an 
operation  requiring  an  expenditure  of  work  or  an  equivalent  consumption  of 
heat ;  and  conversely,  in  chemical  combination,  motion  is  transformed  into 
heat.  When  bodies  attract  each  other  chemically  their  molecules  move 
towards  each  other  with  gradually  increasing  velocity,  and  when  impact  has 
taken  place  the  progressive  motion  of  the  molecules  ceases,  and  is  converted 
into  a  rotating,  vibrating,  or  progressive  motion  of  the  molecules  of  the  new- 
body. 

The  heat  produced  by  chemical  combination  of  two  elements  may  be 
compared  to  that  due  to  the  impact  of  bodies  against  each  other.  Thus  the 
action  of  the  atoms  of  oxygen,  which,  in  virtue  of  their  progressive  motion, 
and  of  chemical  attraction,  rush  against  ignited  carbon,  has  been  likened  by 
Tyndall  to  the  action  of  meteorites  which  fall  into  the  sun. 

484.  Heat  disengaged  during-  combustion. — Many  physicists,  more 
especially  Lavoisier,  Rumford,  Dulong,  Despretz,  Hess,  Favre  and  Silber- 
mann  and  Andrews,  have  investigated  the  quantity  of  heat  disengaged  by 
various  bodies  in  chemical  combinations. 

In  these  experiments  Lavoisier  used  the  ice  calorimeter  already  described. 
Rumford  used  a  calorimeter  known  by  his  name,  which  consists  of  a  rect- 
angular copper  canister  filled  with  water.  In  this  canister  there  is  a  worm 
which  passes  through  the  bottom  of  the  box,  and  terminates  below  in  an 
inverted  funnel.  Under  this  funnel  is  burnt  the  substance  experimented 
upon.  The  products  of  combustion,  in  passing  through  the  worm,  heat  the 
water  of  the  canister,  and  from  the  increase  of  its  temperature  the  quantity 
of  heat  evolved  is  calculated.  Despretz  and  Dulong  successively  modified 
Rumford's  calorimeter  by  allowing  the  combustion  to  take  place,  not 


-485]  Animal  Heat.  423 

outside  the  canister,  but  in  a  chamber  placed  in  the  liquid  itself ;  the 
oxygen  necessary  for  the  combustion  entered  by  a  tube  in  the  lower  part  of 
the  chamber,  and  the  products  of  combustion  escaped  by  another  tube 
placed  at  the  upper  part  and  twisted  in  a  serpentine  form  in  the  mass  of  the 
liquid  to  be  heated.  Favre  and  Silbermann  have  improved  this  calorimeter 
very  greatly  (463),  not  only  by  avoiding  or  taking  account  of  all  possible 
sources  of  error,  but  by  arranging  it  for  the  determination  of  the  heat  evolved 
in  other  chemical  actions  than  those  of  ordinary  combustion. 

The  experiments  of  Favre  and  Silbermann  are  the  most  trustworthy,  as 
having  been  executed  with  the  greatest  care.  They  agree  very  closely  with 
those  of  Dulong.  Taking  as  thermal  unit  the  heat  necessary  to  raise  the 
temperature  of  a  pound  of  water  through  one  degree  Centigrade,  the  follow- 
ing table  gives  the  thermal  units  in  round  numbers  disengaged  by  a  pound 
of  each  of  the  substances  in  burning  in  oxygen  : — 

Hydrogen       ....  34462  Diamond       ....     7770 

Marsh  gas      ....  13063  Absolute  alcohol    .         .         .7180 

Olefiant  gas   ....  11858  Coke 7000 

Oil  of  turpentine    .         .         .  10852  Phosphorus   ....     5750 

Olive  oil         ....  9860  Wood,  dry     ....     4025 

Ether 9030  Bisulphide  of  carbon     .         .     3401 

Anthracite      ....  8460  Wood,  moist.         .         .         .3100 

Charcoal        ....  8080  Carbonic  oxide      .         .         .     2400 

Coal 8000  Sulphur          ....     2220 

Tallow 8000  Iron 1576 

Bunsen's  calorimeter  (451)  has  been  used  for  studying  the  heat  produced 
in  chemical  reactions  for  cases  in  which  only  very  small  quantities  are 
available. 

The  experiments  of  Dulong,  of  Despretz,  and  of  Hess  prove  that  a  body 
in  burning  always  produces  the  same  quantity  of  heat  in  reaching  the  same 
degree  of  oxidation,  whether  it  attains  this  at  once  or  only  reaches  it  after 
passing  through  intermediate  stages.  Thus  a  given  weight  of  carbon  gives 
out  the  same  amount  of  heat  in  burning  directly  to  carbonic  acid  as  if  it 
were  first  changed  into  carbonic  oxide,  and  then  this  were  burnt  into  carbonic 
acid. 

485.  Animal  heat. — In  all  the  organs  of  the  human  body,  as  well  as 
those  of  all  animals,  processes  of  oxidation  are  continually  going  on.  Oxygen 
passes  through  the  lungs  into  the  blood,  and  so  into  all  parts  of  the  body.  In 
like  manner  the  oxidisible  bodies,  which  are  principally  hydrocarbons,  pass 
by  the  process  of  digestion  into  the  blood,  and  likewise  into  all  parts  of  the 
body,  while  the  products  of  oxidation,  carbonic  acid  and  water,  are  eliminated 
by  the  skin,  the  lungs,  &c.  Oxidation  in  the  muscle  produces  motions  of  the 
molecules,  which  are  changed  into  contraction  of  the  muscular  fibres  ;  aH 
other  oxidations  produce  heat  directly.  When  the  body  is  at  rest,  all  its 
functions,  even  involuntary  motions,  are  transformed  into  heat.  When  the 
body  is  at  work,  the  more  vigorous  oxidations  of  the  working  parts  are 
transferred  to  the  others.  Moreover,  a  great  part  of  the  muscular  work  is 
changed  into  heat,  by  friction  of  the  muscle  and  of  the  sinews  in  their  sheaths, 
and  of  the  bones  in  their  sockets.  Hence  the  heat  produced  by  the  body 


424  On  Heat.  [485- 

when  at  work  is  greater  than  when  at  rest.  The  blood  distributes  heat 
uniformly  through  the  body,  which  in  a  normal  condition  has  a  temperature 
of  37°'5-  The  blood  of  mammalia  has  the  same  temperature,  that  of  birds  is 
somewhat  higher.  In  fever  the  temperature  rises  to  42°-44°,  and  in  cholera, 
or  when  near  death,  sinks  to  35°. 

The  function  of  producing  work  in  the  animal  organism  was  formerly  con- 
sidered as  separate  from  that  of  the  production  of  heat.  The  latter  was  held 
to  be  due  to  the  oxidation  of  the  hydrocarbons  of  the  fat,  while  the  work 
was  ascribed  to  the  chemical  activity  of  the  nitrogenous  matter.  This  view 
has  now  been  generally  abandoned  ;  for  it  has  been  found  that  during  work 
there  is  no  increase  in  the  secretion  of  urea,  which  is  the  result  of  the  oxida- 
tion of  nitrogenous  matter  ;  moreover,  the  organism  while  at  rest  produces 
less  carbonic  acid,  and  requires  less  oxygen  than  when  it  is  at  work  j  and 
the  muscle  itself,  both  in  the  living  organism  and  also  when  removed  from 
it  and  artificially  stimulated,  requires  more  oxygen  in  a  state  of  activity  than 
when  at  rest.  For  these  reasons  the  production  of  work  is  also  ascribed  to 
the  oxidation  of  organic  matter. 

The  process  of  vegetation  in  the  living  plant  is  not  in  general  connected 
with  any  oxidation.  On  the  contrary,  under  the  influence  of  the  sun's  rays, 
the  green  parts  of  plants  decompose  the  carbonic  acid  of  the  atmosphere 
into  free  oxygen  gas  and  into  carbon,  which,  uniting  with  the  elements  of 
water,  form  cellulose,  starch,  sugar,  and  so  forth.  In  order  to  effect  this, 
an  expenditure  of  heat  is  required  which  is  stored  up  in  the  plant  and  re- 
appears during  the  combustion  of  wood  or  of  the  coal  arising  from  its  de- 
composition. 

At  the  time  of  blossoming  a  process  of  oxidation  goes  on,  which,  as  in 
the  case  of  the  blossoming  of  the  Victoria  regia,  is  attended  with  an  appreci- 
able increase  of  temperature. 

HEATING. 

486.  Different  kinds   of  heating-. — Heating  is  the  art  of  utilising  for 
domestic  and  industrial  purposes  the  sources  of  heat  which  nature  offers  to  us. 

Our  principal  source  of  artificial  heat  is  the  combustion  of  coal,  coke, 
turf,  wood,  and  charcoal. 

We  may  distinguish  five  kinds  of  heating,  according  to  the  apparatus 
used  :  ist,  heating  with  an  open  fire  ;  2nd,  heating  with  an  enclosed  fire,  as 
with  a  stove  ;  3rd,  heating  by  hot  air  ;  4th,  heating  by  steam  ;  5th,  heating 
by  the  circulation  of  hot  water. 

487.  Fire-places. — Fire-places  are   open  hearths  built   against  a  wall 
under  a  chimney,  through  which  the  products  of  combustion  escape. 

However  much  they  may  be  improved,  fire-places  will  always  remain  the 
most  imperfect  and  costly  mode  of  heating,  for  they  only  render  available 
13  per  cent,  of  the  total  heat  yielded  by  coal  or  coke,  and  6  per  cent,  of  that 
by  wood.  This  enormous  loss  of  temperature  arises  from  the  fact  that  the 
current  of  air  necessary  for  combustion  always  carries  with  it  a  large  quantity 
of  the  heat  produced,  which  is  dissipated  in  the  atmosphere.  Hence 
Franklin  said  'fire-places  should  be  adopted  in  cases  where  the  smallest 
quantity  of  heat  was  to  be  obtained  from  a  given  quantity  of  fuel.'  Not- 


-488]  Draught  of  Fire-places.  425 

withstanding  their  want  of  economy,  however,  they  will  always  be  preferred 
as  the  healthiest  and  pleasantest  mode  of  heating,  on  account  of  the  cheerful 
light  which  they  emit,  and  the  ventilation 
which  they  ensure. 

488.  Draught  of  fire-places  __  The 
draught  of  a  fire  is  the  upward  current  in  the 
chimney  caused  by  the  ascent  of  the  pro- 
ducts of  combustion  ;  when  the  current  is 
rapid  and  continuous,  the  chimney  is  said 
to  draw  well. 

The  draught  is  caused  by  the  difference 
between  the  temperature  of  the  inside  and 
that  on  the  outside  of  the  chimney  ;  for,  in 
consequence  of  this  difference,  the  gaseous 
substances  which  fill  the  chimney  are  lighter 
than  the  air  of  the  room,  and  consequently 
equilibrium  is  impossible.  The  weight  of 
the  column  of  gas  CD,  fig.  383,  in  the 
chimney  being  less  than  that  of  the  external 
column  of  air  AB  of  the  same  height,  there 
is  a  pressure  from  the  outside  to  the  inside  which  causes  the  products  of 
combustion  to  ascend  the  more  rapidly  in  proportion  as  the  difference  in 
weight  of  the  two  gaseous  masses  is  greater.  . 

The  velocity  of  the  draught  of  a  chimney  may  be  determined  theoreti- 
cally by  the  formula 


Fig.  382. 


in  which  g  is  the  acceleration  of  gravity,  a  the  coefficient  of  the  expansion 
of  air,  h  the  height  of  the  chimney,  f  the  mean  temperature  of  the  air  in- 
side the  chimney,  and  /  the  temperature  of  the  surrounding  air. 

The  currents  caused  by  the  difference  in  temperature  of  two  communi- 
cating gaseous  masses  may  be  demonstrated  by  placing  a  candle  near  the 
top  and  near  the  bottom  of  the  partially-opened  door  of  a  warm  room 
At  the  top,  the  flame  will  be  turned  from  the  room  towards  the  outside, 
while  the  contrary  effect  will  be  produced  when  the  candle  is  placed  on  the 
ground.  The  two  effects  are  caused  by  the  current  of  heated  air  which 
issues  by  the  top  of  the  door,  while  the  cold  air  which  replaces  it  enters  at 
the  bottom. 

In  order  to  have  a  good  draught,  a  chimney  ought  to  satisfy  the  following 
conditions  : 

i.  The  section  of  the  chimney  ought  not  to  be  larger  than  is  necessary  to 
allow  an  exit  for  the  products  of  combustion  ;  otherwise  ascending  and  de- 
scending currents  are  produced  in  the  chimney,  which  cause  it  to  smoke.  It 
is  advantageous  to  place  on  the  top  of  the  chimney  a  conical  pot  narrower 
than  the  chimney,  so  that  the  smoke  may  escape  with  sufficient  velocity  to 
resist  the  action  of  the  wind. 

ii.  The  chimney  ought  to  be  sufficiently  high,  for,  as  the  draught  is  caused 
by  the  excess  of  the  external  over  the  internal  pressure,  this  excess  is  greater 
in  proportion  as  the  column  of  heated  air  is  longer. 


426  On  Heat.  [488- 

iii.  The  external  air  ought  to  pass  into  the  chamber  with  sufficient  rapidity 
to  supply  the  wants  of  the  fire.  In  an  hermetically-closed  room  the  com- 
bustibles would  not  burn,  or  descending  currents  would  be  formed  which 
would  drive  the  smoke  into  the  room.  Usually  air  enters  in  sufficient 
quantity  by  the  crevices  of  the  doors  and  windows. 

iv.  Two  chimneys  should  not  communicate,  for  if  one  draws  better  than 
the  other,  a  descending  current  of  air  is  produced  in  the  latter,  which  carries 
smoke  with  it. 

For  the  strong  fires  required  by  steam  boilers  and  the  like,  very  high 
chimneys  are  needed  :  of  course  the  increase  in  height  would  lose  its  effect 
if  the  hot  column  above  became  cooled  down.  Hence  chimneys  are  often 
made  with  hollow  walls — that  is,  of  separate  concentric  layers  of  masonry — 
the  space  between  them  containing  air. 

489.  Stoves. — Stoves  are  apparatuses  for  heating  with  a  detached  fire, 
placed  in  the  room  to  be  heated,  so  that  the  heat  radiates  in  all  directions 
round  the  stove.     At  the  lower  part  is  the  draught  hole  by  which  the  air 
necessary  for  combustion  enters.     The  products  of  combustion  escape  by 
means  of  iron  chimney  pipes.     This  mode  of  heating  is  one  of  the  most 
economical,  but  it  is  by  no  means  so  healthy  as  that  by  open  fire-places, 
for  the  ventilation  is  very  bad,  more  especially  where,  as  in  Sweden  and  in 
Germany,  the  stoves  are  fed  from  the  outside  of  the  room.     These  stoves 
also  emit  a  bad  smell,  probably  arising  from  the  decomposition  of  organic 
substances  in   the  air  by  their  contact  with  the  heated  sides  of  the  chimney 
pipes  ;  or  possibly,  as  Deville  and  Troost's  researches  seem  to  show,  from 
the  diffusion  of  gases  through  the  heated  sides  of  the  stove. 

The  heating  is  very  rapid  with  blackened  metal  stoves,  but  they  also  cool 
very  rapidly.  Stoves  constructed  of  polished  earthenware,  which  are  common 
on  the  Continent,  heat  more  slowly,  but  more  pleasantly,  and  they  retain  the 
heat  longer. 

490.  Heating:  by  steam. — Steam,  in  condensing,  gives  up  its  latent  heat 
of  vaporisation,  and  this  property  has  been  used  in  heating  baths,  workshops, 
public  buildings,  hothouses,  &c.     For  this  purpose  steam  is  generated  in 
boilers  similar  to  those  used  for  steam-engines,  and  is  then  made  to  circulate 
in  pipes  placed  in  the  room  to  be  heated.     The  steam  condenses,  and  in 
doing  so  imparts  to  the  pipes  its  latent  heat,  which  becomes  free,  and  thus 
heats  the  surrounding  air. 

491.  Heating:  by  not  air. — Heating  by  hot  air  consists  in  heating  the 
air  in  the  lower  part  of  a  building,  from  whence  it  rises  to  the  higher  parts 
in  virtue  of  its  lessened  density.     The  apparatus  is  arranged  as  represented 
in  fig.  383. 

A  series  of  tubes,  AB,  only  one  of  which  is  shown  in  the  figure,  is 
placed  in  a  furnace,  F,  in  the  cellar.  The  air  passes  into  the  tubes  through 
the  lower  end  A,  where  it  becomes  heated,  and,  rising  in  the  direction  of 
the  arrows,  reaches  the  room  M  by  a  higher  aperture  B.  The  various 
rooms  to  be  heated  are  provided  with  one  or  more  of  these  apertures,  which 
are  placed  as  low  in  the  room  as  possible.  The  conduit  O  is  an  ordinary 
chimney.  These  apparatuses  are  more  economical  than  open  fire-places,  but 
they  are  less  healthy,  unless  special  provision  is  made  for  ventilation. 


493] 


Various  Sources  of  Cold. 


427 


492.  Heating  by  hot  water. — This  consists  of  a  continuous  circulation 
of  water,  which,  having  been  heated  in  a  boiler,  rises  through  a  series  of  tubes, 
and  then,  after  becoming 
cool,  passes  into  the  boiler 
again  by  a  similar  series. 

Figure  384  represents  an 
apparatus  for  heating  a 
building  of  several  stories. 
The  heating  apparatus, 
which  is  in  the  basement, 
consists  of  a  bell -shaped 
boiler,  o  o,  with  an  internal 
flue,  F.  A  long  pipe,  M,  fits 
in  the  upper  part  of  the 
boiler,  and  also  in  the  reser- 
voir Q,  placed  in  the  upper 
part  of  the  building  to  be 
heated.  At  the  top  of  this 
reservoir  there  is  a  safety 
valve,  j,  by  which  the  pres- 


sure of  the    vapour    in   the 

interior  can  be  regulated.  Fig.  3g3> 

The  boiler,  the  pipe  M, 

and  a  portion  of  the  reservoir  Q,  being  filled  with  water,  as  it  becomes 
heated  in  the  boiler,  an  ascending  current  of  hot  water  rises  to  the  reservoir 
Q,  while  at  the  same  time  descending  currents  of  colder  and  denser  water 
pass  from  the  lower  part  of  the  reservoir  Q  into  receivers  £,  d,  /,  filled  with 
water.  The  water  from  these  passes  again  through  pipes  into  other  re- 
ceivers, a,  c,  e,  and  ultimately  reaches  the  lower  part  of  the  boiler. 

During  this  circulation  the  hot  water  heats  the  pipes  and  the  receivers, 
which  thus  become  true  water  stoves.  The  number  and  the  dimensions  of 
these  parts  are  determined  from  the  fact  that  a  cubic  foot  of  water  in  falling 
through  a  temperature  of  one  degree  can  theoretically  impart  the  same 
increase  of  temperature  to  3,200  cubic  feet  of  air  (460).  In  the  interior  of  the 
receivers,  #,  £,  <r,  d,  e,f,  there  are  cast-iron  tubes  which  communicate  with 
the  outside  by  pipes,  P,  placed  underneath  the  flooring.  The  air  becomes 
heated  in  these  tubes,  and  issues  at  the  upper  part  of  the  receiver. 

The  principal  advantage  of  this  mode  of  heating  is  that  of  giving  a  tem- 
perature which  is  constant  for  a  long  time,  for  the  mass  of  water  only  cools 
slowly.  It  is  much  used  in  hothouses,  baths,  artificial  incubation,  drying 
rooms,  and  generally  wherever  a  uniform  temperature  is  desired. 


SOURCES  OF  COLD. 

493.  Various  sources  of  cold. — Besides  the  cold  caused  by  the  passage 
of  a  body  from  a  solid  to  the  liquid  state,  of  which  we  have  already  spoken, 
cold  is  produced  by  the  expansion  of  gases,  by  radiation  in  general,  and  more 
especially  by  nocturnal  radiation. 


428 


On  Heat. 


[494- 


494.  Cold  produced  by  the  expansion  of  erases.     Zee  machines. — We 

have  seen  that  when   a  gas  is  compressed,  the   temperature  rises.      The 
reverse   of  this  is  also   the  case  :    when  a  gas  is   rarefied,  a  reduction  of 

temperature  ensues, 
because  a  quantity 
of  sensible  heat  dis- 
appears when  the 
gas  becomes  in- 
creased to  a  larger 
volume.  This  may 
be  shown  by  placing 
a  delicate  Breguet's 
thermometer  under 
the  receiver  of  an 
air  -  pump,  and  ex- 
hausting ;  at  each 
stroke  of  the  piston 
the  needle  moves  in 
the  direction  of  zero, 
and  regains  its 
original  temperature 
when  air  is  admitted. 
The  production 
of  cold  when  a  gas 
is  expanded  has  been 
extensively  applied 
in  machines  for  arti- 
ficial refrigeration  on 
a  large  scale.  By 


Fig.  384- 


Windhausen's  ice  machine,  by  means  of  a  steam-engine  of  from  6  to  20  horse- 
power, from  15,000  to  1 50,000  feet  of  air  can  be  cooled  in  an  hour,  through  40 
to  100  degrees  in  temperature.  The  essential  parts  of  this  machine  are  repre- 
sented in  fig.  385.  The  piston  B  in  the  cylinder  A  is  worked  to  the  right  by  a 
steam-engine  and  to  the  left  by  a  steam-engine  and  by  the  compressed  air. 
As  it  moves  towards  the  right  the  valve  a  opens,  and  air  under  the  ordinary 
atmospheric  pressure  enters  the  space  Ar  When  this  is  full  the  piston  moves 
towards  the  left,  the  air  in  A  is  compressed  to  about  2  atmospheres,  the 
valve  a  is  closed,  the  valve  b  opens,  and  air  passes  in  the  direction  of  the 
arrows  into  the  cooler,  C.  By  its  compression  it  has  become  strongly 
heated,  and  the  necessary  cooling  is  effected  by  means  of  pipes  through 
which  cold  water  circulates,  entering  at  5  and  emerging  at  6.  The  air,  thus 
compressed  and  cooled,  passes  out  through  the  valve  c,  which  is  automatically 
worked  by  the  machine,  into  the  space  A2,  where,  in  conjunction  with  the 
steam-engine,  it  moves  the  piston  to  the  left,  and  compresses  the  air  in  A1  ; 
for  at  a  certain  position  of  the  piston  the  valve  c  is  closed,  the  compressed 
air  in  the  cylinder  A3  expands,  and  thereby  is  cooled  far  below  the  freezing 
point.  As  the  piston  moves  again  to  the  right,  the  valve  d  is  opened  by  the 
working  of  the  machine,  and  the  cooled  air  emerges  through  the  tube  4  to 
its  destination.  If  it  passes  into  an  ordinary  room  it  fills  it  with  snowflakes. 
Machines  of  this  kind  are  extensively  employed  in  the  arts ;  in  breweries, 


-496]  Absolute  Zero  of  Temperature.  429 

oil  refineries,  in  the  artificial  production  of  ice,  in  cooling  rooms  for  the 
transport  of  dead  meat,  &c. 

495.  Cold  produced  toy  nocturnal  radiation. — During  the  day,  the 
ground  receives  from  the  sun  more  heat  than  radiates  into  space,  and  the 
temperature  rises.  The  reverse  is  the  case  during  night.  The  heat  which 
the  earth  loses  by  radiation  is  no  longer  compensated  for,  and  consequently 


Fig.  385- 

a  fall  of  temperature  takes  place,  which  is  greater  according  as  the  sky  is 
clearer,  for  clouds  send  towards  the  earth  rays  of  greater  intensity  than 
those  which  come  from  the  celestial  spaces.  In  some  winters  it  has  been 
found  that  rivers  have  not  frozen,  the  sky  having  been  cloudy,  although  the 
thermometer  has  been  for  several  days  below  —4°;  while  in  other  less 
severe  winters  the  rivers  freeze  when  the  sky  is  clear.  The  emissive  power 
exercises  a  great  influence  on  the  cold  produced  by  radiation ;  the  greater  it 
is,  the  greater  is  the  cold. 

In  Bengal,  the  nocturnal  cooling  is  used  in  manufacturing  ice.  Large 
flat  vessels  containing  water  are  placed  on  non-conducting  substances,  such 
as  straw  or  dry  leaves.  In  consequence  of  the  radiation  the  water  freezes, 
even  when  the  temperature  of  the  air  is  10°  C.  The  same  method  can  be 
applied  in  all  cases  with  a  clear  sky. 

It  is  said  that  the  Peruvians,  in  order  to  preserve  the  shoots  of  young 
plants  from  freezing,  light  great  fires  in  their  neighbourhood,  the  smoke  of 
which,  producing  an  artificial  cloud,  hinders  the  cooling  produced  by  radiation. 

496.  Absolute  zero  of  temperature — As  a  gas  is  increased  ^  of  its 
volume  for  each  degree  Centigrade,  it  follows  that  at  a  temperature  of  273° 
C.  the  volume  of  any  gas  measured  at  zero  is  doubled.  In  like  manner,  if 
the  temperature  of  a  given  volume  at  zero  were  lowered  through  -  273°,  the 
contraction  would  be  equal  to  the  volume  :  that  is,  the  volume  would  not 
exist.  At  this  temperature  the  motion  of  the  molecules  of  the  gas  would 
completely  cease,  and  the  pressure  thereby  occasioned.  In  all  probability, 
before  reaching  this  temperature,  gases  would  undergo  some  change. 

This  point  on  the  Centigrade  scale  is  called  the  absolute  zero  of  tempera- 
ture ;  the  temperatures  reckoned  from  this  point  are  called  absolute  tem- 
peratures. They  are  clearly  obtained  by  adding  273  to  the  temperature  on 
the  Centigrade  scale.  Thus  -35°  C.  is  238°  on  the  absolute  scale  of  tem- 
perature, and  +  15°  C.  is  288°. 


43o  On  Heat.  [497- 


CHAPTER   XII. 

MECHANICAL  EQUIVALENT   OF   HEAT. 

497.  Mechanical  equivalent  of  heat. — If  the  various  instances  of  the 
production  of  heat  by  motion  be  examined,  it  will  be  found  that  in  all  cases 
mechanical  force  is  consumed.  Thus  in  rubbing  two  bodies  against  each 
other,  motion  is  apparently  destroyed  by  friction  ;  it  is  not,  however,  lost, 
but  appears  in  the  form  of  a  motion  of  the  particles  of  the  body  ;  the  motion 
of  the  mass  is  transformed  into  a  motion  of  the  molecules. 

Again,  if  a  body  be  allowed  to  fall  from  a  height,  it  strikes  against  the 
ground  with  a  certain  velocity.  According  to  older  views,  its  motion  is  de- 
stroyed, vis  viva  is  lost.  This,  however,  is  not  the  case ;  the  vis  viva  of 
the  body  appears  as  vis  viva  of  its  molecules. 

In  the  case,  too,  of  chemical  action,  the  most  productive  artificial  source 
of  heat,  it  is  not  difficult  to  conceive  that  there  is,  in  the  act  of  combining, 
an  impact  of  the  dissimilar  molecules  against  each  other,  an  effect  analogous 
to  the  production  of  heat  by  the  impact  of  masses  of  matter  against  each 
other  (483). 

In  like  manner,  heat  may  be  made  to  produce  motion,  as  in  the  case  of 
the  steam-engine,  and  the  propulsion  of  shot  from  a  gun. 

Traces  of  a  view  that  there  is  a  connection  between  heat  and  motion  are 
to  be  met  with  in  the  older  writers,  Bacon  for  example  ;  and  Locke  says, 
'  Heat  is  a  very  brisk  agitation  of  the  insensible  parts  of  the  object,  which 
produces  in  us  that  sensation  from  whence  we  denominate  the  object  hot  ; 
so  that  what  in  our  sensation  is  heat,  in  the  object  is  nothing  but  motion.3 
Rumford,  in  explaining  his  great  experiment  of  the  production  of  heat  by 
friction,  was  unable  to  assign  any  other  cause  for  the  heat  produced  than 
motion  ;  and  Davy,  in  the  explanation  of  his  experiment  of  melting  ice  by 
friction  in  vacua,  expressed  similar  views.  Carnot,  in  a  work  on  the  steam- 
engine,  published  in  1824,  also  indicated  a  connection  between  heat  and 
work. 

The  views,  however,  which  had  been  stated  by  isolated  writers  had  little 
or  no  influence  on  the  progress  of  scientific  investigation,  and  it  is  in  the 
year  1842  that  the  modern  theories  may  be  said  to  have  had  their  origin. 
In  that  year  Dr.  Mayer,  a  physician  in  Heilbronn,  formally  stated  that  there 
exists  a  connection  between  heat  and  work  ;  and  he  it  was  who  first  intro- 
duced into  science  the  expression  '  mechanical  equivalent  of  heat?  Mayer 
also  gave  a  method  by  which  this  equivalent  could  be  calculated  ;  the  par- 
ticular results,  however,  are  of  no  value,  as  the  method,  though  correct  in 
principle,  is  founded  on  incorrect  data. 

In  the  same  year,  too,  Colding  of  Copenhagen  published  experiments  on 


-497J 


Mechanical  Equivalent  of  Heat. 


431 

the  production  of  heat  by  friction,  from  which  he  concluded  that  the  evolu- 
tion of  heat  was  proportional  to  the  mechanical  energy  expended. 

About  the  same  time  as  Mayer,  but  quite  independently  of  him,  Joule 
commenced  a  series  of  experimental  investigations  on  the  relation  between 
heat  and  work.  These  first  drew  the  attention  of  scientific  men  to  the  sub- 
ject, and  were  admitted  as  a  proof  that  the  transformation  of  heat  into  me- 
chanical energy,  or  of  mechanical  energy  into  heat,  always  takes  place  in  a 
definite  numerical  ratio. 

Subsequently  to  Mayer  and  Joule,  several  physicists,  by  their  theoretical 
and  experimental  investigations,  have  contributed  to  establish  the  mechanical 
theory  of  heat  :  namely,  in  this  country,  Sir  W.  Thomson  and  Rankine  ;  in 
Germany,  Helmholtz,  Clausius,  and  Holtzmann  ;  and  in  France,  Clapeyron 
and  Regnault. 

The  following  are  some  of  the  most  important  and  satisfactory  of  Joule's 
experiments. 

A  copper  vessel,  B  (fig.  386),  was  provided  with  a  brass  paddle-wheel 
(indicated  by  the  dotted  lines),  which  could  be  made  to  rotate  about  a 


Fig.  386 


vertical  axis.  Two  weights,  E  and  F,  were  attached  to  cords  which  passed 
over  the  pulleys  C  and  D,  and  were  connected  with  the  axis  A.  These 
weights  in  falling  cause  the  wheel  to  rotate.  The  height  of  the  fall,  which  in 
Joule's  experiments  was  about  63  feet,  was  indicated  on  the  scales  G  and  H. 
The  roller  A  was  so  constructed  that  by  detaching  a  pin  the  weights  could 
be  raised  without  moving  the  wheel.  The  vessel  B  was  filled  with  water 
and  placed  on  a  stand,  and  the  weights  allowed  to  sink.  When  they  had 
reached  the  ground,  the  roller  was  detached  from  the  axis, 'and  the  weights 
again  raised,  the  same  operations  being  repeated  20  times.  The  heat  pro- 
duced was  measured  by  ordinary  calorimetric  methods  (447). 

The  work  expended  is  measured  by  the  product  of  the  weight  into  the 
height  through  which  it  falls,  or  ph,  less  the  work  lost  by  the  friction  of  the 
various  parts  of  the  apparatus.  This  is  diminished  as  far  as  possible  by  the 
use  of  friction  wheels  (78),  and  its  amount  is  determined  by  connecting  C 


432  On  Heat.  [497- 

and  D  without  causing  them  to  pass  over  A,  and  then  determining  the 
weight  necessary  to  communicate  to  them  a  uniform  motion. 

In  this  way  it  has  been  found  that  a  thermal  unit — that  is,  the  quantity  of 
heat  by  which  a  pound  of  water  is  raised  through  i°  C— is  generated  by  the 
expenditure  of  the  same  amount  of  work  as  would  be  required  to  raise  1,392 
pounds  through  I  foot,  or  i  pound  through  1,392  feet.  This  is  expressed  by 
saying  that  the  mechanical  equivalent  of  the  thermal  unit  is  1,392  foot- 
pounds. 

The  friction  of  an  iron  paddle-wheel  in  mercury  gave  1,397  foot-pounds, 
and  that  of  the  friction  of  two  iron  plates  gave  1,395  foot-pounds,  as  the 
mechanical  equivalent  of  one  thermal  unit. 

In  another  series  of  experiments,  the  air  in  a  receiver  was  compressed 
by  means  of  a  force  pump,  both  being  immersed  in  a  known  weight  of  water 
at  a  known  temperature.  After  300  strokes  of  the  piston,  the  heat,  C,  was 
measured  which  the  water  had  gained.  This  heat  was  due  to  the  compression 
of  the  air  and  to  the  friction  of  the  piston.  To  eliminate  the  latter  influence, 
the  experiment  was  made  under  the  same  conditions,  but  leaving  the  re- 
ceiver open.  The  air  was  not  compressed,  and  300  strokes  of  the  piston 
developed  C'  thermal  units.  Hence  C  — C'  is  the  heat  produced  by  the  com- 
pression of  the  gas.  Representing  the  foot-pounds  expended  in  producing 

this  heat  by  W,  we  have  — ,  for  the  value  of  the  mechanical  equivalent* 

By  this  method  Joule  obtained  the  number  1,442. 

The  mean  number  which  Joule  adopted  for  the  mechanical  equivalent  of 
one  thermal  unit  on  the  Centigrade  scale  is  1,390  foot-pounds  ;  on  the 
Fahrenheit  scale  it  is  772  foot-pounds.  The  number  is  called  Joules  equi- 
valent, and  is  usually  designated  by  the  symbol  J. 

On  the  metrical  system  424  metres  usually  are  taken  as  the  height  through 
which  a  kilogramme  of  water  must  fall^  to  raise  its  temperature  I  degree 
Centigrade. 

Professor  Rowland  of  Baltimore  has  recently  made  a  very  careful  and 
complete  determination  of  the  mechanical  equivalent  of  heat,  by  Joule's 
method,  in  which  he  has  examined  and  allowed  for  all  possible  sources  of 
error.  His  results  give  426-9  kilogramme  metres  as  the  mean  value  of  this 
constant  for  the  latitude  of  Baltimore. 

Hirn  has  made  the  following  determination  of  the  mechanical  equivalent 
by  means  of  the  heat  produced  by  the  compression  of  lead.  A  large  block 
of  sandstone,  CD  (fig.  387),  is  suspended  vertically  by  cords  ;  its  weight  is  P. 
E  is  a  piece  of  lead,  fashioned  so  that  its  temperature  may  be  determined 
by  the  introduction  of  a  thermometer.  The  weight  of  this  is  II,  and  its 
specific  heat  c.  AB  is  a  cylinder  of  cast  iron,  whose  weight  is^.  If  this  be 
raised  to  A'B',  a  height  of  h,  and  allowed  to  fall  again,  it  compresses  the 
lead,  E,  against  the  anvil,  CD.  It  remains  to  measure  on  the  one  hand  the 
work  lost,  and  on  the  other  the  heat  gained. 

The  hammer  AB  being  raised  to  a  height  ^,  the  work  of  its  fall  is  ph  \ 
but  as,  by  its  elasticity,  it  rises  again  to  a  height  h^  the  work  is  p  (h  —  h^). 
The  anvil,  CD,  on  the  other  hand,  has  been  raised  through  a  height  H  to  C'D', 
and  has  required  in  so  doing  PH  units  of  work.  The  work,  W,  definitely 
absorbed  by  the  lead  is  p(h—h^  —  'Pl{.  On  the  other  hand,  the  lead  has 


-497]  MecJianical  Equivalent  of  Heat.  433 

been  heated  by  6,  it  has  gained  UcO  thermal  units,  c  being  the  specific  heat 
of  lead,  and  the  mechanical  equivalent  J  is  equal  to  the  quotient   -W .     A 


Fig.  387- 

series  of  six  experiments  gave  1,394  for  the  mechanical  equivalent  as  thus 
obtained. 

The  following  is  the  method  which  Mayer  employed  in  calculating  the 
mechanical  equivalent  of  heat.  It  is  taken,  with  slight  modifications,  from 
Prof.  Tyndall's  work  on  Heat^  who,  while  strictly  following  Mayer's  reason- 
ing, has  corrected  his  data. 

Let  us  suppose  that  a  rectangular  vessel  with  a  section  of  a  square  foot 
contains  at  o°  a  cubic  foot  of  air  under  the  ordinary  atmospheric  pressure  ; 
and  let  us  suppose  that  it  is  enclosed  by  a  piston  without  weight. 

Suppose  now  that  the  cubic  foot  of  air  is  heated  until  its  volume  is 
doubled  ;  from  the  coefficient  of  expansion  of  air  we  know  that  this  is  the 
case  at  273°  C.  The  gas  in  doubling  its  volume  will  have  raised  the  piston 
through  a  foot  in  height ;  it  will  have  lifted  the  atmospheric  pressure  through 
this  distance.  But  the  atmospheric  pressure  on  a  square  foot  is  in  round 
numbers  15  x  144  =  2,160  pounds.  Hence  a  cubic  foot  of  air,  in  doubling  its 
volume,  has  lifted  a  weight  of  2,160  pounds  through  a  height  of  a  foot. 

Now  a  cubic  foot  of  air  at  zero  weighs  i'2g  ounce,  and  the  specific  heat 
of  air  under  constant  pressure — that  is,  when  it  can  expand  freely — as  com- 
pared with  that  of  an  equal  weight  of  water,  is  0*24  ;  so  that  the  quantity 
of  heat  which  will  raise  1-29  ounce  of  air  through  273°  will  only  raise 
0-24  x  i -29  =  0-3 1  oz.  of  water  through  the  same  temperature  ;  but  0-31  oz.  of 
water  raised  through  273°  is  equal  to  5-29  pounds  of  water  raised  through 
i°C. 

That  is,  the  quantity  of  heat  which  will  double  the  volume  of  a  cubic  foot 
of  air,  and  in  so  doing  will  lift  2,160  pounds  through  a  height  of  a  foot,  is 
5-29  thermal  units. 

Now  in  the  above  case  the  gas  has  been  heated  under  constant  pressure, 
that  is,  when  it  could  expand  freely.  If,  however,  it  had  been  heated  under 
constant  volume,  its  specific  heat  would  have  been  less  in  the  ratio  i  :  1*414 
(460),  so  that  the  quantity  of  heat  required  under  these  circumstances  to 

raise  the  temperature  of  a  cubic  foot  of  air  would  be  5-29  x     |     =  374.     De- 

U 


434 


On  Heat. 


[497- 


ducting  this  from  5*29,  the  difference  1-55  represents  the  weight  of  water 
which  would  have  been  raised  i°  C.  by  the  excess  of  heat  imparted  to  the 
air  when  it  could  expand  freely.  But  this  excess  has  been  consumed  in  the 
work  of  raising  2,160  pounds  through  a  foot.  Dividing  this  by  1-55  we  have 
1,393.  Hence  the  heat  which  will  raise  a  pound  of  water  through  i°  C.  will 
raise  a  weight  of  1,393  pounds  through  a  height  of  a  foot ;  a  numerical  value 
of  the  mechanical  equivalent  of  heat  agreeing  as  closely  as  can  be  expected 
with  that  which  Joule  adopted  as  the  most  certain  of  his  experimental 
results. 

The  law  of  the  relation  of  heat  to  mechanical  energy  may  be  thus  stated : — 
Heat  and  mechanical  energy  are  mutually  convertible;  and  heat  reqtiires  for 
its  production,  and  produces  by  its  disappearance,  mechanical  energy  in  the 
ratio  of  1,390  foot-pounds  for  every  thermal  unit. 

A  variety  of  experiments  may  in  like  manner  be  adduced  to  show  that 
whenever  heat  disappears  work  is  produced.  For  example,  if  in  a  reservoir 
immersed  in  water  the  air  be  compressed  to  the  extent  of  10  atmospheres  : 
supposing  that  now,  when  the  compressed  air  has  acquired  the  temperature 
of  the  water,  it  be  allowed  to  act  upon  a  piston  loaded  by  a  weight,  the 
weight  is  raised.  At  the  sa,me  time  the  water  becomes  cooler,  showing  that 
a  certain  quantity  of  heat  had  disappeared  in  producing  the  mechanical 
effort  of  raising  the  weight.  This  may  also  be  illustrated  by  the  following 
experiment,  due  to  Prof.  Tyndall  : — 

A  strong  metal  box  is  taken,  provided  with  a  stopcock,  on  which  can  be 
screwed  a  small  condensing  pump.  Haying  compressed  the  air  by  its  means 
as  it  becomes  heated  by  this  process,  the  box  is  allowed  to  stand  for  some 


time,  until  it  has  acquired  the  temperature  of  the  surrounding  medium.  On 
opening  the  stopcock,  the  air  rushes  out ;  it  is  expelled  by  the  expansive 
force  of  the  internal  air  ;  in  short,  the  air  drives  itself  out.  Work  is  there- 
fore performed  by  the  air,  and  there  should  be  a  disappearance  of  heat  ; 
and  if  the  jet  of  air  be  allowed  to  strike  against  the  thermo-pile,  the  galvano- 


-498] 


Dissipation  of  Energy. 


435 


meter  is  deflected,  and  the  direction  of  its  deflection  indicates  a  cooling 
(fig.  388).  The  same  effect  is  observed  when,  on  opening  a  bottle  of 
soda  water,  the  carbonic  gas  which  escapes  is  allowed  to  impinge  against 
the  thermo-pile. 

If,  on  the  contrary,  the  experiment  is  made  with  an  ordinary  pair  of 
bellows,  and  the  current  of  air  is  allowed  to  strike  against  the  pile, 
the  deflection  of  the  galvanometer  is  in  the  opposite  direction,  indicating 
an  increase  of  temperature  (fig.  389).  In  this  case  the  hand  of  the  experi- 
menter performs  the  work,  which  is  converted  into  heat. 

Joule  placed  in  a  calorimeter  two  equal  copper  reservoirs,  which  could 
be  connected  by  a  tube.  One  of  these  contained  air  at  22  atmospheres,  the 
other  was  exhausted.  When  they  were  connected,  they  came  into  equili- 
brium under  a  pressure  of  1 1  atmospheres  ;  but  as  the  gas  in  expanding  had 
done  no  work,  there  was  no  alteration  in  temperature.  When,  however,  the 


Fig.  389. 

second  reservoir  was  full  of  water,  the  air  in  entering  was  obliged  to  expel 
it  and  thus  perform  work,  and  the  temperature  sank,  owing  to  an  absorption 
of  heat. 

For  further  information  the  student  of  this  subject  is  referred  to  the 
following  works  : — Tyndall  on  Heat  as  a  Mode  of  Motion,  Maxwell  on  Heat, 
Wormell's  Thermodynamics  (Longmans),  and  Tait  on  Thermodynamics 
(Edmonston  and  Douglas).  A  condensed,  though  complete  and  systematic 
account  of  the  dynamical  theory  of  heat  is  met  with  in  Professor  Foster's 
articles  on  'Heat,'  in  Watts's  Dictionary  of  Chemistry. 

498.  Dissipation  of  energy. — Rankine  has  the  following  interesting 
observations  on  a  remarkable  consequence  of  the  mutual  convertibility  which 
has  been  shown  to  exist  between  heat  and  other  fonns  of  energy  : — Sir  W. 
Thomson  has  pointed  out  the  fact  that  there  exists,  at  least  in  the  present 
state  of  the  known  world,  a  predominating  tendency  to  the  conversion  of  all 
the  other  forms  of  physical  energy  into  heat,  and  to  the  uniform  diffusion  of 
all  heat  throughout  all  matter.  The  form  in  which  we  generally  find  energy 
originally  collected  is  that  of  a  store  of  chemical  power  consisting  of  uncom- 

U  2 


436  On  Heat  [498- 

bined  elements.  The  combination  of  these  elements  produces  energy  in  the 
form  known  by  the  name  of  electrical  currents,  part  only  of  which  can  be 
employed  in  analysing  chemical  compounds,  and  thus  reconverted  into  a 
store  of  chemical  power ;  the  remainder  is  necessarily  converted  into  heat  ; 
a  part  only  of  this  heat  can  be  employed  in  analysing  compounds  or  in  re- 
producing electric  currents.  If  the  remainder  of  the  heat  be  employed  in 
expanding  an  elastic  substance,  it  may  be  converted  entirely  into  visible 
motion,  or  into  a  store  of  visible  mechanical  power  (by  raising  weights,  for 
example),  provided  the  elastic  substance  is  enabled  to  expand  until  its 
temperature  falls  to  the  point  which  corresponds  to  the  absolute  privation 
of  heat ;  but  unless  this  condition  is  fulfilled,  a  certain  proportion  only  of 
the  heat,  depending  on  the  range  of  temperature  through  which  the  elastic 
body  works,  can  be  converted,  the  rest  remaining  in  the  state  of  heat.  On 
the  other  hand,  all  visible  motion  is  of  necessity  ultimately  converted  into 
heat  by  the  agency  of  friction.  There  is,  then,  in  the  present  state  of  the 
known  world,  a  tendency  towards  the  conversion  of  all  physical  energy  into 
the  sole  form  of  heat. 

Heat,  moreover,  tends  to  diffuse  itself  uniformly  by  conduction  and 
radiation,  until  all  matter  shall  have  acquired  the  same  temperature.  There 
Is,  consequently,  so  far  as  we  understand  the  present  condition  of  the 
universe,  a  tendency  towards  a  state  in  which  all  physical  energy  will  be  in 
the  state  of  heat,  and  that  heat  so  diffused,  that  all  matter  will  be  at  the 
same  temperature  ;  so  that  there  will  be  an  end  of  all  physical  phenomena. 

Vast  as  this  speculation  may  seem,  it  appears  to  be  soundly  based  on 
experimental  data,  and  to  truly  represent  the  present  condition  of  the  uni- 
verse as  far  as  we  know  it. 


-499]  Theories  of  Light.  437 


BOOK   VII. 

ON   LIGHT. 


CHAPTER    I. 
TRANSMISSION,   VELOCITY,   AND   INTENSITY  OF   LIGHT. 

499.  Theories  of  light. — Light  is  the  agent  which,  by  its  action  on  the 
retina,  excites  in  us  the  sensation  of  vision.  That  part  of  physics  which  deals 
with  the  properties  of  light  is  known  as  optics. 

In  order  to  explain  the  origin  of  light,  various  hypotheses  have  been  made, 
the  most  important  of  which  are  the  emission  or  corpuscular  theory,  and  the 
undulatory  theory. 

On  the  emission  theory  it  is  assumed  that  luminous  bodies  emit,  in  all 
directions,  an  imponderable  substance,  which  consists  of  molecules  of  an 
extreme  degree  of  tenuity  ;  these  are  propagated  in  right  lines  with  an  almost 
infinite  velocity.  Penetrating  into  the  eye  they  act  on  the  retina,  and  deter- 
mine the  sensation  which  constitutes  vision. 

On  the  undulatory  theory,  all  bodies,  as  well  as  the  celestial  spaces,  are 
filled  by  an  extremely  subtle  elastic  medium,  which  is  called  the  luminiferous 
ct/icr.  The  luminosity  of  a  body  is  due  to  an  infinitely  rapid  vibratory  motion 
of  its  molecules,  which,  when  communicated  to  the  ether,  is  propagated  in  all 
directions  in  the  form  of  spherical  waves,  and  this  vibratory  motion,  being 
thus  transmitted  to  the  retina,  calls  forth  the  sensation  of  vision.  The 
vibrations  of  the  ether  take  place  not  in  the  direction  of  the  wave,  but  in  a 
plane  at  right  angles  to  it.  The  latter  are  called  the  transversal  vibrations. 
An  idea  of  these  may  be  formed  by  shaking  a  rope  at  one  end.  The  vibra- 
tions, or  to  and  fro  movements,  of  the  particles  of  the  rope,  are  at  right 
angles  to  the  length  of  the  rope,  but  the  onward  motion  of  the  wave's  form 
is  in  the  direction  of  the  length. 

On  the  emission  theory  the  propagation  of  light  is  effected  by  a  motion 
of  translation  of  particles  of  light  thrown  out  from  the  luminous  body,  as  a 
bullet  is  discharged  from  a  gun  ;  on  the  undulatory  theory  there  is  no  pro- 
gressive motion  of  the  particles  themselves,  but  only  of  the  state  of  disturb- 
ance which  was  communicated  by  the  luminous  body  ;  it  is  a  motion  of 
oscillation,  and,  like  the  propagation  of  waves  in  water,  takes  place  by  a  series 
of  vibrations. 

The  luminiferous  ether  penetrates  all  bodies,  but  on  account  of  its 
extreme  tenuity  it  is  uninfluenced  by  gravitation  ;  it  occupies  space,  and 
although  it  presents  no  appreciable  resistance  to  the  motion  of  the  denser 
bodies,  it  is  possible  that  it  hinders  the  motion  of  the  smaller  comets.  It  has 


438  On  Light.  [499- 

been  found,  for  example,  that  Encke's  comet,  whose  period  of  revolution  is 
about  3|  years,  has  its  period  diminished  by  about  o-ii  of  a  day  at  each 
successive  rotation,  and  this  diminution  is  ascribed  by  some  to  the  resistance 
of  the  ether. 

The  fundamental  principles  of  the  undulatory  theory  were  enunciated  by 
Huyghens,  and  subsequently  by  Euler.  The  emission  theory,  principally 
owing  to  Newton's  powerful  support,  was  for  long  the  prevalent  scientific 
creed.  The  undulatory  theory  was  adopted  and  advocated  by  Young,  who 
showed  how  a  large  number  of  optical  phenomena,  particularly  those  of 
diffraction,  were  to  be  explained  by  that  theory.  Subsequently  to,  though 
independently  of,  Young,  Fresnel  showed  that  the  phenomena  of  diffraction, 
and  also  that  of  polarisation,  are  explicable  on  the  same  theory,  which,  since 
his  time,  has  been  generally  accepted. 

The  undulatory  theory  not  only  explains  the  phenomena  of  light,  but  it 
reveals  an  intimate  connection  between  these  phenomena  and  those  of  heat 
(429) ;  it  shows,  also,  how  completely  analogous  the  phenomena  of  light  are 
to  those  of  sound,  regard  being  had  to  the  differences  of  the  media  in  which 
these  two  classes  of  phenomena  take  place. 

500.  Xiuminous,  transparent,  translucent,  and  opaque  bodies. — Lumi- 
nous bodies  are  those  which  emit  light,  such  as  the  sun,  and  ignited  bodies. 
Transparent  or  diaphanous  bodies  are  those  which  readily  transmit  light, 
and  through  which  objects  can  be  distinguished ;  water,  gases,  polished  glass, 
are  of  this  kind.     Translucent  bodies  transmit  light,  but  objects  cannot  be 
distinguished  through  them  :  ground  glass,  oiled  paper,  &c.,  belong  to  this 
class.     Opaque  bodies  do  not  transmit  light ;  for  example,  wood,  metals,  £c. 
No  bodies  are  quite  opaque ;  they  are  all  more  or  less  translucent  when  cut 
in  sufficiently  thin  leaves. 

Foucault  has  shown  that  when  the  object  glass  of  a  telescope  is  thinly 
silvered,  the  layer  is  so  transparent  that  the  sun  can  be  viewed  through  it 
without  danger  to  the  eyes,  since  the  metallic  surface  reflects  the  greater 
part  of  the  heat  and  light. 

501.  luminous  ray  and  pencil. — A  luminous  ray  is  the  direction  of  the 
line  in  which  light  is  propagated  ;  a  luminous  pencil  is  a  collection  of  rays 
from  the  same  source  ;  it  is  said  to  be  parallel  when   it  is  composed  of 
parallel  rays,  divergent  when  the  rays  separate  from  each  other,  and  con- 
vergent when  they  tend  towards  the  same  point.    Every  luminous  body  emits 
divergent  rectilinear  rays  from  all  its  points,  and  in  all  directions. 

502.  Propagation  of  light  in  a  homogeneous  medium. — A  medium  is 
any  space  or  substance  which  light  can  traverse,  such  as  a  vacuum,  air,  water, 
glass,  &c.     A  medium  is  said  to  be  homogeneous  when  its  chemical  compo- 
sition and  density  are  the  same  in  all  parts. 

In  every  homogeneous  medium  light  is  propagated  in  a  right  line.  For, 
if  an  opaque  body  is  placed  in  the  right  line  which  joins  the  eye  and  the 
luminous  body,  the  light  is  intercepted.  The  light  which  passes  into  a  dark 
room  by  a  small  aperture  leaves  a  luminous  trace,  which  is  visible  from  the 
light  falling  on  the  particles  of  dust  suspended  in  the  atmosphere. 

Light  changes  its  direction  on  meeting  an  object  which  it  cannot  pene- 
trate, or  when  it  passes  from  one  medium  to  another.  These  phenomena 
will  be  described  under  the  heads  reflection  and  refraction. 


-503]  Shadow,  Penumbra.  439 

503.  Shadow,  penumbra.— When  light  falls  upon  an  opaque  body  it 
cannot  penetrate  into  the  space  immediately  behind  it,  and  this  space  is 
called  the  shadow. 

In  determining  the  extent  and  the  shape  of  a  shadow  projected  by  a  body, 
two  cases  are  to  be  distinguished ;  that  in  which  the  source  of  light  is  a 
single  point,  and  that  in  which  it  is  a  body  of  any  given  extent. 

In  the  first  case,  let  S  (fig.  390)  be  the  luminous  point,  and  M  a  spherical 
body,  which  causes  the  shadow.     If  an  infinitely  long   straight  line,  SG, 
move  round  the 
sphere    M    tan- 
gentially,  always 
passing  through 
the  point  S,  this 
line  will  produce 
a     conical    sur- 
face, which,  be- 
yond the  sphere,  Fig.  390. 
separates      that 

portion  of  space  which  is  in  shadow  from  that  which  is  illuminated.  In  the 
present  case,  on  placing  behind  the  opaque  body  a  screen,  PQ,  the  limit 
of  the  shadow  HG  will  be  sharply  defined.  This  is  not,  however,  usually 
the  case,  for  luminous  bodies  have  always  a  certain  magnitude,  and  are  not 
merely  luminous  points. 

vSuppose  that  the  luminous  and  illuminated  bodies  are  two  spheres,  SL 
and  MN  (fig.  391).     If  an  infinite  straight  line,  AG,  moves  tangentially  to 
both  spheres,  al- 
ways cutting  the 
line  of  the  centre 
in  the  point  A,  it 
will    produce     a 
conical      surface 
with    this    point 
for  a  summit,  and 
which  traces  be- 
hind the  sphere  Fig.  39i. 
MN    a   perfectly 

dark  space,  MGHN.  If  a  second  right  line,  LD,  which  cuts  the  line  of 
centre  in  B,  moves  tangentially  to  the  two  spheres,  so  as  to  produce  a  new 
conical  surface,  BDC,  it  will  be  seen  that  all  the  space  outside  this  surface 
is  illuminated,  but  that  the  part  between  the  two  conical  surfaces  is  neither 
quite  dark  nor  quite  light.  So  that  if  a  screen,  PQ,  is  placed  behind  the 
opaque  body,  the  portion  cGdH  of  the  screen  is  quite  in  the  shadow,  while 
the  space  ab  receives  light  from  certain  parts  of  the  luminous  body,  and  not 
from  others.  It  is  brighter  than  the  true  shadow,  and  not  so  bright  as  the 
rest  of  the  screen,  and  it  is  accordingly  called  the  penumbra. 

Shadows  such  as  these  are  geometrical  shadows;  physical  shadows,  or 
those  which  are  really  seen,  are  by  no  means  so  sharply  defined.  A  certain 
quantity  of  light  passes  into  the  shadow,  even  when  the  source  of  light  is  a 
mere  point,  and  conversely  the  shadow  influences  the  illuminated  part.  This 


440  On  Light.  [503- 

phenomenon,  which  will  be  afterwards  described,  is  known  by  the  name  of 
diffraction  (646). 

504.  Images  produced  by  small  apertures.— When  luminous  rays, 
which  pass  into  a  dark  chamber  through  a  small  aperture,  are  received  upon 
a  screen,  they  form  images  of  external  objects.  These  images  are  inverted, 
their  shape  is  always  that  of  the  external  objects,  and  is  independent  of  the 
shape  of  the  aperture. 

The  inversion  of  the  images  arises  from  the  fact  that  the  luminous  rays 
proceeding  from  external  objects,  and  penetrating  into  the  chamber,  cross 
one  another  in  passing  the  aperture,  as  shown  in  fig.  392.  Continuing  in  a 

straight  line,  the 
rays  from  the 
higher  parts  meet 
the  screen  at  the 
lower  parts,  and, 
conversely,  those 
which  come  from 
the  lower  parts 
meet  the  higher 
Fig.  392.  parts  of  the  screen. 

Hence  the  inver- 
sion of  the  image.  In  the  article  Camera  Obscura,  it  will  be  seen  how  the 
brightness  and  precision  of  these  images  are  increased  by  means  of  lenses. 

In  order  to  show  that  the  shape  of  the  image  is  independent  of  that  of 
the  aperture,  when  the  latter  is  sufficiently  small  and  the  screen  at  an  ade- 
quate distance,  imagine  a  triangular  aperture,  O  (fig.  393),  made  in  the  door 

of  a  dark  chamber, 
and  let  ab  be  a 
screen  on  which  is 
received  the  image 
of  a  flame,  AB.  A 
divergent  pencil 
from  each  point  of 
the  flame  penetrates 
through  the  aper- 
Fig.  393.  ture,  and  forms  on 

the  screen  a  triangu- 
lar image  resembling  the  aperture.  But  the  union  of  all  these  partial  images 
produces  a  total  image  of  the  same  form  as  the  luminous  object.  For  if  we 
conceive  that  an  infinite  straight  line  moves  round  the  aperture,  with  the  con- 
dition that  it  is  always  tangential  to  the  luminous  object  AB,  and  that  the 
aperture  is  very  small,  the  straight  line  describes  two  cones,  the  apex  of  which 
is  the  aperture,  while  one  of  the  bases  is  the  luminous  object  and  the  other  the 
luminous  object  on  the  screen — that  is,  the  image.  Hence,  if  the  screen  is 
perpendicular  to  the  right  line  joining  the  centre  of  the  aperture  and  the 
centre  of  the  luminous  body,  the  image  is  similar  to  the  body ;  but  if  the 
screen  is  oblique,  the  image  is  elongated  in  the  direction  of  its  obliquity. 
This  is  what  is  seen  in  the  shadow  produced  by  foliage  ;  the  luminous  rays 
passing  through  the  leaves  produce  images  of  the  sun,  which  are  either  round 


-506]        Apparatus  for  determining  the  Velocity  of  Light.       441 

or  elliptical,  according  as  the  ground  is  perpendicular  or  oblique  to  the  solar 
rays,  and  this  is  the  case  whatever  be  the  shape  of  the  aperture  through 
which  the  light  passes. 

505.  Velocity  of  light. — Light  moves  with  such  a  velocity  thatat  the  surface 
of  the  earth  there  is,  to  ordinary  observation,  no  appreciable  interval  between 
the  occurrence  of  any  luminous  phenomenon  and  its  perception  by  the  eye. 
And  accordingly,  this  velocity  was  first  determined  by  means  of  astronomical 
observations.  Romer,  a  Danish  astronomer,  in  1675,  first  deduced  the 
velocity  of  light  from  an  observation  of  the  eclipses  of  Jupiter's  first  satellite. 

Jupiter  is  a  planet,  round  which  four  satellites  revolve,  as  the  moon  does 
round  the  earth.  This  first  satellite,  E  (fig.  394),  suffers  occultation — that 
is,  passes  into  Jupi- 
ter's shadow  —  at 
equal  intervals  ol 
time,  which  are 
42h.  28m.  365. 
While  the  earth 
moves  in  that  part 
of  its  orbit,  ab, 
nearest  Jupiter,  its 
distance  from  that  Fig.  3^4. 

planet     does      not 

materially  alter,  and  the  intervals  between  two  successive  occultations  of 
the  satellite  are  approximately  the  same  ;  but,  in  proportion  as  the  earth 
moves  away  in  its  revolution  round  the  sun,  S,  the  interval  between  two 
occultations  increases,  and  when,  at  the  end  of  six  months,  the  earth  has 
passed  from  the  position  T  to  the  position  T',  a  total  retardation  of  i6m. 
365.  is  observed  between  the  time  at  which  the  phenomenon  is  seen  and 
that  at  which  it  is  calculated  to  take  place.  But  when  the  earth  was  in  the 
position  T,  the  sun's  light  reflected  from  the  satellite  E  had  to  traverse  the 
distance  ET,  while  in  the  second  position  the  light  had  'to  traverse  the 
distance  ET'.  This  distance  exceeds  the  first  by  the  quantity  TT',  for, 
from  the  great  distance  of  the  satellite  E,  the  rays  ET  and  ET'  may  be 
considered  parallel.  Consequently,  light  requires  i6m.  365.  to  travel  the 
diameter  TT'  of  the  terrestrial  orbit,  or  twice  the  distance  of  the  earth  from 
the  sun,  which  gives  for  its  velocity  190,000  miles  in  a  second. 

The  stars  nearest  the  earth  are  separated  from  it  by  at  least  206,265 
times  the  distance  of  the  sun.  Consequently,  the  light  which  they  send 
requires  3^  years  to  reach  us.  Those  stars,  which  are  only  visible  by  means 
of  the  telescope,  are  possibly  at  such  a  distance  that  thousands  of  years 
would  be  required  for  their  light  to  reach  our  planetary  system.  They  might 
have  been  extinguished  for  ages  without  our  knowing  it. 

506.  Foucault's  apparatus  for  determining:  tbe  velocity  of  light. — 
Notwithstanding  the  prodigious  velocity  of  light,  Foucault  has  succeeded  in 
determining  it  experimentally  by  the  aid  of  an  ingenious  apparatus,  based 
on  the  use  of  the  rotating  mirror,  which  was  adopted  by  Wheatstone  in 
measuring  the  velocity  of  electricity. 

In  the  description  of  this  apparatus,  a  knowledge  of  the  principal  pro- 
perties of  mirrors  and  of  lenses  is  presupposed.  Fig.  395  represents  the 


442  On  Light.  [506- 

principal  parts  of  Foucault's  arrangement.  The  window  shutter,  K,  of  a 
(lark  chamber  is  perforated  by  a  square  aperture,  behind  which  the  platinum 
wire,  0,  is  stretched  vertically.  A  beam  of  solar  light  reflected  from  the  out- 
side upon  a  mirror  enters  the  dark  room  by  the  square  aperture,  meets  the 
platinum  wire,  and  then  traverses  an  achromatic  lens,  L,  with  a  long  focus, 
placed  at  a  distance  from  the  platinum  wire  less  than  double  the  principal 
focal  distance.  The  image  of  the  platinum  wire,  more  or  less  magnified, 
would  thus  be  formed  on  the  axis  of  the  lens ;  but  the  luminous  pencil, 
having  traversed  the  lens,  impinges  on  a  plane  mirror,  m,  rotating  with  great 
velocity ;  it  is  reflected  from  this,  and  forms  in  space  an  image  of  the 
platinum  wire,  which  is  displaced  with  an  angular  velocity  double  that  of  the 
mirror  (520).  This  image  is  reflected  by  a  concave  mirror,  M,  whose  centre 


Fig-  395-  Fig.  396. 

of  curvature  coincides  with  the  axis  of  rotation  of  the  mirror  »/,  and  with  its 
centre  of  figure.  The  pencil  reflected  from  the  mirror  M  returns  upon  itself, 
is  again  reflected  from  the  mirror  ;;/,  traverses  the  lens  a  second  time,  and 
forms  an  image  of  the  platinum  wire,  which  appears  on  the  wire  itself  so 
long  as  the  mirror  m  turns  slowly. 

In  order  to  see  this  image  without  hiding  the  pencil  of  light  which  enters 
by  the  aperture  in  K,  a  mirror  of  unsilvered  glass,  V,  with  parallel  faces,  is 
placed  between  the  lens  and  the  wire,  and  is  inclined  so  that  the  reflected 
rays  fall  upon  a  powerful  eyepiece,  P. 

The  apparatus  being  arranged,  if  the  mirror  m  is  at  rest,  the  ray  after 
meeting  M  is  reflected  to  m,  and  from  thence  returns  along  its  former  path, 
till  it  meets  the  glass  plate  V  in  a,  and  being  partially  reflected,  forms  at  d — 
the  distance  ad  being  equal  to  ao — an  image  of  the  wire,  which  the  eye  is 
enabled  to  observe  by  means  of  the  eyepiece,  P.  If  the  mirror,  instead  of 
being  fixed,  is  moving  slowly  round— its  axis  being  at  right  angles  to  the 
plane  of  the  paper — there  will  be  no  sensible  change  in  the  position  of  the 
mirror  m  during  the  brief  interval  elapsing  while  light  travels  from  m  to  M 
and  back  again,  but  the  image  will  alternately  disappear  and  reappear.  If 
now  the  velocity  of  M  is  increased  to  upwards  of  30  turns  per  second,  the 


-507]  Experiments  of  Fizeau*  443 

interval  between  the  disappearance  and  reappearance  is  so  short  that 
the  impression  on  the  eye  is  persistent,  and  the  image  appears  perfectly 
steady. 

Lastly,  if  the  mirror  turns  with  sufficient  velocity,  there  is  no  appreciable 
change  in  its  position  during  the  time  which  the  light  takes  in  making  the 
double  journey  from  m  to  M,  and  from  M  to  m  ;  the  return  ray,  after  its 
reflection  from  the  mirror  /«,  takes  the  direction  mb,  and  forms  its  image 
at  i  ;  that  is,  the  image  has  undergone  a  total  deviation  di.  Speaking  pre- 
cisely, there  is  a  deviation  as  soon  as  the  mirror  turns,  even  slowly  ;  but  it  is 
only  appreciable  when  it  has  acquired  a  certain  magnitude,  which  is  the  case 
when  the  velocity  of  rotation  is  sufficiently  rapid,  or  the  distance  M;//  suffi- 
ciently great,  for  the  deviation  necessarily  increases  with  the  time  which  the 
light  takes  in  returning  on  its  own  path. 

In  Foucault's  experiment  the  distance  Mw  was  only  13^  feet  ;  when  the 
mirror  rotated  with  a  velocity  of  600  to  800  turns  in  a  second,  deviations  of 
^  to  i  of  a  millimetre  were  obtained. 

Taking  MJ»  -  /,  Lm  =  ?,  oL  =  r^  and  representing  by  n  the  number  of  turns 
in  a  second,  by  5  the  absolute  deviation  dt\  and  by  V  the  velocity  of  light, 
Foucault  arrived  at  the  formula 

Srr/v/r 


from  which  the  velocity  of  light  is  calculated  at  185,157  miles  in  a  second  ; 
this  number,  which  is  less  than  that  ordinarily  assumed,  agrees  remarkably 
well  with  the  value  deduced  from  the  new  determinations  of  the  value  of  the 
solar  parallax. 

In  this  apparatus  liquids  can  be  experimented  upon.  For  that  purpose 
a  tube,  AB,  10  feet  long,  and  filled  with  distilled  water,  is  placed  between  the 
turning  mirror  ;«,  and  a  concave  mirror  M',  identical  with  the  mirror  M. 
The  luminous  rays  reflected  by  the  rotating  mirror,  in  the  direction  mM\ 
traverse  the  column  of  water  AB  twice  before  returning  to  V.  But  the  return 
ray  then  becomes  reflected  at  <:,  and  forms  its  image  at  h  :  the  deviation  is 
consequently  greater  for  rays  which  have  traversed  water  than  for  those  which 
have  passed  through  air  alone  ;  hence  the  velocity  of  light  is  less  in  water 
than  in  air. 

This  is  the  most  important  part  of  these  experiments.  For  it  had  been 
shown  theoretically  that  on  the  undulatory  theory  the  velocity  of  light  must 
be  less  in  the  more  highly  refracting  medium  (638),  while  the  opposite  is  a 
necessary  consequence  of  the  emission  theory.  Hence  Foucault's  result  may 
be  regarded  as  a  crucial  test  of  the  validity  of  the  undulatory  theory. 

The  mechanism  by  which  the  mirror  was  turned  consisted  of  a  small 
steam  turbine,  bearing  a  sort  of  resemblance  to  the  syren,  and,  like  that 
instrument,  giving  a  higher  sound  as  the  rotation  is  more  rapid  ;  in  fact,  it 
is  by  the  pitch  of  the  note  that  the  velocity  of  the  rotation  is  determined. 

507.  Experiments  of  Fizeau  —  In  1849  Fizeau  measured  directly  the 
velocity  of  light,  by  ascertaining  the  time  it  took  to  travel  from  Suresnes  to 
Montmartre  and  back  again.  The  apparatus  employed  was  a  toothed  wheel, 
capable  of  being  turned  more  or  less  quickly,  and  with  a  velocity  that  could 
be  exactly  ascertained.  The  teeth  were  made  of  precisely  the  same  width 


444  On  Light.  [507- 

as  the  intervals  between  them.  The  apparatus  being  placed  at  Suresnes,  a 
pencil  of  parallel  rays  was  transmitted  through  an  interval  between  two 
teeth  to  a  mirror  placed  at  Montmartre.  The  pencil,  directed  by  a  properly- 
arranged  system  of  tubes  and  lenses,  returned  to  the  wheel.  As  long  as  the 
apparatus  was  at  rest  the  pencil  returned  exactly  through  the  same  interval 
as  that  through  which  it  first  set  out.  But  when  the  wheel  was  turned 
sufficiently  fast,  a  tooth  was  made  to  take  the  place  of  an  interval,  and  the 
ray  was  intercepted.  By  causing  the  wheel  to  turn  more  rapidly,  it  re- 
appeared when  the  interval  between  the  next  two  teeth  had  taken  the  place 
of  the  former  tooth  at  the  instant  of  the  return  of  the  pencil. 

The  distance  between  the  two  stations  was  28,334  ft.  By  means  of  the 
data  furnished  by  this  distance,  by  the  dimensions  of  the  wheel,  its  velocity 
of  rotation,  &c.,  Fizeau  found  the  velocity  of  light  to  be  196,000  miles  per 
second — a  result  agreeing  with  that  given  by  astronomical  observation  as 
closely  as  can  be  expected  in  a  determination  of  this  kind. 

Cornu  has  recently  investigated  the  velocity  of  light  by  Fizeau's  method, 
but  with  improvements  so  that  the  probable  error  did  not  exceed  ^  of  the 
total  amount ;  the  two  stations,  which  were  6*4  miles  apart,  were  a  pavilion 
of  the  £cole  Polytechnique  and  a  room  in  the  barracks  of  Mont  Valerien. 
He  thus  obtained  the  number  185,420  miles — a  result  closely  agreeing  with 
that  of  Foucault,  and  which  is  supported  by  calculations  based  on  the  results 
of  astronomical  observations  of  the  transit  of  Venus  in  1874. 

Michelson  has  made  a  determination  of  the  intensity  of  light  by  Foucault's 
method,  by  which  he  obtained  the  result  186,380,  with  a  possible  error 
of  33  miles. 

508.  Laws  of  the  intensity  of  light. — The  intensity  of  illumination  is 
the  quantity  of  light  received  on  the  unit  of  surface ;  it  is  subject  to  the  fol- 
lowing laws  : — 

I.  The  intensity  of  illumination  on  a  given  surface  is  inversely  as  the 
square  of  its  distance  from  the  source  of  light. 

II.  The  intensity  of  illumination  which  is  received  obliquely  is  propor- 
tional to  the  cosine  of  the  angle  which   the  luminous  rays  make  with  the 
normal  to  the  illuminated  surface. 

In  order  to  demonstrate  the  first  law,  let  there  be  two  circular  screens, 
CD  and  AB  (fig.  397),  one  placed  at  a  certain  distance  from  a  source  of 

light,  L,  and  the  other  at 
double  this  distance,  and 
let  >$•  and  S  be  the  areas 
of  the  two  screens.  If 
a  be  the  total  quantity  of 
light  which  is  emitted  by 
the  source  in  the  direc- 
tion of  the  cone  ALB, 
the  intensity  of  the  light 
Fig.  397.  on  the  screen  CD — that 

is,    the    quantity    which 

falls  on  the  unit  of  surface— is  *,  and  the  intensity  on  the  screen  AB  is  a . 
Now,  as  the  triangles  ALB  and  CLD  are  similar,  the  diameter  of  AB  is 


-509]  Photometers.  445 

double  that  of  CD  ;  and  as  the  surfaces  of  circles  are  as  the  squares  of  their 
diameters,  the  surface  S  is  four  times  j,  consequently  the  intensity  £  is  one- 

o 

fourth  that  of  f . 
s 

The  same  law  may  also  be  demonstrated  by  an  experiment  with  the 
apparatus  represented  in  fig.  399.  It  is  made  by  comparing  the  shadows 
of  an  opaque  rod  cast  upon  a  glass  plate,  in  one  case  by  the  light  of  a  single 
candle,  and  in  another  by  that  of  a  lamp  equalling  four  candles,  placed  at 
double  the  distance  of  the  first.  In  both  cases  the  shadows  have  the  same 
intensity. 

Figure  397  shows  that  it  is  owing  to  the  divergence  of  the  luminous 
rays  emitted  from  the  same  source  that  the  intensity  of  light  is  inversely  as 
the  square  of  the  distance.  The  illumination  of  a  surface  placed  in  a  beam 
of  parallel  luminous  rays  is  the  same  at  all  distances,  at  any  rate  in  a 
vacuum,  for  in  air  and  in  other  transparent  media  the  intensity  of  light  de- 
creases in  consequence  of  absorption,  but  far  more  slowly  than  the  square  of 
the  distance. 

The  second  law  of  intensity  corresponds  to  the  law  which  we  have  found 
to  prevail  for  heat :  it  may  be  theoretically  deduced  as  follows  : — Let  DA, 
EB  (fig.  398)  be  a  pencil  of  parallel 
rays  falling  obliquely  on  a  surface, 
AB,  and  let  om  be  the  normal  to 
this  surface.  If  S  is  the  section 
of  the  pencil,  a  the  total  quan- 
tity of  light  which  falls  on  the 
surface  AB,  and  I  that  which  falls 
on  the  unit  of  surface — that  is,  the 
intensity  of  illumination — we  have 

I  =  ^.  But  as  S  is  only  the  projection  of  AB  on  a  plane  perpendicular  to 
the  pencil,  we  know  from  trigonometry  that  S=AB  cos  a,  from  which 
AB  —  _  —  This  value,  substituted  in  the  above  equation,  gives  I  =  " 

cos  a  ;  a  formula  which  demonstrates  the  law  of  the  cosine,  for  as  a  and  S 
are  constant  quantities,  I  is  proportional  to  cos  a. 

The  law  of  the  cosine  applies  also  to  rays  emitted  obliquely  by  a  luminous 
surface  ;  that  is,  the  rays  are  less  intense  in  proportion  as  they  are  more  in- 
clined to  the  surface  which  emits  them.  In  this  respect  they  correspond  to 
the  third  law  of  the  intensity  of  radiant  heat. 

509.  Photometers. — A  photometer  is  an  apparatus  for  measuring  the 
relative  intensities  of  different  sources  of  light. 

Rumfords pJiotomcter. — This  consists  of  aground  glass  screen,  in  front 
of  which  is  fixed  an  opaque  rod  (fig.  399) ;  the  lights  to  be  compared — for 
instance,  a  lamp  and  a  candle — are  placed  at  a  certain  distance  in  such  a 
manner  that  each  projects  on  the  screen  a  shadow  of  the  rod.  The 
shadows  thus  projected  are  at  first  of  unequal  intensity,  but  by  altering 
the  position  of  the  lamp,  it  may  be  so  placed  that  the  intensity  of  the  two 
shadows  is  the  same.  Then,  since  the  shadow  thrown  by  the  lamp  is 


446 


On  Light. 


[509- 


illuminated  by  the  candle,  and  that  thrown  by  the  candle  is  illuminated 
by  the  lamp,  the  illumination  of  the  screen  due  to  each  light  is  the  same. 
The  intensities  of  the  two  lights — that  is,  the  illuminations  which  they 
would  give  at  equal  distances — are  then  directly  proportional  to  the  squares 
of  their  distances  from  the  shadows  ;  that  is  to  say,  that  if  the  lamp  is  three 


Fig.  399- 

times  the  distance  of  the  candle,  its  illuminating  power  is  nine  times  as 
great. 

For  if  i  and  i'  are  the  intensities  of  the  lamp  and  the  candle  at  the  unit 
of  distance,  and  d  and  d'  their  distances  from  the  shadows,  it  follows,  from 
the  first  law  of  the  intensity  of  light,  that  the  intensity  of  the  lamp  at  the 

distance  d  is  *     and  that  of  the  candle 4,7, at  the  distanced.  On  the  screen 
d~  d  * 

these  two  intensities  are  equal ;  hence  4*  =  -fo    or  -.,-  =    »« >  which  was  to  be 

d"      a'~          i       a* 
proved. 

Bunserts  photometer. — When  a  grease  spot  is  made  on  a  piece  of  bibu- 
lous paper,  the  part  appears  translucent.  If  the  paper  be  illuminated  by  a 


Fig.  400. 


light  placed  in  front,  the  spot  appears  darker  than  the  surrounding  space  ; 
if,  on  the  contrary,  it  be  illuminated  from  behind,  the  spot  appears  light  on 
a  dark  ground.  If  the  greased  part  and  the  rest  appear  unchanged,  the  in- 
tensity of  illumination  on  both  sides  is  the  same.  Bunsen's  photometer 
depends  on  an  application  of  this  principle.  Its  essential  features  are  re- 
presented in  fig.  400.  A  circular  spot  is  made  on  a  paper  screen  by  means 


-510]      Relative  Intensities  of  Various  Sources  of  Light.          447 

of  a  solution  of  spermaceti  in  naphtha  :  on  one  side  of  this  is  placed  a  light 
of  a  certain  intensity,  which  serves  as  a  standard ;  in  London  it  is  a  sperm 
candle  of  six  to  the  pound,  and  burning  120  grains  in  an  hour.  The  light  to 
be  tested,  a  petroleum  lamp  or  a  gas  burner  consuming  a  certain  volume  in  a 
given  time,  is  then  moved  in  a  right  line  to  such  a  distance  on  the  other  side 
of  the  screen  that  there  is  no  difference  in  brightness  between  the  greased 
part  and  the  rest  of  the  screen.  By  measuring  the  distances  of  the  lights 
from  the  screen  by  means  of  the  scale,  their  relative  illuminating  powers  are 
respectively  as  the  squares  of  their  distances  from  the  screen. 

By  this  kind  of  determination  the  degree  of  accuracy  which  can  be 
attained  is  not  so  great  as  in  many  physical  determinations,  more  especially 
when  the  lights  to  be  compared  are  of  different  colours ;  one,  for  instance, 
being  yellow,  and  the  other  of  a  bluish  tint.  It  gives,  however,  results  which 
are  sufficiently  accurate  for  practical  purposes,  and  is  almost  universally 
employed  for  determining  the  illuminating  power  of  coal  gas  and  of  other 
artificial  lights. 

WheatstonJs  photometer. — The  principal  part  of  this  instrument  is  a 
steel  bead,  P  (fig.  401),  fixed  on  the  edge  of  a  disc,  which  rotates  on  a 
pinion,  o,  working  in  a  larger  toothed  F 
wheel.  The  wheel  fits  in  a  cylin- 
drical brass  box,  which  is  held  in  one 

hand,  while  the  other  works  a  handle,  '^^^M  iff 

A,  which  turns  a  central  axis,  the 
motion  of  which  is  transmitted  by  a 
spoke,  a,  to  the  pinion  o.  In  this 
way  the  latter  turns  on  itself,  and 

,  .  ,  j      ,  rig.  401.  rig.  402. 

at  the  same  time  revolves  round  the 

circumference  of  the  box  ;  the  bead  shares  the  double  motion,  and  con- 
sequently describes  a  curve  in  the  form  of  a  rose  (fig.  402). 

Now,  let  M  and  N  be  the  two  lights  whose  intensities  are  to  be  com- 
pared ;  the  photometer  is  placed  between  them  and  rapidly  rotated.  The 
brilliant  points  produced  by  the  reflection  of  the  light  on  the  two  opposite 
sides  of  the  bead  give  rise  to  two  luminous  bands,  arranged  as  represented  in 
fig.  402.  If  one  of  them  is  more  brilliant  than  the  other — that  which  pro- 
ceeds from  the  light  M,  for  instance — the  instrument  is  brought  nearer  the 
other  light  until  the  two  bands  exhibit  the  same  brightness.  The  distance 
of  the  photometer  from  each  of  the  two  lights  being  then  measured,  their 
intensities  are  proportional  to  the  squares  of  the  distances. 

5 10.  Relative  intensities  of  various  sources  of  light. — The  light  of  the 
sun  is  600,000  times  as  powerful  as  that  of  the  moon  ;  and  16,000,000,000 
times  as  powerful  as  that  of  a  Centauri,  the  third  in  brightness  of  all  the 
stars.  The  moon  is  thus  27,000  times  as  bright  as  this  star  ;  the  sun  is  5,000 
million  times  as  bright  as  Jupiter,  and  80  billion  times  as  bright  as  Neptune. 
Its  light  is  estimated  to  be  equal  to  that  of  5,500  wax  candles  at  a  distance  of 
i  foot.  According  to  Fizeau  and  Foucault  the  electric  light  produced  by  50 
Bunsen's  cells  is  about  \  as  strong  as  sunlight. 

A  difference  in  the  strength  of  light  or  shadow  is  perceived  when  the 
duller  light  is  -|j§  of  the  brightness  of  the  other,  and  both  are  near  together, 
especially  when  the  shadow  is  moved  about. 


448 


On  Light. 


[511- 


CHAPTER   II. 

REFLECTION  OF  LIGHT.     MIRRORS. 

511.  Xiaws  of  the  reflection  of  light. — When  a  luminous  ray  meets  a 
polished  surface,  it  is  reflected  according  to  the  following  two  laws,  which, 
as  we  have  seen,  also  prevail  for  heat : — 

I.  The  angle  of  reflection  is  equal  to  the  angle  of  incidence. 

II.  The  incident  and  the  reflected  ray  are  both  in  the  same  plane,  ivhicli 
is  perpendicular  to  the  reflecting  surface. 

The  words  are  here  used  in  the  same  sense  as  in  article  411,  and  need 
no  further  explanation. 

First  proof. — The  two  laws  may  be  demonstrated  by  the  apparatus 
represented  in  fig.  403.  It  consists  of  a  graduated  circle  in  a  vertical  plane. 

Two  brass  slides  move  round  the  cir- 
cumference ;  on  one  of  them  there  is 
a  piece  of  ground  glass,  P,  and  on  the 
other  an  opaque  screen,  N,  in  the 
centre  of  which  is  a  small  aperture. 
Fixed  to  the  latter  slide  there  is  also 
a  mirror,  M,  which  can  be  more  or  less 
inclined,  but  always  remains  in  a  plane 
perpendicular  to  the  plane  of  the  gra- 
duated circle.  Lastly,  there  is  a  small 
polished  metallic  mirror,  ;;z,  placed 
horizontally  in  the  centre  of  the  circle. 
In  making  the  experiment,  a  pencil 
of  solar  light,  S,  is  caused  to  impinge 
on  the  mirror  M,  which  is  so  inclined 
that  the  reflected  light  passes  through 
the  aperture  in  N,  and  falls  on  the 
centre  of  the  mirror  m.  The  luminous 
pencil  then  experiences  a  second  re- 
flection in  a  direction  ;«P,  which  is 
ascertained  by  moving  P  until  an 
image  of  the  aperture  is  found  in  its  centre.  The  number  of  degrees  com- 
prised in  the  arc  AN  is  then  read  off,  and  likewise  that  in  AP  ;  these  being 
equal,  it  follows  that  the  angle  of  reflection  AwP  is  equal  to  the  angle  of 
incidence  AmM. 

The  second  law  follows  from  the  arrangement  of  the  apparatus,  the  plane 
of  the  rays  Mm  and  mP  being  parallel  to  the  plane  of  the  graduated  circle, 
and,  consequently,  perpendicular  to  the  mirror  m. 


-513]  Formation  of  Images  by  Plane  Mirrors.  449 

Second  proof .— The  law  of  the  reflection  of  light  may  also  be  demon- 
strated by  the  following  experiment,  which  is  susceptible  of  greater  accuracy 
than  that  just  described  :— In  the  centre  of  a  graduated  circle,  M  (fig.  404), 
placed  in  a  vertical  position,  there  is  a  small  telescope  movable  in  a  plane 
parallel  to  the  limb  ;  at  a  suitable  distance  there  is  a  vessel  D  full  of  mercury, 
which  forms  a  perfectly  horizontal  plane  mirror.  Some  particular  star  of 
the  first  or  second  magnitude  is  viewed  through  the  telescope  in  the  direction 
AE,  and  the  telescope  is  then  inclined  so  as  to  receive  the  ray  AD  coming 
from  the  star  after  being  reflected  from  the  brilliant  surface  of  the  mercury. 


In  this  way  the  two  angles  formed  by  the  rays  EA  and  DA,  with  the  hori- 
zontal AH,  are  found  to  be  equal,  from  which  it  may  easily  be  shown  that 
the  angle  of  incidence  E'DE  is  equal  to  the  angle  of  reflection  EDA.  For 
if  DE  is  the  normal  to  the  surface  of  the  mercury,  it  is  perpendicular  to  AH, 
and  AED,  ADE  are  the  complements  of  the  equal  angles  EAH,  DAH  ; 
therefore  AED,  ADE  are  equal ;  but  the  two  rays  AE  and  DE'  may  be 
considered  parallel,  in  consequence  of  the  great  distance  of  the  star,  and 
therefore  the  angles  EDE'  and  DEA  are  equal,  for  they  are  alternate  angles, 
and,  consequently,  the  angle  E'DE  is  equal  to  the  angle  EDA. 


REFLECTION   OF  LIGHT   FROM   PLANE  SURFACES. 

512.  Mirrors.     Images. — Mirrors  are  bodies   with    polished   surfaces, 
which  show  by  reflection  objects  presented  to  them.     The  place  at  which 
objects  appear  is  their  image.     According  to  their  shape,  mirrors  are  divided 
into  plane,  concave,  convex,  spherical,  parabolic,  conical,  &c. 

513.  Formation  of  image*  by  plane  mirrors — The  determination  of 
the  position  and  size  of  images  resolves  itself  into  investigating  the  images 
of  a  series  of  points.     And  first,  the  case  of  a  single  point,  A,  placed  before 
a  plane  mirror.  MN  (fig.  405),  will  be  considered.     Any  ray,  AB,  incident 
from  this  point  on  the  mirror,  is  reflected  in  the  direction  BO,  making  the 
angle  of  reflection  DBO  equal  to  the  angle  of  incidence  DBA. 

If,  now,  a  perpendicular,  AN,  be  let  fall  from  the  point  A  on  the  mirror, 


450  On  Light.  [513- 

and  if  the  ray  OB  be  prolonged  below  the  mirror  until  it  meets  this  perpen- 
dicular in  the  point  a,  two  triangles  are  formed,  ABN,  and  EN  a,  which  are 
equal,  for  they  have  the  side  BN  common  to  both,  and  the  angles  ANB, 
ABN,  equal  to  the  angles  <zNB,  «BN  ;  for  the  angles  ANB  and  <zNB  are 
right  angles,  and  the  angles  ABN  and  aBN  are  each  equal  to  the  angle 
OEM.  From  the  equality  of  these  triangles,  it  follows  that  #N  is  equal  to 
AN  ;  that  is,  that  any  ray,  AB,  takes  such  a  direction  after  being  reflected, 
that  its  prolongation  below  the  mirror  cuts  the  perpendicular  Aa  in  the  point 
a,  which  is  at  the  same  distance  from  the  mirror  as  the  point  A.  This  ap- 
plies also  to  the  case  of  any  other  ray  from  the  point  A — AC,  for  example. 


Fig.  405.  Fig.  406. 

From  this  the  important  consequence  follows,  that  all  rays  from  the  point 
A,  reflected  from  the  mirror,  follow,  after  reflection,  the  same  direction  as  if 
they  had  all  proceeded  from  the  point  a.  The  eye  is  deceived,  and  sees  the 
point  A  at  a,  as  if  it  were  really  situated  at  a.  Hence  in  plane  mirrors  the 
image  of  any  point  is  formed  behind  tJie  mirror  at  a  distance  equal  to  that  of 
the  given  point,  and  on  the  perpendicular  let  fall  from  this  point  on  the 
mirror. 

It  is  manifest  that  the  image  of  any  object  will  .be  obtained  by  construct- 
ing according  to  this  rule  the  image  of  each  of  its  points,  or,  at  least,  of  those 
which  are  sufficient  to  determine  its  form.  Fig.  406  shows  how  the  image 
ab  of  any  object,  AB,  is  formed. 

It  follows  from  this  construction  that  in  plane  mirrors  the  image  is  of  the 
same  size  as  the  object,  for  if  the  trapezium  ABCD  be  applied  to  the  trapezium 
DCab,  they  are  seen  to  coincide,  and  the  object  AB  agrees  with  its  image. 

A  further  consequence  from  the  above  construction  is,  that  in  plane 
mirrors  the  image  is  symmetrical  in  reference  to  the  object,  and  not  inverted. 

514.  Virtual  and  real  images. — There  are  two  cases  relative  to  the 
direction  of  rays  reflected  by  mirrors  according  as  the  rays  after  reflection 
are  convergent  or  divergent.  In  the  first  case  the  reflected  rays  do  not  meet, 
but  if  they  are  supposed  to  be  produced  on  the  other  side  of  the  mirror,  their 
prolongations  coincide  in  the  same  point,  as  shown  in  figs.  404  and  405. 
The  eye  is  then  affected,  just  as  if  the  rays  proceeded  from  this  point,  and 
it  sees  an  image.  But  the  image  has  no  real  existence,  the  luminous  rays  do 
not  come  from  the  other  side  of  the  mirror;  this  appearance  is  called  the 
virtual  image.  The  images  of  real  objects  produced  by  plane  mirrors  are 
of  this  kind.  . 

In  the  second  case,  where  the  reflected  rays  converge,  ©f  which  we  shall 


-516]  Multiple  Images  from  two  Plane  Mirrors.  451 

soon  have  an  example  in  concave  mirrors,  the  rays  coincide  at  a  point  in 
front  of  the  mirror,  and  on  the  same  side  as  the  object.  They  form  there  an 
image  called  the  real  image,  for  it  can  be  received  on  a  screen.  The  dis- 
tinction may  be  expressed  by  saying  that  real  images  arc  those  formed  by  the 
reflected  rays  themselves,  and  virtual  images  those  formed  by  their  prolon- 
gations. 

515.  Multiple   images  formed   by    glass    mirrors.— Metallic   mirrors 
which  have  but  one  reflecting  surface  only  give  one  imagi-  ;  glass  mirrors 
give  rise  to  several  images,  which  are  readily  ob- 
served when   the  image  of  a  candle   is   looked   at 

obliquely  in  a  looking-glass.  A  very  feeble  image 
is  first  seen,  and  then  a  very  distinct  one  ;  behind 
this  there  are  several  others,  whose  intensities  gra- 
dually decrease  until  they  disappear. 

This  phenomenon  arises  from  the  looking-glass 
having  two  reflecting  surfaces.  When  the  rays 
from  the  point  A  meet  the  same  surface,  a  part  is 
reflected  and  forms  an  image,  a,  of  the  point  A,  on 
the  prolongation  of  the  ray  £E,  reflected  by  this 

surface  ;  the  other  part  passes  into  the  glass,  and  is  reflected  at  c,  from  the 
layer  of  metal  which  covers  the  hinder  surface  of  the  glass,  and  reaching  the 
eye  in  the  direction  dH  gives  the  image  a'.  This  image  is  distant  from  the 
first  by  double  the  thickness  of  the  glass.  It  is  more  distinct,  because  metal 
reflects  better  than  glass. 

In  regard  toother  images  it  will  be  remarked,  that  whenever  light  is 
transmitted  from  one  medium  to  another — for  instance,  from  glass  to  air — 
only  some  of  the  rays  get  through,  the  remainder  are  reflected  at  the  surface 
which  bounds  the  two  media.  Consequently  when  the  pencil  cd,  reflected 
from  <:,  attempts  to  leave  the  glass  at  d,  most  of  the  rays  composing  it  pass 
into  the  air,  but  some  are  reflected  at  d,  and  continue  within  the  glass. 
These  are  again  reflected  by  the  metallic  surface,  and  form  a  third  image  of 
A;  after  this  reflection  they  come  to  MN,  when  many  emerge  and  render 
the  third  image  visible ;  but  some  are  again  reflected  within  the  glass,  and  in 
a  similar  manner  give  rise  to  a  fourth,  fifth, 
&c.,  image,  thereby  completing  the  series 
above  described.  It  is  manifest  from  the 
above  explanation  that  each  image  must  be 
much  feebler  than  the  one  preceding  it,  and 
consequently  not  more  than  a  small  number 
are  visible — ordinarily  not  more  than  eight 
or  ten  in  all. 

This  multiplicity  of  images  is  objection- 
able in  observations,  and,  accordingly,  me- 
tallic mirrors  are  to  be  preferred  in  optical 
instruments. 

516.  Multiple   images  from  two  plane  Fig.  408. 
mirrors.  —  When  an   object  is    placed  be- 
tween two  plane  mirrors,  which  form  an  angle  with  each  other,  either  right 
or  acute,  images  of  the  object  are  formed,  the  number  of  which  increases 


452  On  Light.  [516- 

with  the  inclination  of  the  mirrors.  If  they  are  at  right  angles  to  each 
other,  three  images  are  seen,  arranged  as  represented  in  fig.  408.  The  rays 
OC  and  OD  from  the  point  O,  after  a  single  reflection,  give  the  one  an 
image  O',  and  the  other  an  image  O",  while  the  ray  OA,  which  has  under- 
gone two  reflections  at  A  and  B,  gives  the  third  image  O'".  When  the 
angle  of  the  mirrors  is  60°,  five  images  are  produced,  and  seven  if  it  is  45°. 
The  number  of  images  continues  to  increase  in  proportion  as  the  angle 
diminishes,  and  when  it  is  zero — that  is,  when  the  mirrors  are  parallel — the 
number  of  images  is  theoretically  infinite.  This  multiplicity  arises  from  the 
fact  that  the  luminous  rays  undergo  an  increasing  number  of  reflections 
from  one  mirror  to  the  other. 

The  kaleidoscope,  invented  by  Sir  D.  Brewster,  depends  on  this  property 
of  inclined  mirrors.  It  consists  of  a  tube,  in  which  are  three  mirrors  inclined 
at  60° ;  one  end  of  the  tube  is  closed  by  a  piece  of  ground  glass,  and  the 
other  by  a  cap  provided  with  an  aperture.  Small  irregular  pieces  of  coloured 
glass  are  placed  at  one  end  between  the  ground  glass  and  another  glass  disc, 
and  on  looking  through  the  aperture,  the  other  end  being  held  towards  the 
light,  the  objects  and  their  images  are  seen  arranged  in  beautiful  symmetrical 
forms  ;  by  turning  the  tube,  an  almost  endless  variety  of  these  shapes  is 
obtained. 

517.  Multiple  images  in  two  parallel  mirrors. — In  this  case  the  num- 
ber of  images  of  an  object  placed  between  them  is  theoretically  infinite. 
Physically  the  number  is  limited,  for  as  the  incident  light  is  never  totally  re- 
flected, some  of  it  being  always  absorbed,  the  images  gradually  become 
fainter,  and  are  ultimately  quite  extinguished. 

Fig.  409  shows  how  the  pencil  La  reflected  once  from  M  gives  at  I  the 
image  of  the  object  L  at  a  distance  MI  =  ML  ;  then  the  pencil  L&  reflected 


Fig.  409. 

once  from  the  mirror  M,  and  once  from  N,  furnishes  the  image  I'  at  a  distance 
«I'  =  #I ;  in  like  manner  the  pencil  Lc  after  two  reflections  on  M,  and  one 
on  N,  forms  the  image  V  at  a  distance  ;#I"  =  »*I',  and  so  on  for  an  infinite 


-520]     Reflection  of  a  Ray  of  Light  in  a  Rotating  Mirror.      453 

series.     The  images  /,  /',  i"  are  formed  in  the  same  manner  by  rays  of  light, 
which  emitted  by  the  object  L  fall  first  on  the  mirror  N. 

518.  Irregular  reflection.     Diffused  ligrnt.— The  reflection  from  the 
surfaces  of  polished  bodies,  the  laws  of  which  have  just  been  stated,  is  called 
the  regular  or  specular  reflection  ;  but  the  quantity  thus  reflected  is  less  than 
that  of  the  incident  light.     The  light  incident  on  an  opaque  body  separates 
in  fact  into  three  parts  ;  one  is  reflected  regularly,  another  irregularly — that 
is,  in  all  directions  ;  while  a  third  is-  extinguished,  or  absorbed  by  the  reflect- 
ing body.     If  light  falls  on  a  transparent  body,  a  considerable  portion  is 
transmitted  with  regularity. 

The  irregularly  reflected  light  is  called  scattered  light :  it  is  that  which 
makes  bodies  visible.  The  light  which  is  reflected  regularly  does  not  give 
us  the  images  of  the  reflecting  surface,  but  that  of  the  body  from  which  the 
light  proceeds.  If,  for  example,  a  beam  of  sunlight  be  incident  on  a  well- 
polished  mirror  in  a  dark  room,  the  more  perfectly  the  light  is  reflected  the 
less  visible  is  the  mirror  in  the  different  parts  of  the  room.  The  eye  does 
not  perceive  the  image  of  the  mirror,  but  that  of  the  sun.  If  the  reflecting 
power  of  the  mirror  be  diminished  by  sprinkling  on  it  a  light  powder,  the 
solar  image  becomes  feebler,  and  the  mirror  is  visible  from  all  parts  of  the 
room.  Perfectly  smooth,  polished  reflecting  surfaces,  if  such  there  were, 
would  be  invisible.  The  air  diffuses  the  light  which  falls  on  it  from  the  sun 
in  all  directions,  so  that  it  is  light  in  places  which  do  not  receive  the  direct 
rays  of  the  sun.  Thus,  the  upper  layers  of  the  air  diffuse  the  light  which 
they  receive  before  sunrise  and  sunset,  and  accordingly  give  rise  to  the 
phenomenon  of  twilight. 

519.  Intensity  of  reflected  light. — The  intensity  of  reflected  light  is 
always  less  than  that  of  the  incident,  for  some  of  the  original  vibrations  are 
converted  into  vibrations  of  the  reflecting  surfaces.     The  intensity  increases 
with  the  obliquity  of  the  incident  ray.     For  instance,  if  a  sheet  of  white 
paper  be  placed  before  a  candle,  and  be  looked  at  very  obliquely,  an  image 
of  the  flame  is  seen  by  reflection,  which  is  not  the  case  if  the  eye  receives 
less  oblique  rays. 

The  intensity  of  the  reflection  varies  with  different  bodies,  even  when 
the  degree  of  polish  and  the  angle  of  incidence  are  the  same.  Thus  with  a 
perpendicular  incidence  the  reflected  light  is  f  of  the  incident  in  the  case  of 
that  reflected  from  a  metal  mirror,  f  from  mercury,  ^  from  glass,  and  ±  from 
water.  It  also  varies  with  the  nature  of  the  medium  which  the  ray  is  tra- 
versing before  and  after  reflection.  Polished  glass  immersed  in  water  loses 
a  great  part  of  its  reflecting  power. 

520.  Reflection  of  a  ray  of  ligrnt  in  a  rotating:  mirror. — When  a  hori- 
zontal ray  of  light  falls  on  a  plane  mirror  which  can  rotate  about  a  vertical 
axis,  if  the  mirror  is  turned  through  an  angle  a,  the  reflected  ray  is  turned 
through  double  the  angle. 

Let  nm  (fig.  410)  be  the  first  position  of  the  mirror,  n'm'  its  position  alter 
it  has  been  turned  through  the  angle  a ;  and  let  OD  be  the  fixed  incident 
ray.  If  from  the  centre  of  rotation  C,  with  any  radius  we  describe  the  cir- 
cumference O;«TZ,  and  from  the  point  O,  where  it  cuts  the  incident  ray, 
chords  OO'  and  O  O"  are  drawn  perpendicular  respectively  to  mn  andm'u'  • 
the  points  O'  and  O"  are  the  images  ot  the  point  O  in  the  two  positions  of 


454 


On  Light. 


[520- 


the  mirror,  and  the  angles  CO'D  and  CO"D'  are  each  equal  to  COD.  The 
lines  O'D  and  O"D',  thus  making  equal  angles  with  O'C  and  O"C,  the 
angle  between  the  two  former  lines  is  equal 
to  that  between  the  two  latter  ;  that  is,  it  will  be 
equal  to  O'CO"  and  will  be  measured  by  the 
arc  O'O".  The  rotations  of  the  reflected  ray 
and  of  the  mirror  are  thus  measured  by  the  two 
arcs  O'O"  and  mm'  respectively. 

Now  the  two  angles  O'OO"  and  m£,m'  are 
equal,  for  they  have  their  sides  perpendicular 
each  to  each  ;  but  the  angle  O'OO",  which  is 
an  angle  at  the  circumference,  is  measured  by 
half  the  arc  O'O",  and  the  angle  mCm'  by  the 
Fig.  4I0.  whole  arc  mm' ;  hence  O'O"  is  the  double  of 

mm',  which    shows    that  when  the  mirror  has 
turned  through  an  angle  a,  the  reflected  ray  has  turned  through  2a. 

521.  Hartley's  reflecting-  sextant. — The  principal  features  of  this  in- 
strument, which  is  used  to  measure  the  angular  distance  of  any  two  distant 
objects,  are  represented  in  fig.  41 1.  It  consists  of  a  metal  sector,  the  arc,  ^/, 
of  which  is  graduated.  About  the  centre  of  the  sector,  an  index  arm,  ab, 
turns  ;  this  is  provided  with  a  vernier  and  a  micrometer  screw,  by  which  the 
index  may  be  accurately  adjusted  and  also  clamped.  A  mirror  at  a  is  fixed 
perpendicularly  to  the  arm  ab,  and  therefore  moves  with  it.  A  telescope  de 
is  permanently  fixed  to  the  arm  acy  and  opposite  to  it  is  a  second  mirror  m, 
also  permanently  fixed  ;  the  lower  half  of  this  is  silvered,  and  the  axis  of 

the  telescope  just  traverses 

^  s  I  the  boundary  of  the  silvered 

/  and   unsilvered   part  of  the 

mirror. 

V     •  /  In  making  an  observation 

the  sextant  is  held  so  that 
its  plane  may  pass  through 
both  the  objects  whose  angu- 
lar distance  is  to  be  mea- 
sured. The  index  arm  is  at 
the  zero  of  the  graduation, 
which  indicates  the  paral- 
lelism of  the  two  mirrors. 
One  of  the  objects  is  then 
viewed  in  the  direction,  omy 
through  the  telescope,  and 
the  unsilvered  part  of  the 
mirror  m.  The  index  arm 
is  then  moved  until  the  eye 
sees  simultaneously  with  this 

the  image  of  another  object  gy  which  reaches  the  eye  after  successive  reflec- 
tions from  the  mirror  «,  and  from  the  silvered  part  of  the  mirror  m  ;  that 
is,  by  the  path  game  do.  The  angle  mha  which  the  two  mirrors  now  form 
is  measured  by  the  graduation  of  the  sector  cdy  and  is  half  the  angle  gom. 


-523]  M mice  s  Heliograph.  455 

For  when  the  two  mirrors  were  parallel,  the  angular  deflection  of  the  ray 
ga,  after  two  reflections,  would  be  zero,  and  its  deflection  is  now  the  angle 
gom  ;  whence,  by  the  last  article,  the  mirror  a  must  have  turned  through  half 

that  angle,  the  mirror  m  having  been  fixed  in  position  throughout. 

522.  Measurement  of  small  angles  by  reflection  from  a  mirror An 

important  application  is  made  of  the  law  of  reflection  in  measuring  small 
angles  of  deflection    in 

magnetic  and  other  ob-  * 

serrations.      The    prin-  - 

ciple  of  this  method  will 
be  understood  from  fig. 
412,  in  which  AO  repre- 
sents a  telescope,  under-  *g~~s  oj 
neath  which,  and  at  right 
angles  to  its  axis,  is  fixed 
a  graduated  scale  ss ; 
the  centre  of  which,  the 
zero,  corresponds  to  the 
axis  of  the  telescope. 

Let  NS  be  the  object  Fig.  412.. 

whose  angular  deflection 

is  to  be  measured,  a  magnet  for  instance,  and  let  mm  represent  a  small  per- 
fectly plane  mirror  fixed  rigidly  at  right  angles  to  the  axis  of  the  magnet.  If 
now,  at  the  beginning  of  the  observation,  the  telescope  is  adjusted  so  that 
the  image  of  the  zero  appears  behind  the  cross  wires,  its  axis  is  perpendicular 
to  the  mirror.  Now  when  the  mirror  is  turned,  by  whatever  cause,  through 
an  angle  «,  the  eye  will  see  through  the  telescope  the  image  of  another 
division  of  the  scale,  a  for  instance,  the  ray  proceeding  from  which  makes 
with  the  line  cOA.  the  angle  2a. 

From  the  distance  of  this  division  Oa  from  the  zero  of  the  scale  and  the 

distance  Oc  from  the  mirror  we  have  tan  2a  =  _f*.     Thus,  for  instance,  if  Oa 

is  12  millimetres  and  Oc  5,000  millimetres,  then  tan  2<z=  —  -  from  which 

5,000 

2a  =  8'  1 5".  As  a  practised  eye  can  easily  read  ±  of  a  millimetre,  it  is  pos- 
sible by  such  an  arrangement  to  read  off  an  angular  deflection  of  two  seconds. 

523.  Mance's  heliograph. — The  reflection  of  light  from  mirrors  has  been 
lately  applied  by  Mance  in  signalling  at  great  distances  by  means  of  the 
sun's  light. 

The  apparatus  consists  essentially  of  a  mirror  about  4  inches  in  diameter 
mounted  on  a  tripod,  and  provided  with  suitable  adjustments  so  that  the 
sun's  light  can  be  received  upon  it  and  reflected  to  a  distant  station.  An 
observer  then  can  see  through  a  telescope  the  reflection  of  the  sun's  rays  as 
a  spot  of  light.  The  mirror  has  an  adjustment  by  which  it  can  be  made  to 
follow  the  sun  in  its  apparent  motion.  There  is  also  a  lever-key  by  which  the 
signaller  can  deflect  the  mirror  through  a  very  small  angle  either  to  the 
right  or  left,  and  thus  the  observer  at  the  distant  station  sees  corresponding 
flashes  to  the  right  or  left.  Under  the  subject  of  Telegraphy,  it  will  be  seen 
how  these  alternate  motions  can  be  used  to  form  an  alphabet. 


456  On  Light.  [523- 

The  heliograph  has  proved  of  essential  service  in  the  recent  campaigns 
in  Africa  and  Afghanistan.  Instead  of  any  special  form  of  apparatus,  an 
ordinary  shaving  mirror  or  hand  glass  is  frequently  used  ;  and  the  proper 
inclination  having  been  given  so  as  to  send  the  sun's  rays  to  the  distant 
station,  which  is  very  easily  effected,  the  signals  are  produced  by  obscuring 
the  mirror  by  sliding  a  piece  of  paper  over  it  for  varying  lengths  of  time. 
In  this  way  longer  or  shorter  flashes  of  light  are  produced,  which,  properly 
combined,  form  the  alphabet. 

Of  course  this  mode  of  signalling  can  only  be  used  where  the  sun's  light 
is  available,  but  it  has  the  advantage  of  being  cheap,  simple,  and  portable. 
Signals  have  been  sent  at  the  rate  of  12  words  a  minute,  through  distances, 
in  very  fine  weather,  of  40  miles. 


REFLECTION   OF  LIGHT   FROM   CURVED   SURFACES. 

524.  Spherical  mirrors. — It  has  been  already  stated  (512)  that  there  are 
several  kinds  of  curved  mirrors  ;  those  most  frequently  employed  are 
spherical  and  parabolic  mirrors. 

Spherical  mirrors  are  those  whose  curvature  is  that  of  a  sphere  ;  their 
surface  may  be  supposed  to  be  formed  by  the  revolution  of  an  arc  MN  (fig. 
413),  about  the  radius  CA,  which  unites  the  middle  of  the  arc  to  the  centre 
of  the  circle  of  which  it  is  a  part.  According  as  the  reflection  takes  place 
from  the  internal  or  from  the  external  face  of  the  mirror  it  is  said  to  be  concave 
or  convex.  C,  the  centre  of  the  hollow  sphere,  of  which  the  mirror  forms  part, 
is  called  the  centre  of  curvature  or  geometrical  centre  :  the  point  A  is  the 
centre  of  the  figure.  The  infinite  right  line,  AL,  which  passes  through  A 
and  C,  is  the  principal  axis  of  the  mirror;  any  right  line  which  simply 
passes  through  the  centre  C,  and  not  through  the  point  A,  is  a  secondary 
axis.  The  angle  MCN,  formed  by  joining  the  centre  and  extremities  of  the 
mirror,  is  the  aperture.  A  principal  or  meridional  section  is  any  section 
made  by  a  plane  through  its  principal  axis.  In  speaking  of  mirrors  those 
lines  alone  will  be  considered  which  lie  in  the  same  principal  section. 

The  theory  of  the  reflection  of  light  from  curved  mirrors  is  easily  deduced 
from  the  laws  of  reflection  from  plane  mirrors,  by  considering  the  surface  of 
the  former  as  made  up  of  an  infinitude  of  extremely  small  plane  surfaces, 
which  are  its  elements.  The  normal  to  the  curved  surface  at  a  given  point  is 

the  perpendicular,  to  the 
corresponding  element,  or, 
what  is  the  same  thing, 
to  its  corresponding  tan- 
gent plane.  It  is  shown  in 
geometry  that  in  spheres 
all  the  normals  pass 
through  the  centre  of  cur- 

*&•  4T3-  vature,  so  that  the  normal 

may  readily  be  drawn  to  any  point  of  a  spherical  mirror. 

525.  Focus  of  a  spherical  concave  mirror. — In  a  curved  mirror  the 
focus  is  a  point  in  which  the  reflected  rays  meet  or  tend  to  meet,  if  produced 


-525 J  Focus  of  a  Spherical  Concave  Mirror.  457 

either  backwards  or  forwards  ;  there  may  either  be  a  real  focus  or  a  virtual 
focus. 

Real  focus.— We  shall  first  consider  the  case  in  which  the  luminous  rays 
are  parallel  to  the  principal  axis,  which  presupposes  that  the  luminous  body 
is  at  an  infinite  distance  ;  let  GD  (fig.  413)  be  such  a  ray. 

From  the  hypothesis  that  curved  mirrors  are  composed  of  a  number  of 
infinitely  small  plane  elements,  this  ray  would  be  reflected  from  the  element 
corresponding  to  the  poi  nt  D,  according  to  the  laws  of  the  reflection  from 
plane  mirrors  (513)  ;  that  is,  that  CD  being  the  normal  at  the  point  of 
incidence  D,  the  angle  of  reflection  CDF  is  equal  to  the  angle  of  incidence 
GDC,  and  is  in  the  same  plane.  It  follows  from  this,  that  the  point  F, 
where  the  reflected  ray  cuts  the  principal  axis,  divides  the  radius  of  curva- 
ture AC  very  nearly  into  two  equal  parts.  For  in  the  triangle  DFC,  the 
angle  DCF  is  equal  to  the  angle  CDG,  for  they  are  alternate  and  opposite 
angles  ;  likewise  the  angle  CDF  is  equal  to  the  angle  CDG,  from  the  laws 
of  reflection  ;  therefore  the  angle  FDC  is  equal  to  the  angle  FCD,  and  the 
sides  FC  and  FD  are  equal  as  being  opposite  to  equal  angles.  Now  the 
smaller  the  arc,  AD,  the  more  nearly  does  DF  equal  AF  ;  and  when  the 
arc  is  only  a  small  number  of  degrees,  the  right  lines  AF  and  FC  may  be 
taken  as  approximately  equal,  and  the  point  F  may  be  taken  as  the  middle 
of  AC.  So  long  as  the  aperture  of  the  mirror  does  not  exceed  8  to  10  degrees 
any  other  ray,  HB,  will,  after  reflection,  pass  very  nearly  through  the  point  F. 
Hence,  when  a  pencil  of  rays  parallel  to  the  axis  falls  on  a  concave  mirror 
the  rays  intersect  after  reflection  in  the  same  point,  which  is  at  an  equal 
distance  from  the  centre  of  curvature,  and  from  the  mirror.  This  point  is 
called  the  principal  focus  of  the  mirror,  and  the  distance  AF  is  the  principal 
focal  distance. 

All  rays  parallel  to  the  axis  meet  in  the  point  F  ;  and,  conversely,  if  a 
luminous  point  be  placed  at  F,  the  rays  emitted  by  this  point  will  after 
reflection  take  the  directions  DG,  BH,  parallel  to  the  principal  axis  ;  for  in 
this  case  the  angles  of  incidence  and  reflection  have  changed  places ;  but 
these  angles  always  remain  equal. 

The  case  is  now  to  be  considered  in  which  the  rays  are  emitted  from  a 
luminous  point,  L  (fig.  414),  placed  on  the  principal  axis,  but  at  such  a  dis- 
tance that  they  are  not 
parallel,  but  divergent.  The 
angle  LKC,  which  the  in- 
cident ray  LK  forms  with 
the  normal  KC,  is  smaller 
than  the  angle  SKC,  which 
the  ray  SK,  parallel  to  the 
axis,  forms  with  the  same 
normal,  and,  consequently, 
the  angle  of  reflection  corre- 
sponding to  the  ray  LK  must  be  smaller  than  the  angle  C  K  F,  corresponding 
to  the  ray  SK.  And,  therefore,  the  ray  LK  will  meet  the  axis  after  reflection 
at  a  point,  /,  between  the  centre  C  and  the  principal  focus  F.  So  long  as 
the  aperture  of  the  mirror  does  not  exceed  a  small  nnmber  of  degrees,  all 
the  rays  from  the  point  L  will  intersect  after  reflection  in  the  point  /.  This 

X 


458  On  Light.  [525- 

point  is  called  the  conjugate  focus ;  for  there  is  this  connection  between  the 
points  L  and  /,  that  if  the  luminous  point  were  transferred  to  /,  its  conjugate 
focus  would  be  at  L,  /K  being  the  incident  and  KL  the  reflected  ray. 

On  considering  the  figure  414  it  will  be  seen  that  when  the  point  L  is 
brought  near  to  or  removed  from  the  centre  C,  its  conjugate  focus  approaches 
or  recedes  in  a  corresponding  manner,  for  the  angles  of  incidence  and  re- 
flection increase  or  decrease  together. 

If  the  point  L  coincides  with  the  centre  C,  the  angle  of  incidence  is 
null,  and  as  the  angle  of  reflection  must  be  the  same,  the  ray  is  reflected  on 
itself,  and  the  focus  coincides  with  the  luminous  point.  When  the  luminous 
point  is  between  the  centre  C  and  the  principal  focus,  the  conjugate  focus  in 
turn  is  on  the  other  side  of  the  centre,  and  is  further  from  the  centre  accord- 
ing as  the  luminous  point  is  nearer  the  principal  focus.  If  the  luminous  point 
coincides  with  the  principal  focus,  the  reflected  rays,  being  parallel  to  the 
axis,  will  not  meet,  and  there  is,  consequently,  no  focus, 

Virtual  Jocits. — There  is,  lastly,  the  case  in  which  the  point  is  placed  at 
L,  between  the  principal  focus  and  the  mirror  (fig.  415).  Any  ray,  LM, 
emitted  from  the  point  L,  makes  with  the  normal  CM  an  angle  of  incidence, 
LMC,  greater  than  FMC  ;  the  angle  of  reflection  must  be  greater  than  CMS, 
and  therefore  the  reflected  ray  ME  diverges  from  the  axis  AK.  This  is  also 
the  case  with  all  rays  from  the  point  L,  and  hence  these  rays  do  not  intersect, 
and,  consequently,  form  no  conjugate  focus  ;  but  if  they  are  conceived  to  be 
prolonged  on  the  other  side  of  the  mirror,  their  prolongations  will  intersect 

in  the  same 
point,  /,  on 
the  axis,  and 
the  eye  ex- 
periences the 
same  i  im- 
pression as 
if  the  rays 
were  directly 

Fig.  415.  Fig.  416.  emitted  from 

the  point  /.     Hence  a  virtual  focus  is  formed  quite  analogous  to'those  formed 
by  plane  mirrors  (514). 

In  all  these  cases  it  is  seen  that  the  position  of  the  principal  focus  is 
constant,  while  that  of  the  conjugate  foci  and  of  the  virtual  foci  vary.  The 
principal  and  the  conjugate  foci  are  always  on  the  same  side  of  the  mirror  as  the 
luminous  point,  while  the  virtual  focus  is  always  on  the  other  side  of  the  mirror. 
Hitherto  the  luminous  point  has  always  been  supposed  to  be  placed  on 
the  principal  axis  itself,  and  then  the  focus  is  formed  on  this  axis.  In  the 
casein  which  the  luminous  point  is  situate  on  a  secondary  axis,  LB  (fig.  416), 
by  applying  to  this  axis  the  same  reasoning  as  in  the  preceding  case,  it  will 
be  seen  that  the  focus  of  the  point  L  is  formed  at  a  point  /,  on  the  secondary 
axis,  and  that,  according  to  the  distance  of  the  point  L,  the  focus  may  be 
either  principal,  conjugate,  or  virtual. 

526.  Foci  of  convex  mirrors. — In  convex  mirrors  there  are  only  virtual 
foci.  Let  SI,  TK  ,  »  .  (fig.  417)  be  rays  parallel  to  the  principal  axis  of  a 
convex  mirror.  These  rays,  after  reflection,  take  the  diverging  directions 


-527]         Determination  of  Principal  Focus  of  a  Mirror.         459 

IM,  KH,  which,  when  continued,  meet  in  a  point,  F,  which  is  the  principal 
•virtual focus  of  the  mirror.  By  means  of  the  triangle  CKF,  it  may  be  shown, 
in  the  same  manner  as  with  concave  mirrors,  that  the  point  F  is  approxi- 
mately the  middle  of  the  radius  of  curvature,  CA. 


Fig-  4*7. 

If  the  incident  luminous  rays,  instead  of  being  parallel  to  the  axis,  pro- 
ceed from  a  point  L.  situated  on  the  axis  at  a  finite  distance,  it  is  at  once  seen 
that  a  virtual  focus  will  be  formed  at  a  point  /,  between  the  principal  focus  F 
and  the  mirror. 

527.  Determination  of  the  principal  focus. — In  the  applications  of 
concave  and  convex  mirrors,  it  is  often  necessary  to  know  the  radius  of 
curvature.  This  is  tantamount  to  finding  the  principal  focus  ;  for  being 
situated  at  the  middle  of  the  radius,  it  is  simply  necessary  to  double  the  focal 
distance. 

To  find  this  focus  with  a  concave  mirror,  it  is  exposed  to  the  sun's  rays, 
so  that  its  principal  axis  is  parallel  to  them,  and  then  with  a  small  screen  of 
ground  glass  the  point  is  sought  at  which  the  image  is  formed  with  the 
greatest  intensity  ;  this  is  the  principal  focus.  The  radius  of  the  mirror  is 
double  this  distance. 

If  the  mirror  is  convex,  it  is  covered  with  paper  ;  but  two  small  portions, 
H  and  I,  are  left  exposed  at  equal  distances  from  the  centre  of  the  figure  A, 
and  on  the  same  principal  section  (fig.  418).  A  screen,  MN,  in  the  centre 
of  which  is  an  opening  larger 
than  the  distance  H  I,  is  placed 
before  the  mirror.  If  a  pen- 
cil of  solar  rays,  SH,  S'l, 
parallel  to  the  axis,  fall  on  the 
mirror,  the  light  is  reflected 
at  H  and  I,  on  the  parts 
where  the  mirror  is  left  ex- 
posed, and  forms  on  the  screen 
two  brilliant  images  at  h  and  *". 


Fig.  418. 


By  moving  the  screen  MN  nearer  to  or  farther  from  the  mirror,  a  position  is 
found  at  which  the  distance  hi  is  double  that  [of  HI.  The  distance  AD 
from  the  screen  to  the  mirror  then  equals  the  principal  focal  distance.  For 
the  arc  HAI  does  not  sensibly  differ  from  its  chord,  and  because  the 

triangles  FHI  and  F///are  similar,  -J^E^  ;   but  HI    is   half  of  ///,  and 

X2 


460         .  On  Light.  [527- 

therefore  also  FA  is  the  half  of  FD,  and  therefore  AD  is  equal  to  AF. 
Further,  FA  is  the  principal  focal  distance  ;  for  the  rays  SH  and  S'l  are 
parallel  to  the  axis  :  consequently  also  twice  the  distance  AD  equals  the 
radius  of  curvature  of  the  mirror. 

528.  Formation  of  images  in  concave  mirrors. — Hitherto  it  has  been 
supposed  that  the  luminous  or  illuminated  object  placed  in  front  of  the 
mirror  was  simply  a  point ;  but  if  this  object  has  a  certain  magnitude,  we 
can  conceive  a  secondary  axis  drawn  through  each  of  its  points,  and 
thus  a  series  of  real  or  virtual  foci  could  be  determined,  the  collection  of 
which  composes  the  image  of  the  object.  By  the  aid  of  the  construc- 
tions which  have  served  for  determining  the  foci,  we  shall  investigate  the 
position  and  magnitude  of  these  images  in  concave  and  in  convex  mirrors. 

Real  image. — We  shall  first  take  the  case  in  which  the  mirror  is  concave, 
and  the  object  AB  (fig.  419)  is  on  the  other  side  of  the  centre.  To  obtain 
the  image  or  the  focus  of  any  point,  A,  a  secondary  axis,  AE,  is  drawn  from 
this  point,  and  then  drawing  from  the  point  A  an  incident  ray,  AD,  the 
normal  to  this  point,  CD,  is  taken,  and  the  angle  of  reflection  CDa  is  made 
equal  to  the  angle  of  incidence  ADC.  The  point  a,  where  the  reflected  ray 


Fig.  419. 

•cuts  the  secondary  axis  AE,  is. the  conjugate  focus  of  the  point  A,  because 
every  other  ray  drawn  from  this  point  passes  through  a.  Similarly  if  a 
secondary  axis,  BI,  be  drawn  from  the  point  B,  the  rays  from  this  point 
meet  after  reflection  in  b,  and  form  the  conjugate  focus  of  B.  And  as  the 
images  of  all  the  points  of  the  object  are  formed  between  a  and  b,  ab  is  the 
complete  image  of  AB.  From  what  has  been  said  about  foci  (525),  it  follows 
that  this  image  is  real,  inverted,  smaller  than  the  object,  and  placed  between 
the  centre  of  curvature  and  the  principal  focus.  This  image  may  be  seen  in 
two  ways  ;  by  placing  the  eye  in  the  continuation  of  the  reflected  rays,  and 
then  it  is  an  aerial  image  which  is  seen  ;  or  the  rays  are  collected  on  a 
screen,  on  which  the  image  appears  to  be  depicted. 

If  the  luminous  or  illuminated 
object  is  placed  at  ab,  between 
the  principal  focus  and  the 
centre,  its  image  is  formed  at 
AB.  It  is  then  a  real  but  in- 
verted image ;  it  is  larger  than 
the  object,  and  the  larger  as  the 
object,  ab,  is  nearer  the  focus. 
Fig-  42°-  If  the  object  is  placed  in  the 

principal  focus  itself,  no  image  is  produced  ;  for  then  the  rays  emitted  from 


-530]  Formula  for  Spherical  Mirrors.  461 

each  point  form,  after  reflection,  as  many  pencils  respectively  parallel  to 
the  secondary  axis,  which  is  drawn  through  the  point  from  which  they  are 
emitted  (524),  and  hence  neither  foci  nor  images  are  formed. 

When  all  points  of  the  object  AB  are  above  the  principal  axis  (fig.  420), 
by  repeating  the  preceding  construction,  it  is  readily  seen  that  the  image  of 
the  object  is  formed  at  ab. 

Virtual  image. — The  case  remains  in  which  the  object  is  placed  between 
the  principal  focus  and  the  mirror.  Let  AB  be  this  object  (fig.  421) ;  the 
incident  rays  after  reflection 
take  the  directions  DI  and  KH, 
and  their  prolongations  form  a 
virtual  image,  a,  of  the  point  A, 
on  the  secondary  axis.  Simi- 
larly, an  image  of  B  is  formed 
at  b ;  consequently  the  eye  sees 
at  ab  the  image  of  AB.  This 
image  is  virtual,  erect,  and 
larger  than  the  object. 

From  what  has  been  stated, 
it  is  seen  that,  according  to  the 

distance  of  the  object,  concave  mirrors  produce  two  kinds  of  images,  or  none 
at  all  ;  a  person  notices  this  by  placing  himself  before  a  concave  mirror.  At 
a  certain  distance  he  sees  an  image  of  himself  inverted  and  smaller  ;  this  is 
the  real  image  ;  at  a  less  distance  the  image  becomes  confused,  and  dis- 
appears when  he  is  at  the  focus  ;  still  nearer  the  image  appears  erect,  but 
larger — it  is  then  a  virtual  image. 

529.  Formation  of  images  in  convex  mirrors. — Let  AB  (fig.  422)  be 
an  object  placed  before  a  mirror  at  any  given  distance.     AC  and  BC  are 
secondary  axes,  and  it  follows,  from 

what  has  been  already  stated,  that 
all  the  rays  from  A  are  divergent 
after  reflection,  and  that  their  pro- 
longations pass  through  a  point,  a, 
which  is  the  virtual  image  of  the 
point  A.  Similarly  the  rays  from 
B  form  a  virtual  image  of  it  in  the 
point  b.  The  eye  which  receives 
the  divergent  rays  DE,  KA,  .  . 

sees  in  ab  an  image  of  AB.  Hence,  whatever  the  position  of  an  object 
before  a  convex  mirror,  the  image  is  always  virtual,  erect,  and  smaller  than 
the  object. 

530.  Formulae    for   spherical    mirrors. — The    relation    between    the- 
position  of  an  object  and  that  of  its  image  in  spherical  mirrors  may  be 
expressed  by  a  very  simple  formula.     In  the  case  of  concave  mirrors,  let 
R  be  its  radius  of  curvature,  p  the  distance  LA  of  the  object,  L  (fig.  423), 
and/'  the  distance  /A  of  the  image  from  the  mirror.     In  the  triangle  LM/, 
the  normal   MC  divides  the   angle  LM/  into  two   equal  parts,    and  from 
geometry  it  follows  that  the  two  segments  LC,  C/  are  to  each  other  as  the 
two  sides  containing  the  angle  ;  that  is, 


462  On  Light.  [530- 

K>  rCT::  therefore  CL  x  LM  =  CL  x  /M.  \ 

If  the  arc  AM  does  not  exceed  5  or  6  degrees,  the  lines  ML  and  M/  are 

approximately  equal  to  AL  and  A/  ; 
that  is,  to/  and/'. 

Further,     C/=CA-A/=R-/', 
and  also     CL  =  AL-AC=/-R. 

The   values   substituted  in  the 
preceding  equations  give 

(R 

From  which  transposing  and  reducing  we  have 


'  =  2//'     '.  (i) 

If  the  terms  of  this  equation  be  all  divided  by//'R,  we  obtain 

»  =  K  '        '         '        "    •« 

which  is  the  usual  form  of  the  equation. 
From  the  equation  (i)  we  get 

/'--^-  (3) 

.       €      2/-R  U; 

which  gives  the  distance  of  the  image  from  the  mirror,  in  terms  of  the 
distance  of  the  object,  and  of  the  radius  of  curvature. 

531:  Discussion  of  the  formulae  for  mirrors.  —  We  shall  now  in- 
vestigate the  different  values  of  /',  according  to  the  values  of  p  in  the 
formula  (3). 

i.  Let  the  object  be  placed  at  an  infinite  distance  on  the  axis,  in  which 
case  the  incident  rays  are  parallel.  To  obtain  the  value  of/',  both  terms  of 
the  fraction  (3)  must  be  divided  by  /,  which  gives 

'-—  K 

,-*        ....         (4) 

•p  TD 

as  p  is  infinite,  --is  zero,  and  we  have/'  =  —  ;  that  is,  the  image  is  formed 

in  the  principal  focus,  as  ought  to  be  the  case,  for  the  incident  rays  are 
parallel  to  the  axis. 

ii.  If  the  object  approaches  the  mirror,  p  decreases,  and  as  the  denomi- 
nator of  the  formula  (4)  diminishes,  the  value  of/7  increases  ;  consequently 
the  image  approaches  the  centre  at  the  same  time  as  the  object,  but  it  is 
always  between  the  principal  focus  and  the  centre,  for  so  long  as 

p  is  >  R,  we  have        ^  >  ?and  <  R. 

2-5        2 

p 

iii.  When  the  object  coincides  with  the  centre,  p  =  R,  and,  consequently, 
p'  =  R  ;  that  is,  the  image  coincides  with  the  object. 

iv.  When  the  luminous  object  is  between  the  centre  and  the  principal 


-533]  Spherical  Aberration.     Caustics.  463 

focus,  /<R,  and  hence  from  the  formula  (4),  /'>R;  that  is,  the  image  is 
formed  on  the  other  side  of  the  centre.  When  the  object  is  in  the  focus, 

•p  ID 

p  =  v  which  gives/'--  -=  °°  ;  that  is,  the  image  is  at  an  infinite  distance, 

for  the  reflected  rays  are  parallel  to  the  axis. 

v.  Lastly,  if  the  object  is  between  the  principal  focus  and  the  mirror,  we 

•D 

get  p  <[  —  ;  p'  is  then  negative,  because  the  denominator  of  the  formula  (4) 

is  negative.  Therefore,  the  distance  p'  of  the  mirror  from  the  image  must 
be  calculated  on  the  axis  in  a  direction  opposite  to/.  The  image  is  then 
virtual,  and  is  on  the  other  side  of  the  mirror. 

Making/'  negative  in  the  formula  (2),  it  becomes  I  —  .1-  =  3.-  in  this 

P     P     R 
form  it  comprehends  all  cases  of  virtual  images  in  concave  mirrors. 

In  the  case  of  concave  mirrors,  the  image  is  always  virtual  (525)  ;  /'  and 
R  are  of  the  same  sign,  since  the  image  and  the  centre  are  on  the  same  side 
of  the  mirror,  while  the  object  being  on  the  opposite  side,  /  is  of  the  contrary 
sign  ;  hence  in  the  formula  (2)  we  get 


P' 

as  the  formula  for  convex  mirrors.  It  may  also  be  found  directly  by  the 
same  geometrical  considerations  as  those  which  have  led  to  the  formula  (2) 
for  concave  mirrors. 

It  must  be  observed  that  the  preceding  formulae  are  not  rigorously  true, 
inasmuch  as  they  depend  upon  the  assumption  that  the  lines  LM  and  /M 
(fig.  423)  are  equal  to  LA  and  A/;  although  this  is  not  true,  the  error 
diminishes  without  limit  with  the  angle  MCA  :  and  when  this  angle  does 
not  exceed  a  few  degrees,  the  error  is  so  small  that  it  may,  in  practice,  be 
neglected. 

532.  Calculation  of  the  magnitude  of  images.  —  By  means  of  the  above 
formulas  the  magnitude  of  an  image  may  be  calculated,  when  the  distance  of 
the  object,  its  magnitude, 
and  the  radius  of  the  mirror 
are  given.  For  if  BD  be 
the  object  (fig.  424),  bd  its 
image,  and  if  the  distance 
A  and  the  radius  AC  be 
known,  A0  can  be  calculated 
by  means  of  formula  (3)  of 
article  530.  A0  known,  oC  *ig.  424. 

can  be   calculated.     But  as 

the  triangles  BCD  and  dCb  are  similar,  their  bases  and  heights  are  in  thfe 
proportion  bd  :  BD  =C0  :  CK,  or 

Length  of  the  image  :  length  of  the  object 

=  Distance  from  image  to  centre  :  distance  from  the  object  to  the  centre. 

533.  spherical  aberration.     Caustic*.—  In  the  foregoing  theory  of  the 
foci  and  images,  of  spherical  mirrors,  it  has  already  been  observed  that  the 


464  On  Light.  [533- 

reflected  rays  only  pass  through  a  single  point  when  the  aperture  of  the 
mirror  does  not  exceed  8  or  10  degrees  (531).  With  a  larger  aperture  the 
rays  reflected  near  the  edges  meet  the  axis  nearer  the  mirror  than  those  that 
are  reflected  at  a  small  distance  from  the  neighbourhood  of  the  centre  of 
the  mirror.  Hence  arises  a  want  of  precision  in  these  images,  which  is  called 
spherical  aberration  by  reflection,  to  distinguish  it  from  the  spherical  aber- 
ration by  refraction,  which  occurs  in  the'case  of  lenses. 

Every  reflected  ray  cuts  the  one  next  to  it  (fig.  425),  and  their  points  of 
intersection  form  in  space  a  curved  surface,  which  is  called  the  caustic  by 

reflection.  The  curve  FM  repre- 
sents one  of  the  branches  of  a 
section  of  this  surface  made  by  the 
plane  of  the  paper.  When  the 
light  of  a  candle  is  reflected  from 
the  inside  of  a  cup  or  tumbler,  a 
section  of  the  caustic  surface  can 
be  seen  by  partly  filling  the  cup  or 
tumbler  with  milk. 

534.  Applications  of  Mirrors.  Beliostat. — The  applications  of  plane 
mirrors  in  domestic  economy  are  well  known.  Mirrors  are  also  frequently 
used  in  physical  apparatus  for  sending  light  in  a  certain  direction.  The 
solar  light  can  only  be  sent  in  a  constant  direction  by  making  the  mirror 
moveable.  It  must  have  a  motion  which  compensates  for  the  continual 
change  in  the  direction  of  the  sun's  rays  produced  by  the  apparent  diurnal 
motion  of  the  sun.  This  result  is  obtained  by  means  of  a  clockwork  motion, 
to  which  the  mirror  is  fixed,  and  which  causes  it  to  follow  the  course  of  the 
sun.  This  apparatus  is  called  the  heliostat.  We  have  already  seen  an 
application  of  this  in  the  heliograph  (523).  The  reflection  of  light  is  also 
used  to  measure  the  angles  of  crystals  by  means  of  the  instruments  known 
as  reflecting  goniometers. 

Concave  spherical  mirrors  are  also  often  used.  They  are  applied  for 
magnifying  mirrors,  as  in  a  shaving  mirror.  They  have  been  employed  for 

burning  mirrors,  and  are  still  used  in 
telescopes.  They  also  serve  as  reflec- 
tors, for  conveying  light  to  great  dis- 
tances, by  placing  a  luminous  object 
in  their  principal  focus.  For  this 
purpose,  however,  parabolic  mirrors 
are  preferable. 

While  the  images  of  objects  seen 
in  concave  or  convex  mirrors  appear 
smaller  or  larger,  but  otherwise  similar 
geometrically,  this  is  not  the  case  with 
cylindrical  or  with  conical  mirrors. 
Objects  seen  in  such  mirrors  appear 

ludicrously  distorted.  From  the  laws  of  reflection  the  shape  of  such  a 
distorted  figure  can  be  geometrically  constructed.  In  like  manner  distorted 
images  of  objects  can  be  constructed  which,  seen  in  such  mirrors,  appear 
in  their  normal  proportions. '  They  are  called  anamorphoses. 


-535]  Parabolic  Mirrors.  465 

535.  Parabolic  mirrors. — Parabolic  mirrors  are  concave  mirrors,  whose 
surface  is  generated  by  the  revolution  of  the  arc  of  a  parabola,  AM,  about 
its  axis,  AX  (fig.  426). 

It  has  been  already  stated  that  in  spherical  mirrors  the  rays  parallel  to 
the  axis  converge  only  approximately  to  the  principal  focus,  and  reciprocally 
when  a  source  of  light  is  placed  in  the  principal  focus  of  these  mirrors  the 
reflected  rays  are  not  exactly  parallel  to  the  axis.  Parabolic  mirrors  are  free 
from  this  defect ;  they  are  more  difficult  to  construct,  but  are  better  for  re- 
flectors. It  is  a  property  of  a  parabola  that  the  right  line  FM,  drawn  from 
the  focus,  F,  to  any  point,  M,  of  the  curve,  and  the  line  ML,  parallel  to  the 
axis  AF,  make  equal  angles  with  the  tangent  TT'  at  this  point.  Hence  all 
rays  parallel  to  the  axis  after  reflection  meet  in 
the  focus  of  the  mirror  F  ;  and  conversely,  when 
a  source  of  light  is  placed  in  the  focus,  the  rays 
incident  on  the  mirror  are  reflected  exactly 
parallel  to  the  axis.  The  light  thus  reflected 
tends  to  maintain  its  intensity  even  at  a  great 
distance,  for  it  has  been  seen  (508)  that  it  is  the 
divergence  of  the  luminous  rays  which  princi- 
pally weakens  the  intensity  of  light. 

From  this  property  parabolic  mirrors  are  used 
in  carriage  lamps,  and  in  the  lamps  placed  in 
front  of  and  behind  railway  trains.  These  re- 
flectors were  formerly  used  for  lighthouses,  but 
have  been  replaced  by  lenticular  glasses. 

When  two  equal  parabolic  mirrors  are  cut 
by  a  plane  perpendicular  to  the  axis  passing 
through  the  focus,  and  are  then  united  at  their 
intersections  as  shown  in  figure  427,  so  that 

their  foci  coincide,  a  system  of  reflectors  is  obtained  with  which  a  single 
lamp  illuminates  in  two  directions  at  once.  This  arrangement  is  used  in 
lighting  staircases  and  passages. 


*3 


466  On  Light.  [536- 


CHAPTER   III. 

SINGLE  REFRACTION.      LENSES. 

536.  Phenomenon  of  refraction. — Refraction  is  the  deflection  or  bending1 
which  luminous  rays  experience  in  passing  obliquely  from  one  medium  to 
another  :  for  instance,  from  air  into  water.  We  say  obliquely,  because  if  the 
incident  ray  is  perpendicular  to  the  surface  separating  the  two  media,  it  is 
not  bent,  and  continues  its  course  in  a  right  line. 

The  incident  ray  being  represented  by  SO  (fig.  428),  the  refracted  ray  is 
the  direction  OH  which  light  takes  in  the  second  medium  ;  and  of  the  angles 
SOA  and  HOB,  which  these  rays  form  with  the  line  AB,  at  right  angles  to 
the  surface  which  separates  the  two  media,  the  first' 
is  the  angle  of  incidence,  and  the  other  the  angle  of 
refraction.  According  as  the  refracted  ray  ap- 
proaches or  deviates  from  the  normal,  the  second 
medium  is  said  to  be  more  or  less  refringent  or 
refracting  than  the  first. 

All  the  light  which  falls  on  a  refracting  surface 
does  not  completely  pass  into  it ;  one  part  is  re- 
Fig.  42b.  fleeted  and  scattered  (518),  while  another  penetrates 
into  the  medium. 

Mathematical  analysis  shows  that  the  direction  of  refraction  depends  on 
the  relative  velocity  of  light  in  the  two  media.  On  the  undulatory  theory 
the  more  highly  refracting  medium  is  that  in  which  the  velocity  of  propaga- 
tion is  least. 

In  uncrystallised  media,  such  as  air,  liquids,  ordinary  glass,  the  luminous 
ray  is  singly  refracted  ;  but  in  certain  crystallised  bodies,  such  as  Iceland 
spar,  selenite,  &c.,  the  incident  ray  gives  rise  to  two  refracted  rays.  The 
latter  phenomenon  is  called  double  refraction,  and  will  be  discussed  in  another 
part  of  the  book.  We  shall  here  deal  exclusively  with  single  refraction. 

537.  Itaws  of  single  refraction. — When  a  luminous  ray  is  refracted  in 
passing  from  one  medium  into  another  of  a  different  refractive  power,  the 
following  laws  prevail  : — 

I.  Whatever  the  obliquity  of  the  incident  ray,  the  ratio  which  the  line  of 
the  incident  angle  bears  to  the  sine  of  the  angle  of  refraction  is  constant  for 
the  same  two  media,  but  varies  with  different  media. 

II.  The  incident  and  the  refracted  ray  are  in  the  same  plane,  which  is 
perpendicular  to  the  surface  separating  the  two  media. 

These  have  been  known  as  Descartes'  laws  ;  they  are,  however,  really 
due  to  Willibrod  Snell,  who  discovered  them  in  1620  ;  they  are  demon- 
strated by  the  same  apparatus  as  that  used  for  the  laws  of  reflection  (gn). 
The  plane  mirror  in  the  centre  of  the  graduated  circle  is  replaced  by  a 


-639] 


Effects  produced  by  Refraction. 


467 


semi-cylindrical  glass  vessel,  filled  with  water  to  such  a  height  that  its 
level  is  exactly  the  height  of  the  centre  (fig.  429).  If  the  mirror,  M,  be 
then  so  inclined  that  a  reflected  ray,  MO,  is  directed  towards  the  centre, 
it  is  refracted  on  passing  into  the  water,  but  it  passes  out  without  refraction' 
because  then  its  direction  is  at  right  angles  to  the  curved  sides  of  the 
vessel.  In  order  to  observe  the  course 
of  the  refracted  ray,  it  is  received  on  a 
screen,  P,  which  is  moved  until  the 
image  of  the  aperture  in  the  screen  N 
is  formed  in  its  centre.  In  all  positions 
of  the  screens  N  and  P,  the  sines  of 
the  angles  of  incidence  and  refraction 
are  measured  by  means  of  two  graduated 
rules,  moveable  so  as  to  be  always  hori- 
zontal, and  hence  perpendicular  to  the 

diameter  AD. 

On  reading  off  the  length  of  the  sines 

of  the  angles  MOA  and   DOP   in   the 

scales  I  and  R,  the  numbers  are  found 

to  vary  with  the  position  of  the  screens, 

but  their  ratio  is  constant  ;    that   is,  if 

the  sine  of  incidence  becomes  twice  or 

three  times  as  large,  the  sine  of  refrac- 
tion increases  in  the  same  ratio,  which 

demonstrates  the  first  law.     The  second 

law  follows  from  the  arrangement  of  the 

apparatus,  for  the  plane  of  the  graduated  limb  is  perpendicular  to  the  surface 

of  the  liquid  in  the  semi-cylindrical  vessel. 

538.  Index  of  refraction. — The  ratio  between  the  sines  of  the  incident 
and  refracted  angle  is  called  index  of  refraction  or  refractive  index.     It 
varies  with  the  media  ;  for  example,  from  air  to  water  it  is  f,  and  from  air  to 
glass  it  is  f. 

If  the  media  is  considered  in  an  inverse  order — that  is,  if  light  passes 
from  water  to  air,  or  from  glass  to  air — it  follows  the  same  course,  but  in  a 
contrary  direction,  PO  becoming  the  incident  and  OM  the  refracted  ray. 
Consequently  the  index  of  refraction  is  reversed  ;  from  water  to  air  it  is  then 
4,  and  from  glass  to  air  f. 

539.  Effects  produced  by  refraction. — In  consequence  of  refraction, 
bodies  immersed  in  a  medium  more  highly  refracting  than  air  appear  nearer 
the  surface  of  this  medium,  but  they  appear  to  be  more  distant  if  immersed 
in  a  less  refracting  medium.     Let  L  (fig.  430)  be  an  object  immersed  in  a 
mass  of  water.     In  passing  thence  into  air,  the  rays  LA,  LB  .  .  .  diverge 
from  the  normal  to  the  point  of  incidence,  and  take  the  direction  AC,  BD 
.  .  .  ,  the  prolongations  of  which  intersect  approximately  in  the  point  L', 
placed  on  the  perpendicular  L'K.     The  eye  receiving  these  rays  sees  the 
object  L  at  L'.     The  greater  the  obliquity  of  the  rays  LA,  LB  .  .  .  the  higher 
the  object  appears. 

It  is  for  the  same  reason  that  a  stick  plunged  obliquely  into  water  appears 
bent  (fig.  431),  the  immersed  part  appearing  raised. 


Fig.  429 


468 


On  Light. 


[539- 


Owing  to  an  effect  of  refraction,  stars  are  visible  to  us  even  when  they  are 
below  the  horizon.  For  as  the  layers  of  the  atmosphere  are  denser  in  pro- 
portion as  they  are  nearer  the  earth,  and  as  the  refractive  power  of  a  gas 


Fig.  430. 


Fig.  432. 


increases  with  its  density  (550),  it  follows  that  on  entering  the  atmosphere 
the  luminous  rays  become  bent,  as  seen  in  fig.  432,  describing  a  curve 
before  reaching  the  eye,  so  that  we  can  see  the  star  at  S'  along  the  tangent 
of  this  curve  instead  of  at  S.  In  our  climate  the  atmospheric  refraction 
does  not  raise  the  stars  when  on  the  horizon  more  than  half  a  degree. 
Another  experimental  illustration  of  the  effect  of  refraction  is  the  following : — 
A  coin  is  placed  in  an  empty  porcelain  basin,  and  the  position  of  the  eye  is 
so  adjusted  that  it  is  just  not  visible.  If  now,  the  position  of  the  eye  remaining 
unaltered,  water  be  poured  into  the  basin,  the  coin  becomes  visible.  A  con- 
sideration of  fig.  430  will  suggest  the  explanation  of  this  phenomenon. 

540.  Total  reflection.  Critical  angle. — When  a  luminous  ray  passes 
from  one  medium  into  another  which  is  less  refracting,  as  from  water  into 

air,  it  has  been 
seen  that  the  angle 
of  incidence  is  less 
than  the  angle  of 
refraction.  Hence, 
when  light  is  pro- 
pagated in  a  mass 
of  water  from  S  to 
O  (fig.  433),  there 
is  always  a  value 
of  the  angle  of  in- 
cidence SOB,  such 

that  the  angle  of  refraction,  AOR,  is  a  right  angle,  in  which  case  the  re- 
fracted ray  emerges  parallel  to  the  surface  of  the  water. 

This  angle,  SOB,  is  called  the  critical  angle,  since  for  any  greater  angle, 
FOB,  the  incident  ray  cannot  emerge,  but  undergoes  an  internal  reflection, 
which  is  called  total  reflection,  because  the  incident  light  is  entirely  reflected. 
From  water  to  air  the  critical  angle  is  48°  35' ;  from  glass  to  air,  41°  48'. 

The  occurrence  of  this  internal  reflection  may  be  observed  by  the  follow- 
ing experiment : — An  object,  A,  is  placed  before  a  glass  vessel  rilled  with 
water  (fig.  434) ;  the  surface  of  the  liquid  is  then  looked  at  as  shown  in  the 
figure,  and  an  image  at  the  object  A  is  seen  at  a,  formed  by  the  rays  reflected 
at  m,  in  the  ordinary  manner  of  a  mirror. 


Fig.  432 


Fig.  434. 


-541]  Mirage.  469 

Similar  effects  of  the  total  reflection  of  the  images  of  objects  contained 
in  aquaria  are  frequently  observed,  and  add  much  to  the  interest  of  their 
appearance. 

In  total  reflection  there  is  no  loss  of  light  from  absorption  or  transmission, 
and  accordingly  it  produces  the  greatest  brilliancy.  If  a  test  tube  half  full 
of  water  be  placed  in  water,  the  empty  part  shines  as  brilliantly  as  pure 
mercury.  Bubbles,  again,  in  water  glisten  like  pearls,  and  cracks  in  trans- 
parent bodies  like  strips  of  silver,  for  the  oblique  rays  are  totally  reflected. 
The  lustre  of  transparent  bodies  bounded  by  plane  surfaces,  such  as  the 
lustre  of  chandeliers,  arises  mainly  from  total  reflection.  This  lustre  is  more 
frequent  and  more  brilliant  the  smaller  the  limiting  angle  ;  the  lustre  of  dia- 
mond therefore  is  the  most  brilliant, 

541.  Mirage. — The  mirage  is  an  optical  illusion  by  which  inverted  images 
of  distant  objects  are  seen  as  if  below  the  ground  or  in  the  atmosphere.  This 
phenomenon  is  of  most  frequent  occurrence  in  hot  climates,  and  more 
especially  on  the  sandy  plains  of  Egypt.  The  ground  there  has  often  the 


435- 

aspect  of  a  tranquil  lake,  on  which  are  reflected  trees  and  the  surrounding 
villages.  Monge,  who  accompanied  Napoleon's  expedition  to  Egypt,  was 
the  first  to  give  an  explanation  of  the  phenomenon. 

It  is  a  phenomenon  of  refraction,  which  results  from  the  unequal  density 
of  the  different  layers  of  the  air  when  they  are  expanded  by  contact  with  the 
heated  soil.  The  least  dense  layers  are  then  the  lowest,  and  a  luminous  ray 
from  an  elevated  object,  A  (fig.  435),  traverses  layers  which  are  gradually  less 
refracting  ;  for,  as  will  be  shown  presently  (550),  the  refracting  power  of  a 
gas  diminishes  with  lessened  density.  The  angle  of  incidence  accordingly 
increases  from  one  layer  to  the  other,  and  ultimately  reaches  the  critical 
angle,  beyond  which  internal  reflection  succeeds  to  refraction  (540).  The 
ray  then  rises,  as  seen  in  the  figure,  and  undergoes  a  series  of  successive 
refractions,  but  in  the  direction  contrary7  to  the  first,  for  it  now  passes  through 
layers  which  are  gradually  more  refracting.  The  luminous  ray  then  reaches 
the  eye  with  the  same  direction  as  if  it  had  proceeded  from  a  point  below 
the  ground,  and  hence  it  gives  an  inverted  image  of  the  object,  just  as  if  it 
had  been  reflected  at  the  point  O,  from  the  surface  of  a  tranquil  lake. 


470 


On  Light. 


[541- 


The  effect  of  the  mirage  may  be  illustrated  artificially,  as  Dr.  Wollaston 
showed,  .by  looking  along  the  side  of  a  red-hot  poker  at  a  word  or  object  ten 
or  twelve  feet  distant.  At  a  distance  less  than  three-eighths  of  an  inch  from 
the  line  of  the  poker,  an  inverted  image  was  seen,  and  within  and  without 
that  an  erect  image.  A  more  convenient  arrangement  than  a  red-hot  poker 
is  a  flat  box  closed  at  the  top  and  filled  with  red-hot  charcoal. 

Mariners  sometimes  see  images  in  the  air  of  the  shores  or  of  distant 
vessels.  This  is  due  to  the  same  cause  as  the  mirage,  but  in  a  contrary 
direction,  only  occurring  when  the  temperature  of  the  air  is  above  that  of  the 
sea,  for  then  the  inferior  layers  of  the  atmosphere  are  denser,  owing  to  their 
contact  with  the  surface  of  the  water.  Scoresby  observed  several  such 
cases  in  the  Polar  Seas. 

TRANSMISSION   OF  LIGHT  THROUGH  TRANSPARENT  MEDIA. 

;      542.  Media  with  parallel  faces. — When  light  traverses  a  medium  with 
parallel  faces  the  emergent  rays  are  parallel  to  the  incident  rays. 

Let  MN  (fig.  436)  be  a  glass  plate  with  parallel  faces,  let  SA  be  the 
incident  and  DB  the  emergent  ray,  i  and  r  the  angles  of  incidence  and  of 

refraction  at  the  entrance  of  the  ray,  and, 
lastly,  if  and  r'  the  same  angles  at  its  emer- 
gence. At  A  the  light  undergoes  a  first 

refraction,   the  index  of  which  is  s?n  z  (537). 

sin  r   ' 

At  D  it  is  refracted  a  second  time,  and  the 


index  is  then 


But  we  have  seen  that 


Fig.  436. 


sin  r' 

the  index  of  refraction  of  glass  to  air  is  the  re- 
ciprocal of  its  refraction  from  air  to  glass;  hence 

siHJi  =  s'in_r 
sin  r'    sin  t 

But  as  the  two  normals  AG  and  DE  are  parallel,  the  angles  r  and  if  are 
equal,  as  being  alternate  interior  angles.  As  the  numerators  in  the  above 
equation  are  equal,  the  denominators  must  be  also  equal ;  the  angles  r'  and 
i  are  therefore  equal,  and  hence  DB  is  parallel  to  SA. 

543.  Prism. — In  optics  a  prism  is  any  transparent  medium  comprised 
between  two  plane  faces  inclined  to  each  other.     The  intersection  of  these 

two  faces  is  the  edge  of 
the  prism,  and  their 
inclination  is  its  refract- 
ing angle.  Every  sec- 
tion perpendicular  to  the 
edge  is  called  a  prin- 
cipal section. 

The  prisms  used  for 
experiments   are  gene- 
Fig.  437.  Fig.  438.  rally    right     triangular 

prisms    of     glass,     as 

shown  in  fig.  437,  and  their  principal  section  is  a  triangle  (fig.  438).  In  this 
section  the  point  A  is  called  the  summit  of  the  prism,  and  the  right  line  BC 


-544]        Path  of  Rays  in  Prisms.     Angle  of  Deviation.          471 

is  called  the  base ;  these  expressions  have  reference  to  the  triangle  ABC,  and 
not  to  the  prism. 

544.  Path  of  rays  in  prisms.  Angle  of  deviation. — When  the  laws 
of  refraction  are  known,  the  path  of  the  rays  in  a  prism  is  readily  determined. 
Let  O  be  a  luminous  point  (fig.  438)  in  the  same  plane  as  the  principal  sec- 
tion ABC  of  a  prism,  and  let  OD  be  an  incident  ray.  This  ray  is  refracted 
at  D,  and  approaches  the  normal,  because  it  passes  into  a  more  highly  re- 
fracting medium.  At  K  it  experiences  a  second  refraction,  but  it  then  de- 
viates from  the  normal,  for  it  passes  into  air,  which  is  less  refractive  than 
glass.  The  light  is  thus  refracted  twice  in  the  same  direction,  so  that  the 
ray  is  deflected  towards  the  base,  and  consequently  the  eye  which  receives 
the  emergent  ray  KH  sees  the  object  O  at  O' ;  that  is,  objects  seen  through 
a  prism  appear  deflected  towards  its  summit.  The  angle  OEO',  which  the 
incident  and  emergent  rays  form  with  each  other,  expresses  the  deviation  of 
light  caused  by  the  prism,  and  is  called  the  angle  of  deviation. 


39-  Fig-  440- 

Besides  this,  objects  seen  through  a  prism  appear  in  all  the  colours  of 
the  rainbow ;  this  phenomenon  will  be  described  under  the  name  of  dis- 
persion. 

This  angle  increases  with  the  refractive  index  of  the  material  of  the  prism, 
and  also  with  its  refracting  angle.  It  also  varies  with  the  angle  under  which 
•the  luminous  ray  enters  the  prism.  The  angle  of  deviation  increases  up  to 
a  certain  limit,  which  is  determined  by  calculation,  knowing  the  angle  of 
incidence  of  the  ray,  and  the  refracting  angle  of  the  prism. 

That  the  angle  of  deviation  increases  with  the  refractive  index  may  be 
shown  by  means  of  the  polyprism.  This  name  is  given  to  a  prism  formed 
of  several  prisms  of  the  same  angle  connected  at  their  ends  (fig.  439).  These 
prisms  are  made  of  substances  unequally  refringent,  such  as  flint  glass,  rock 
crystal,  or  crown  glass.  If  any  object — a  line,  for  instance — be  looked  at 
through  the  polyprism,  its  different  parts  are  seen  at  unequal  heights.  The 


472 


On  Light. 


[544- 


highest  portion  is  that  seen  through  the  flint  glass,  the  refractive  index  of 
which  is  greatest ;  then  the  rock  crystal ;  and  so  on  in  the  order  of  the 
decreasing  refractive  indices. 

The  prism  'with  -variable  angle  (fig.  440)  is  used  for  showing  that  the 
angle  of  deviation  increases  with  the  refracting  angle  of  the  prism.  It  con- 
sists of  two  parallel  brass  plates,  B  and  C,  fixed  on  a  support.  Between 
these  are  two  glass  plates,  moving  on  a  hinge,  with  some  friction  against  the 
plates,  so  as  to  close  it.  When  water  is  poured  into  the  vessel  the  angle 
may  be  varied  at  will.  If  a  ray  of  light,  S,  be  allowed  to  fall  upon  one  of 
them,  by  inclining  the  other  more,  the  angle  of  the  prism  increases,  and  the 
deviation  of  the  ray  is  seen  to  increase. 

545.  Application  of  right-angled  prisms  in  reflectors. — Prisms  whose 
principal  section  is  an  isosceles  right-angled  triangle  afford  an  important 

application  of  total  reflection  (540).  For 
let  ABC  (fig.  441)  be  the  principal  section 
of  such  a  prism,  O  a  luminous  point,  and 
OH  a  ray  at  right  angles  to  the  face  BC. 
This  ray  enters  the  glass  without  being  re- 
fracted, and  makes  with  the  face  AB  an 
angle  equal  to  B — that  is,  to  45  degrees — 
and  therefore  greater  than  the  limiting 
Fi«- 44*.  angle  of  glass,  which  is  41°  48'  (540).  The 

ray  OH  undergoes,  therefore,  at  H  total  reflection,  which  imparts  to  it  a 
direction  HI  perpendicular  to  the  second  face  AC.  Thus  the  hypothenuse 

surface  of  this  prism  produces  the 
effect  of  the  most  perfect  plane 
mirror,  and  an  eye  placed  at  I  sees 
O'  the  image  of  the  point  O.  This 
property  of  right-angled  prisms  is  fre- 
quently used  in  optical  instruments. 

546.  Conditions  of  emergence  in 
prisms. — In  order  that  any  luminous 
rays  refracted  at  the  first  face  of  a 
prism  may  emerge  from  the  second,  it 
is  necessary  that  the  refractive  angle  of 
the  prism  be  less  than  twice  the  criti- 
cal angle  of  the  substance  of  which 
the  prism  is  composed.  For  if  LI 

(fig.  442)  be  the  ray  incident  on  the  first  face,  IE  the  refracted  ray,  PI  and 
PE  the  normals,  the  ray  IE  can  only  emerge  from  the  second  face  when  the 
incident  angle  IEP  is  less  than  the  critical  angle  (540).  But  as  the  inci- 
dent angle  LIN  increases,  the  angle  EIP  also  increases,  while  IEP  dimin- 
ishes. Hence,  according  as  the  direction  of  the  ray  LI  tends  to  become 
parallel  with 'the  face  AB,  does  this  ray  tend  to  emerge  at  the  second 

face. 

Let  LI  be  now  parallel  to  AB,  the  angle  r  is  then  equal  to  the  critical 
angle  /  of  the  prism  because  it  has  its  maximum  value.  Further,  the  angle 
EPK,  the  exterior  angle  of  the  triangle  IPE,  is  equal  to  r  +  i'  •  but  the  angles 
EPK  and  A  are  equal,  because  their  sides  are  perpendicular,  and  therefore 


Fig.  442- 


-547]  Minimum  Deviation.  473 

A  =  r+*v;  therefore  also  A  =  /  +  *',  for  in  this  case  r  =  l.  Hence,  if  A  =  2/ 
or  is  >2/,  we  shall  have  i'^l  or  >/,  and  therefore  the  ray  would  not  emerge 
at  the  second  face,  but  would  undergo  internal  reflection,  and  would  emerge 
at  a  third  face,  BC.  This  would  be  much  more  the  case  with  rays  whose 
incident  angle  is  less  than  BIN,  because  we  have  already  seen  that  /'  con- 
tinually increases.  Thus  in  the  case  in  which  the  refracting  angle  of  a  prism 
is  equal  to  2/  or  is  greater,  no  luminous  ray  could  pass  through  the  faces  of 
the  refracting  angle. 

As  the  critical  angle  of  glass  is  41°  48',  twice  this  angle  is  less  than  90°, 
and,  accordingly,  objects  cannot  be  seen  through  a  glass  prism  whose  refract- 
ing angle  is  a  right  angle.  As  the  critical  angle  of  water  is  48°  35',  light 
could  pass  through  a  hollow  rectangular  prism  formed  of  three  glass  plates 
and  filled  with  water. 

If  we  suppose  A  to  be  greater  than  /  and  less  than  2/,  then  of  rays  inci- 
dent at  I  some  within  the  angle  NIB  will  emerge  from  AC,  others  will  not 
emerge,  nor  will  any  emerge  that  are  incident  within  the  angle  NIA.  If  we 
suppose  A  to  have  any  magnitude  less  than  /,  all  rays  incident  at  I  within 
the  angle  NIB  will  emerge  from  AC,  as  also  will  some  of  those  incident 
within  the  angle  NIA. 

547.  Minimum  deviation. — When  a  pencil  of  solar  light  passes  through 
an  aperture  A,  in  the  side  of  a  dark  chamber  (fig.  443),  the  pencil  is  projected 
in  a  straight  line  AC, 
on  a  distant  screen. 
But  if  a  vertical  prism 
be  interposed  be- 
tween the  aperture 
and  the  screen,  the 
pencil  is  deviated  to- 
wards the  base  of  the 
prism,  and  the  image 
is  projected  at  D,  at 
some  distance  from 
the  point  C.  If  the  Fig.  443. 

prism  be  turned  so 

that  the  incident  angle  decreases,  the  luminous  disc  approaches  the  point  C, 
up  to  a  certain  position,  E,  from  which  it  reverts  to  its  original  position  even 
when  the  prism  is  rotated  in  the  same  direction.  Hence  there  is  a  deviation, 
EBC,  less  than  any  other.  It  may  be  demonstrated  mathematically  that 
this  minimum  dmiation  takes  place  when  the  angles  of  incidence  and  of 
emergence  are  equal. 

The  angle  of  minimum  deviation  may  be  calculated  when  the  incident 
angle  and  the  refracting  angle  of  the  prism  are  known.  For  when  the 
deviation  is  least,  as  the  angle  of  emergence  Y*  is  equal  to  the  incident  angle 
/  (fig.  442),  r  must  =/'.  But  it  has  been  shown  above  (546)  that  A.  =  r+i' ; 
consequently, 

A  =  2;- (I) 

If  the  minimum  angle  of  deviation  LD/  be  called  d,  this  angle  being  ex« 
terior  to  the  triangle  DIE,  we  readily  obtain  the  equation 


474 


On  Light. 


[547- 


whence  </=2/—  A  .......        (2) 

which  gives  the  angle  d,  when  i  and  A  are  known. 

From  the  formulas  (i)  and  (2)  a  third  may  be  obtained,  which  serves  to 
calculate  the  index  of  refraction  of  a  prism,  when  its  refracting  angle  and  the 
minimum  of  deviation  are  known.  The  index  of  refraction  n  is  the  ratio  of 

the  sines  of  the  angles  of  incidence  and  refraction  ;  hence  n  = 


sin  r 


re- 


placing i  and  r  from  their  values  in  the  above  equations  (i)  and  (2)  we  get 

sinl 

(3) 

548.  Measurement  of  the   index  of  refraction  in  solids. — By  means 
of  the  preceding  formula  (3)  the  refractive  index  of  a  solid  may  be  calculated 
when  the  angles  A  and  d  are  known. 

In  order  to  determine  the  angle  A,  the  substance  is  cut  in  the  form  of  a 
triangular  prism,  and  the  angle  measured  by  means  of  a  goniometer  (534). 

The  angle  d  is  measured  in  the  following  manner  : — A  ray,  LI,  emitted 
from  a  distant  object  (fig.  444),  is  received  on  the  prism,  which  is  turned 

in  order  to  obtain  the 
minimum  deviation 
EDL'.  By  means  of 
a  telescope  with  a 
graduated  circle,  the 
angle  EDL'  is  read 
off,  which  the  re- 
fracted ray  DE  makes 
with  the  ray  DL',  com- 
ing directly  from  the 
object;  now  this  is  the  angle  of  minimum  deviation,  assuming  that  the 
object  is  so  distant  that  the  two  rays  LI  and  L'D  are  approximately  parallel. 
These  values  then  only  need  to  be  substituted  in  the  equation  (3)  to  give  the 
value  of  n. 

549.  Measurement  of    the    index    of    refraction    of    liquids.— Biot 
applied  Newton's  method  to  determining  the  refractive  index  of  liquids. 

For  this  purpose  a  cylindrical  cavity  O,  of 
ibout  075  in.  diameter,  is  perforated  in  a 
'lass  prism,  PQ  (fig.  445),  from  the  incident 
.ace  to  the  face  of  emergence.  This  cavity  is 
closed  by  two  plates  of  thin  glass  which  are 
cemented  on  the  sides  of  this  prism.  Liquids 
are  introduced  through  a  small  stoppered  aper- 
ture, B.  The  refracting  angle  and  the  minimum 
deviation  of  the  liquid  prism  in  the  cavity  O 
Fig.  445.  .  .  havmg  been  determined,  their  values  are  intro- 
duced into  the  formula  (3),  which  gives  the  index. 

"      550.  Measurement  of  the  index  of  refraction  of  gases. — A  method 
for  this  purpose   founded  on  that   of  Newton  was  devised  by   Biot   and 


Fig.  444. 


-550]      Measurement  of  tJie,  Index  of  Refraction  of  Gases.       475 

Arago.  The  apparatus  which  they  used  consists  of  a  glass  tube  (fig.  446), 
bevelled  at  its  two  ends,  and  closed  by  glass  plates,  which  are  at  an 
angle  of  143°.  This  tube  is  connected  with  a  bell-jar,  H,  in  which  there  is 
a  siphon  barometer,  and  with  a  stopcock  by  means  of  which  the  apparatus 
can  be  exhausted,  and  different  gases  intro- 
duced. After  having  exhausted  the  tube 
AB,  a  ray  of  light,  SA,  is  transmitted,  which 
is  bent  away  from  the  normal  through  an 
angle  r—i  at  the  first  incidence,  and  towards 
it  through  an  angle  i' —  r'  at  the  second. 
These  two  deviations  being  added,  the  total 
deviation  d  is  r-i  +  i' -r'.  In  the  case  of 
a  minimum  deviation,  1  =  ^  and  r=i',  whence 
*/=A-2/,  since  r+z=A  (547).  The  index 
from  vacuum  to  air,  which  is  evidently 

s!n  r.  has  therefore  the  value 
sin  i 


Hence,  in  order  to  deduce  the  refractive 
index  from  vacuum  into  air,  which  is  the 
absolute  index  or  principal  index,  it  is  merely 

necessary  to  know  the  refracting  angle  A,  and  the  angle  of  minimum  devia- 
tion d. 

To  obtain  the  absolute  index  of  any  other  gas,  after  having  produced  a 
vacuum,  this  gas  is  introduced  ;  the  angles  A  and  d  having  been  measured, 
the  above  formula  gives  the  index  of  refraction  from  gas  to  air.  Dividing 
the  index  of  refraction  from  vacuum  to  air  by  the  index  of  refraction  from 
the  gas  to  air,' we  obtain  the  index  of  refraction  from  vacuum  to  the  gas  ;  that 
is,  its  absolute  index. 

By  means  of  this  apparatus  Biot  and  Arago  found  that  the  refractive 
indices  of  gases  are  very  small  as  compared  with  those  of  solids  and  liquids, 
and  that  for  the  same  gas  the  refractive  power  is  proportional  to  the  density  ; 
meaning  by  the  refractive  action  of  a  substance  the  square  of  its  refrac- 
tive index  less  unity  ;  that  is,  n-  —  I.  The  refractive  action  divided  by  the 
density,  or 


is  called  the  absolute  refractive  power. 

Table  of  the  absolute  indices  of  refraction. 

Diamond        .        .         .  2-4710275  Bisulphide  of  carbon     . 

Phosphorus    ....     2-224  Iceland  spar,  ordinary  ray 

Sulphur  .         .         .         .2*115  Iceland  spar,  extraordinary 

Ruby      .....     1-779          ray     .... 


1*67 

1-654 

1-483 


476 


On  Light. 


[550- 


Table  of  the  absolute  indices  of  refraction — continued. 

Flint  glass     ....     1-575  Albumen 

Rock  salt       .        .        .        .i'55°  Ether     • 

Rock  crystal  .     I  -548  Crystalline  lens     . 

Plate  glass,  St.  Gobin  .         .     1-543  Vitreous        „ 

Crown  glass  ....     r6oo  Aqueous         „ 

Turpentine    ....     1-470  Water    . 

Alcohol          ....     1-374  Ice  .         . 

Refractive  indices  of  gases. 


Vacuum    ....  roooooo 

Hydrogen          .         .         .  1-000138 

Oxygen     ....  1-000272 

Air 1-000294 

Nitrogen  ....  1-000300 

Ammonia.         .         .         .  1-000385 


Carbonic  acid  . 
Hydrochloric  acid 
Nitrous  oxide  . 
Sulphurous  acid 
Olefiant  gas 
Chlorine  . 


1-36 

i'358 

1*384 

1*339 

i*357 


i  -000449 
i  -000449 
i  -000503 
i  -000665 
1-000678 
i  -000772 


LENSES.   THEIR  EFFECTS. 

551.  Different  kinds  of  lenses. — Lenses  are  transparent  media,  which, 
from  the  curvature  of  their  surfaces,  have  the  property  of  causing  the  luminous 
rays  which  traverse  them  either  to  converge  or  to  diverge.  According  to 
their  curvature  they  are  either  spherical,  cylindrical,  elliptical,  or  parabolic. 
Those  used  in  optics  are  always  spherical.  They  are  commonly  made  either 
of  crown  glass,  which  is  free  from  lead,  or  sAftint  glass,  which  contains  lead, 
and  is  more  refractive  than  crown  glass. 

The  combination  of  spherical  surfaces,  either  with  each  other  or  with 
plane  surfaces,  gives  rise  to  six  kinds  of  lenses,  sections  of  which  are  repre- 
sented in  fig.  447  ;  four  are  formed  by  two  spherical  surfaces,  and  two  by  a 
plane  and  a  spherical  surface. 

A  is  a  double  convex,^  is  a  plano-convex,  C  is  a  converging  concavo- 
convex,  D  is  a  double  concave,  E  is  a  plano-concave,  and  F  is  a  diverging 
concavo-convex.  The  lenses  C  and  F  are  also  called  meniscus  lenses,  from 
their  resemblance  to  the  crescent-shaped  moon. 

The  first  three,  which  are  thicker  at  the  centre  than  at  the  borders,  are 
converging  ;  the  others,  which  are  thinner  in  the  centre,  are  diverging.  In 
the  first  group,  the  double  convex  lens  only  need  be  considered,  and  in  the 

second  the  double  concave, 
E  F        as  the  properties  of  each  of 

these    lenses    apply    to   all 
those  of  the  same  group. 

In  lenses  whose  two  sur- 
faces are  spherical,  the 
centres  for  these  surfaces  are 
called  centres  of  curvature, 

Fig  447>  and    the    right    line    which 

passes    through    these     two 
centres  is  the  principal  axis.     In  a  plano-concave  or  plano-convex  lens,  the 


-552]  Foci  in  Double  Convex  Lenses.  477 

principal  axis  is  the  perpendicular  let  fall  from  the  centre  of  the  spherical 
face  on  the  plane  face. 

In  order  to  compare  the  path  of  a  luminous  ray  in  a  lens  with  that  in  a 
prism,  the  same  hypothesis  is  made  as  for  curved  mirrors  (525) ;  that  is,  the 
surfaces  of  these  lenses  are  supposed  to  be  formed  of  an  infinity  of  small 
plane  surfaces  or  elements  ;  the  normal  at  any  point  is  then  the  perpen- 
dicular to  the  plane  of  the  corresponding  element.  It  is  a  geometrical 
principle,  that  all  the  normals  to  the  same  spherical  surface  pass  through 
its  centre.  On  the  above  hypothesis  we  can  always  conceive  two  plane 
surfaces  at  the  points  of  incidence  and  convergence,  which  are  inclined  to 
each  other,  and  thus  produce  the  effect  of  a  prism.  Pursuing  this  com- 
parison, the  three  lenses  A,  B,  and  C  may  be  compared  to  a  succession  of 
prisms  having  their  summits  outwards,  and  the  lenses  D,  E,  and  F  to  a 
series  having  their  summits  inwards  ;  from  this  we  see  that  the  first  ought 
to  condense  the  rays,  and  the  latter  to  disperse  them,  for  we  have  already 
seen  that  when  a  luminous  ray  traverses  a  prism  it  is  deflected  towards  the 
base  (536). 

552.  Foci  in  double  convex  lenses. — The  focus  of  a  lens  is  the  point 
where  the  refracted  rays,  or  their  prolongations,  meet.  Double  convex 
lenses  have  both  real  and  virtual  foci,  like  concave  mirrors. 

Real  foci. — We  shall  first  consider  the  case  in  which  the  luminous  rays 
which  fall  on  the  lens  are  parallel  to  its  principal  axis,  as  shown  in  fig. 
448.  In  this  case,  any  incident  ray,  LB,  in  approaching  the  normal  of  the 
point  of  incidence  B,  and 
in  diverging  from  it  at 
the  point  of  emergence 
D,  is  twice  refracted  to- 
wards the  axis,  which  it 
cuts  at  F.  As  all  rays 
parallel  to  the  axis  are 
refracted  in  the  same 
manner,  it  can  be  shown 
by  calculation  that  they 

all  pass  very  nearly  through  the  point  F,  so  long  as  the  arc  DE  does  not 
exceed  10°  to  12°.  This  point  is  called  the  principal  focus,  and  the  dis- 
tance FA  is  the 
principal  focal 
distance.  It  is 
constant  in  the 
same  lens,  but 
varies  with  the 
radii  of  curvature 
and  the  index  of 
refraction.  In  or- 
dinary lenses, 
which  are  of 

crown  glass,  and  in  which  the  radii  of  the  two  surfaces  are  nearly  equal,  the 
principal  focus  coincides  very  closely  with  the  centre  of  curvature. 

We  shall  now  consider  the  case  in  which  the  luminous  point  is  outside 


478  On  Light.  [552- 

the  principal  focus,  but  so  near  that  all  incident  rays  form  a  divergent  pencil 
as  shown  in  fig.  449.  The  luminous  point  being  at  L,  by  comparing  the  path 
of  a  diverging  ray,  LB,  with  that  of  a  ray,  SB,  parallel  to  the  axis,  the  former 
is  found  to  make  with  the  normal  an  angle,  LB«,  greater  than  the  angle 
SBn  ;  consequently,  after  traversing  the  lens,  the  ray  cuts  the  axis  at  a 
point,  /,  which  is  more  distant  than  the  principal  focus  F.  As  all  rays  from 
the  point  L  intersect  approximately  in  the  same  point  /,  this  latter  is  the  con* 
jugate  focus  of  the  point  L  ;  this  term  has  the  same  meaning  here  as  in  the 
case  of  mirrors,  and  expresses  the  relation  existing  between  the  two  points 
L  and  /,  which  is  of  such  a  nature  that,  if  the  luminous  point  is  moved  to/, 
the  focus  passes  to  L. 

According  as  the  luminous  point  comes  nearer  the  lens,  the  convergence 
of  the  emergent  rays  decreases,  and  the  focus  /  becomes  more  distant ;  when 

the  point  L  coin- 
cides with  the  prin- 
cipal focus,  the 
emergent  rays  on 
the  other  side  are 
parallel  to  the  axis, 
and  there  is  no 
focus,  or,  what  is 
the  same  thing,  it 
is  infinitely  distant. 
As  the  refracted 

rays  are  parallel  in  this  case,  the  intensity  of  light  only  decreases  slowly,  and 
a  simple  lamp  can  illuminate  great  distances.  It  is  merely  necessary  to 
place  it  in  the  focus  of  a  double  convex  lens,  as  shown  in  fig.  450. 

Virtual  foci. — A  double  convex  lens  has  a  virtual  focus  when  the  luminous 
object  is  placed  between  the  lens  and  the  principal  focus,  as  shown  in  fig. 

451.  In  this  case  the  inci- 
dent rays  make  with  the 
normal  greater  angles  than 
those  made  with  the  rays  FI 
from  the  principal  focus; 
hence,  when  the  former  rays 
emerge,  they  move  farther 
from  the  axis  than  the  latter, 
and  form  a  diverging  pencil, 
HK,  GM.  These  rays  can- 
not produce  a  real  focus,  but  their  prolongations  intersect  in  some  point, 
/,  on  the  axis,  and  this  point  is  the  virtual  focus  of  the  point  L  (514). 

553.  Foci  in  doable  concave  lenses. — In  double  concave  lenses  there 
are  only  virtual  foci,  whatever  the  distance  of  the  object.  Let  SS'  be  any 
pencil  of  rays  parallel  to  the  axis  (fig.  452),  any  ray,  SI,  is  refracted  at  the 
point  of  incidence,  I,  and  approaches  the  normal  CI.  At  the  point  of  emer- 
gence it  is  also  refracted,  but  diverges  from  the  normal  GC',  so  that  it  is 
twice  refracted  in  a  direction  which  moves  it  from  the  axis  CC'.  As  the 
same  thing  takes  place  for  every  other  ray,  S'KMN,  it  follows  that  the  rays, 
after  traversing  the  lens,  form  a  diverging  pencil,  GHMN.  Hence  there  is 


-555]  Optical  Centre,  Secondary  Axis.  479 

no  real  focus,  but  the  prolongations  of  these  rays  cut  one  another  in  a  point 
F,  which  is  the  principal  virtual  focus. 

In  the  case  in  which  the  rays  proceed  from  a  point,  L  (fig.  453),  on  the 


Fig  452.  *'ig  453- 

axis,  it  is  found  by  the  same  construction  that  a  virtual  focus  is  formed  at  /, 
which  is  between  the  principal  focus  and  the  lens. 

5  54.  Experimental  determination  of  the  principal  focus  of  lenses. — 

To  determine  the  principal  focus  of  a  convex  lens,  it  may  be  exposed  to 
the  sun's  rays  so  that  they  are  parallel  to  its  axis.  The  emergent  pencil 
being  received  on  a  ground-glass  screen,  the  point  to  which  the  rays  conrerge 
is  readily  seen  ;  it  is  the  principal  focus. 

Or  an  image  of  an  object  is  formed  on  a  screen,  their  respective  distances 
from  which  are  then  measured,  and  from  these  distances  the  focus  is  calcu- 
lated from  the  dioptric  formula  (561). 

With  a  double  concave  lens,  the  face  ab  (fig.  454)  is  covered  with  an 
opaque  substance,  such  as  lampblack,  two  small  apertures,  a  and  b,  being 
left  in  the  same  principal  section,  and 
at  an  equal  distance  from  the  axis  ;  a 
pencil  of  solar  light  is  then  received 
on  the  other  face,  and  the  screen 
P,  which  receives  the  emergent 
rays,  is  moved  nearer  to  or  farther 
from  the  'ens,  until  A  and  B,  the 
spots  of  light  from  the  small  aper- 
tures a  and  b,  are  distant  from  each 
other  by  twice  ab.  The  distance  *ig-454- 

DI  is  then  equal  to  the  focal  distance  FD,  because  the  triangles  ¥at>  and 
FAB  are  similar.  Another  method  of  determining  the  focus  of  a  concave 
lens  is  given  in  article  560. 

555.  Optical  centre,  secondary  axis. — In  every  lens  there  is  a  point 
called  the  optical  centre,  which  is  situated  on  the  axis,  and  which  has  the 
property  that  any  luminous  ray  passing  through  it  experiences  no  angular 
deviation  ;  that  is,  that  the  emergent  ray  is  parallel  to  the  incident  ray. 
The  existence  of  this  point  may  be  demonstrated  in  the  following  manner  : — 
Let  two  parallel  radii  of  curvature,  CA  and  C'A'  (fig.  455)  be  drawn  to  the 
two  surfaces  of  a  double  convex  lens.  Since  the  two  plane  elements  of  the 
lens  A  and  A'  are  parallel,  as  being  perpendicular  to  two  parallel  right  lines, 
it  will  be  granted  that  the  refracted  ray  AA'  is  propagated  in  a  medium 
with  parallel  faces.  Hence  a  ray  KA  which  reaches  A  at  such  an  inclination 
that  after  refraction  it  takes  the  direction  AA'  will  emerge  parallel  to  its  first 


480  On  Light.  [555- 

direction  (542) ;  the  point  O,  at  which  the  right  line  cuts  the  axis,  is  there- 
fore the  optical  centre.  The  position  of  this  point  may  be  determined  for 
the  case  in  which  the  curvature  of  the  two  faces  is  the  same,  which  is  the 
usual  condition,  by  observing  that  the  triangles  CO  A  and  C/OA/  are  equal, 
and  therefore  that  OC  =  OC',  which  gives  the  point  O.  If  the  curvatures  are 
unequal,  the  triangles  CO  A  and  CO'A'  are  similar,  and  either  CO  or  C'O  may 
be  found,  and  therefore  also  the  point  O. 

In  double  concave  or  concavo-convex  lenses  the  optical  centre  may  be 
determined  by  the  same  construction.  In  lenses  with  a  plane  face  this  point 
is  at  the  intersection  of  the  axis  by  the  curved  face. 

Every  right  line,  PP'  (fig.  456),  which  passes  through  the  optical  centre 
without  passing  through  the  centres  of  curvature,  is  a  secondary  axis.  From 


Fig-  455-  Fig.  456. 

this  property  of  the  optical  centre,  every  secondary  axis  represents  a  luminous 
rectilinear  ray  passing  through  this  point,  for,  from  the  slight  thickness  of  the 
lenses,  it  may  be  assumed  that  rays  passing  through  the  optical  centre  are  in 
a  right  line  ;  that  is,  that  the  small  deviation  may  be  neglected  which  rays 
experience  in  traversing  a  medium  with  parallel  faces  (fig.  436). 

So  long  as  the  secondary  axes  only  make  a  small  angle  with  the  principal 
axis,  all  that  has  hitherto  been  said  about  the  principal  axis  is  applicable  to 
them  ;  that  is,  that  rays  emitted  from  a  point,  P  (fig.  456),  on  the  secondary 
axis  PP'  nearly  converge  to  a  certain  point  of  the  axis,  P',  and  according  as 
the  distance  from  the  point  P  to  the  lens  is  greater  or  less  than  the  principal 
focal  distance,  the  focus  thus  formed  will  be  conjugate  or  virtual.  This  prin- 
ciple is  the  foundation  of  what  follows  as  to  the  formation  of  images. 

556.  Formation  of  images  in  double  convex  lenses. — In  lenses  as  well 
as  in  mirrors  the  image  of  an  object  is  the  collection  of  the  foci  of  its  several 

points ;  hence  the 
images  furnished  by 
lenses  are  real  or 
virtual  in  the  same 
case  as  the  foci,  and 
their  construction  re- 
solves itself  into  de- 
termining the  position 
of  a  series  of  points, 
Fig.  457.  j  as  was  the  case  with 

mirrors  (528). 

i.  Real  image.  Let  AB  (fig.  457)  be  placed  beyond  the  principal  focus.  If 
a  secondary  axis,  Aa,  be  drawn  from  the  outside  point  A,  any  ray,  AC,  from 


-556]       Formation  of  Images  in  Double  Convex  Lenses.  481 

this  point,  will  be  twice  refracted  at  C  and  D,  and  both  times  in  the  same 
direction,  approaching  the  secondary  axis,  which  it  cuts  at  a.  From  what 
has  been  said  in  the  last  paragraph,  the  other  rays  from  the  point  A  will  inter- 
sect in  the  point  a,  which  is  accordingly  the  conjugate  focus  of  the  point  A. 
If  the  secondary  axis  be  drawn  froVn  the  point  B,  it  will  be  seen,  in  like 
manner,  that  the  rays  from  this  point  intersect  in  the  point  b  ;  and  as  the  points 
between  A  and  B  have  their  foci  between  a  and  b,  a  real  but  inverted  image 
of  AB  will  be  formed  at  ab. 

In  order  to  see  this  image,  it  may  be  received  on  a  white  screen,  on 
which  it  will  be  depicted,  or  the  eye  may  be  placed  in  the  path  of  the  rays 
emerging  from  it. 

Conversely,  if  ab  were  the  luminous  or  illuminated  object  which  emitted 
rays,  its  image  would  be  formed  at  AB.  Two  consequences  important  for 
the  theory  of  optical  instruments  follow  from  this  :  that  1st,  If  an  object,  even 
a  very  large  one,  is  at  a  sufficient  distance  from  a  double  convex  lens,  the  real 
and  inverted  image  which  is  obtained  of  it  is  very  small,  it  is  near  the  prin- 
cipal focus,  but  somewhat  farther  from  the  lens  than  this  is  ;  2nd,  If  a  very 
small  object  be  placed  near  the  principal  focus,  but  a  little  in  front  of  it,  the 
image  u'hich  is  formed  is  at  a  great  distance,  it  is  much  larger,  and  that  in 
proportion  as  the  object  is  near  the  principal  focus.  In  all  cases  the 
object  and  the  image  are  in  the  same  proportion  as  their  distances  from  the 
lens. 

These  two  principles  are  experimentally  confirmed  by  receiving  on  a 
screen  the  image  of  a  lighted  candle,  placed  successively  at  various  distances 
from  a  double  convex  lens. 

ii.  Virtual  image.  There  is  another  case  in  which  the  object  AB  (fig.  458) 
is  placed  between  the  lens  and  its  principal  focus.  If  a  secondary  axis,  O# 
be  drawn  from  the 
point  A,  every  ray, 
AC,  after  having 
been  twice  refrac- 
ted on  emerging, 
diverges  from  this 
axis,  since  the 
point  A  is  at  a  less 
distance  than  the 
principal  focal  dis- 
tance (552).  This 
ray,  continued  in 

an  opposite  direction,  will  cut  the  axis  Oa  in  the  point  a,  which  is  the  virtual 
focus  of  the  point  A.  Tracing  the  secondary  axis  of  the  point  B,  it  will  be 
found,  in  the  same  manner,  that  the  virtual  focus  of  this  point  is  formed  at 
b.  There  is,  therefore,  an  image  of  AB,  at  ab.  This  is  a  virtual  image,  it 
is  erect,  and  larger  than  the  object. 

The  magnifying  power  is  greater  in  proportion  as  the  lens  is  more  con- 
vex, and  the  object  nearer  the  principal  focus.  We  shall  presently  show  how 
the  magnifying  power  may  be  calculated  by  means  of  the  formulae  relating 
to  lenses  (561).  Double  convex  lenses  used  in  this  manner  as  magnifying 
glasses,  are  called  simple  microscopes. 

Y 


482  On  Light.  [557- 

557.  Formation  of  images  in  double  concave  lenses. — Double  con- 
cave lenses,  like  convex  mirrors,  only  give  virtual  images,  whatever  the 
distance  of  the  object. 

Let  AB  (fig.  459)  be  an  object  placed  in  front  of  such  a  lens.     If  the 

secondary  axis  AO  be  drawn  from  the 
point  A,  all  rays,  AC,  AI,  from  this 
point  are  twice  refracted  in  the  same 
direction,  diverging  from  the  axis 
AO  ;  so  that  the  eye,  receiving  the 
emergent  rays  DE  and  GH,  supposes 
them  to  proceed  from  the  point  where 
their  prolongations  cut  the  secondary 
axis  AO  in  the  point  a.  In  like 
manner,  drawing  a  secondary  axis 
Fl.  from  the  point  B,  the  rays  from  this 

»*  459'  .          -  .  -       r     _  „ 

point  form  a  pencil  of  divergent  rays 

the  directions  of  which,  prolonged,  intersect  in  b.     Hence  the  eye  sees  at 
ab  a  virtual  image  of  AB,  which  is  always  erect,  and  smaller  than  the  object. 

558.  Spherical  aberration.     Caustics. — In  speaking    about  foci,  and 
about  the  images  formed  by  different  kinds  of  spherical  lenses,  it  has  been 
hitherto  assumed  that  the  rays  emitted  from  a  single  point  intersect  also 
after  refraction  in  a  single  point.     This  is  virtually  the  case  with  a  lens 
whose  aperture — that  is,  the  angle  obtained  by  joining  the  edges  to  the 
principal  focus — does  not  exceed  io°or  12°. 

Where,  however  the  aperture  is  larger,  the  rays  which  traverse  the  lens 
near  the  edge  are  refracted  to  a  point  F  nearer  the  lens  than  the  point  G, 

which  is  the  focus  of 
the  rays  which  pass 
near  the  axis.  The 
phenomenon  thus  pro- 
duced is  named  sphe- 
rical aberration  by 
refraction  ;  it  is  ana- 
logous to  the  spherical 
aberration  produced 
by  reflection  (533). 
The  luminous  sur- 
faces formed  by  the 
Fig.  460  intersection  of  the  re- 

fracted rays  are  termed  caustics  by  refraction. 

Spherical  aberration  is  prejudicial  to  the  sharpness  and  definition  of  an 
image.  If  a  ground  glass  screen  be  placed  exactly  in  the  focus  of  a  lens, 
the  image  of  an  object  will  be  sharply  defined  in  the  centre,  but  indistinct  at 
the  edges  ;  and,  vice  versa,  if  the  image  is  sharp  at  the  edges,  it  will  be 
indistinct  in  the  centre.  This  defect  is  very  objectionable,  more  especially  in 
lenses  used  for  photography.  It  is  partially  obviated  by  placing  before  the 
lenses  diaphragms,  provided  with  a  central  aperture,  called  stops,  which 
admit  the  rays  passing  near  the  centre,  but  cut  off  those  which  pass  near  the 


^559]  Formula  Relating  to  Lenses.  483 

edges.  The  image  thereby  becomes  sharper  and  more  distinct,  though  the 
illumination  is  less. 

If  a  screen  be  held  between  the  light  and  an  ordinary  double  convex  lens 
which  quite  covers  the  lens,  but  has  two  concentric  series  of  holes,  two 
images  are  obtained,  and  may  be  received  on  a  sheet  of  paper.  By  closing 
one  or  the  other  series  of  holes  by  a  flat  paper  ring,  it  can  be  easily  ascer- 
tained which  image  arises  from  the  central  and  which  from  the  marginal 
rays.  When  the  paper  is  at  a  small  distance  the  marginal  rays  produce  the 
image  in  a  point,  and  the  central  ones  in  a  ring  ;  the  former  are  converged 
to  a  point  and  the  latter  not.  At  a  somewhat  greater  distance  the  marginal 
rays  produce  a  ring  and  the  central  ones  a  point.  It  is  thus  shown  that  the 
focus  of  the  marginal  rays  is  nearer  the  lens  than  that  of  the  central  rays. 

Mathematical  investigation  shows  that  convex  lenses,  whose  radii  of 
curvature  stand  in  the  ratio  expressed  by  the  formula 

r  _  4  —  2/z2  +  n 
r^        2n*  +  n 

are  most  free  from  spherical  aberration,  and  are  called  lenses  of  best  form  • 
in  this  formula  r  is  the  radius  of  curvature  of  the  foci  turned  to  the  parallel 
rays,  and  r^  that  of  the  other  face,  while  n  is  the  refractive  index.  Thus, 

with  a  glass  whose  refractive  index  is  ^,^  =  6^    Spherical  aberration  is  also 

destroyed  by  substituting  for  a  lens  of  short  focus,  two  lenses  of  double 
focal  length,  which  are  placed  at  a  little  distance  apart.  Greater  length  of 
focus  has  the  result  that  for  the  same  diameter  the  aperture  and  also  the 
aberration  are  less  ;  and  as  it  is  not  necessary  to  stop  a  great  part  of  the  lens 
there  is  a  gain  in  luminosity,  which  is  not  purchased  by  indistinctness  of  the 
images,  while  the  combination  of  the  two  lenses  has  the  same  focus  as  that 
of  the  single  lens  (560).  Lenses  which  are  free  from  spherical  aberration 
are  called  aplanatic. 

559.  Formulae  relating:  to  lenses. — In  all  lenses,  the  relations  between 
the  distances  of  the  image  and  object,  the  radii  of  curvature,  and  the  refrac- 


Fig.  461. 

tive  index,  may  be  expressed  by  a  formula.  In  the  case  of  a  double  convex 
lens,  let  P  be  a  luminous  point,  situate  on  the  axis  (fig.  461),  let  PI  be  an 
incident  ray,  IE  its  direction  within  the  lens,  EP'  the  emergent  ray,  so  that  P 
is  the  conjugate  focus  of  P.  Further,  let  C'l  and  CE  be  the  normals  to  the 
points  of  incidence  and  emergence,  and  I  PA  be  put  equal  to  a,  EP'A'  =  P 
ECA'  =  y,  IC'A  =  S,  NIP-/,  ElO-r,  IEO-/',  N'EP'-r. 

Y   2 


484  On  Light.  [559- 

Because  the  angle  i  is  the  exterior  angle  of  the  triangle   PIC',  and  the 

angle  r'  the  exterior  angle  of  the  triangle  CEP7,  therefore,  /  =  a  +  S,  and 
^  =  y  +  /3,  whence 

2-j-r'  =  a  +  £  +  y  +  S       .  ,         ,          .          .          (i) 

But  at  the  point  I,  sin  i  =  n  sin  r,  and  at  the  point  E,  sin  r'  '  =  n  sin  i  (538),  n 
being  the  refractive  index  of  the  lens.  Now  if  the  arc  AI  is  only  a  small 
number  of  degrees,  these  sines  may  be  considered  as  proportional  to  the 
angles  /,  r,  i',  and  r'  ;  whence,  in  the  above  formula,  we  may  replace  the  sines 
by  their  angles,  which  gives  i=*nr  and  r/  =  «zv,  from  which  i  +  r1  '  =  n  (r  +  z'), 
Further,  because  the  two  triangles  IOE  and  COC'  have  a  common  equal 
angle  O,  therefore  r-t-z'  =  y  +  S,  from  which  z  +  r'  =  n  (y  +  8).  Introducing 
this  value  into  the  equation  (i)  we  obtain 

n  (y  +  S)  =  a  +  /3  +  y  +  S,  from  which  (n—  i)  (y  +  S)=a  +  /3.  .  (2) 
Let  CA'  be  denoted  by  R,  C'A  by  R',  PA  by  /,  and  P'A'  by  /'.  Then 
with  centre  P  and  radius  PA  describe  the  arc  A</,  and  with  centre  P'  and 
radius  P'A'  describe  the  arc  A'n.  Now  when  an  angle  at  the  centre  of  a 
circle  subtends  a  certain  arc  of  the  circumference,  the  quotient  of  the  arc 
divided  by  the  radius  measures  the  angle  ;  consequently, 

Ad         Ad    ,        A'n        A'E        ,  ,     AI 
a=PA°r  7)/3=    y?=lT'and8:=R- 

-m,        r         u          u     •       •         •      /   \     /  \    /A'E      AI\       A^/     A'?? 

Therefore  by  substitution  in  (2)    (n-  i)  (  ——-I  -      )  =        +  -—  . 

\   X         K  /        ^         ^ 

Now  since  the  thickness  of  the  lens  is  very  small,  the  angles  are  also  small, 
and  Ad,  AI,  A'E,  A'n  differ  but  little  from  coincident  straight  lines,  and  are 
therefore  virtually  equal.  Hence  the  above  equation  becomes 


This  is  the  formula  for  double  convex  lenses  ;  \tp  be  =  oo  —  that  is,  if  the  rays 
are  parallel—  we  have 

' 


.pr  being  the  principal  focal  distance.     If  this  be  represented  by  /j  we  get 


from  which  the  value  of  /  is  easily  deduced.     Considered  in  reference  to 
equation  (4),  the  equation  (3)  assumes  the  form 

rr?   .....   (5) 

which  is  that  in  which  it  is  usually  employed.     When  the  image  is  virtual 
p'  changes  its  sign,  and  formula  (5)  takes  the  form 


In  double  concave  lenses,  p'  and  /  retain  the  same  sign,  but  that  of  p 
changes  ;  the  equation  (5)  becomes  then 


The  equation  (7)  may  be  obtained  by  the  same  reasonings  as  the  other. 


-561]  Combination  of  Lenses.  485 

560.  Combination  of  lenses.— If  parallel  rays  fall  on  a  convex  lens  A, 
which  has  the  focal  distance  /,  and  then  on  a  similar  lens  B  with  the  focal 
distance  _/",  at  a  distance  d  from  A,  then  the  distance  from  the  lens  B  at 
which  the  image  is  formed  at  F  is 


F      /   f-d 

If  the  lenses  are  close  together,  so  that  d=o,  then 

1   -  l  +  l 

F  77 

if  the  lenses  have  the  same  curvature,  that  is  f=f,  then       =  -   ;  that  is  to 

say  that  the  focal  distance  of  the  combination  is  half  that  of  a  single  lens. 
If  the  second  lens  is  a  dispersing  one  of  the  focal  distance/7,  then 

i          I        j^ 

F"/^     f 
and  if  the  lenses  are  close  together,  then 

I   =  i  _  j_ 

F    7  7 

This  method  can  conversely  be  used  to  determine  the  focal  distance  of  a 
concave  lens,  by  combining  it  with  a  convex  lens  of  longer  focus,  and  deter- 
mining the  focal  distance  of  the  combination. 

561.  Relative  magnitudes  of  image  and  object.  Determination  of 
focus. — From  the  similarity  of  the  triangles  AOB,  aQb  (fig.  457)  we  get 

for  the  relative  magnitudes  of  image  and  object  the  proportion  -     -  =  £-.  • 

T         *t>' 

whence         =  *    where  AB  =  O  is  the  magnitude  of  the  object  and  ab  =  \ 
O      p 

that  of  the  image  ;  while  p  and  p'  are  their  respective  distances  from  the 
lens.     Replacing  p'  by  its  value  from  the  equation  —  +  —  =       where  the 

image  is  real,  or  from  the  equation  _I  —  -L  =  *   where  it  is  virtual,  we  shall 

P     P'     f 

obtain  the  different  values  of  the  ratio  —    for  various  positions  of  the  object. 
In  the  first  case  we  have  v_  m£_f. 

Thus  if  p>2f    I>O 

p  =  2f    1  =  0 

P<2f    I>0 
In  the  second  case  when  the  image  is  virtual  we  shall  have 

_-  =  J-  .  so  that  in  all  cases  I  >  O. 
O      f-p 

By  using  the  above  formula  we  may  easily  deduce  the  focal  length  of  a 
convex  lens,  where  direct  sunlight  is  not  available.  For  if  it  be  placed  in 
front  of  a  scale,  and  if  a  screen  be  placed  on  the  other  side,  then,  by  altering 
the  relative  positions  of  the  lens  and  the  screen,  a  position  may  be  found  by 


486 


On  Light. 


[561- 


Fig.  462. 


trial,  such  that  an  image  of  the  object  is  formed  on  the  screen  of  exactly  the 
same  size.  Dividing  now  by  4,  the  total  distance  between  the  object  and  the 
screen,  we  get  the  focal  distance  of  the  lens. 

562.  Determination  of  refractive  index. — By  measurements  of  focal 
distance  the  refractive  index  of  a  liquid  may  be  ascertained  in  cases  in 

which  only  small  quantities  of  liquid  are  available.  One 
face  of  a  double  convex  lens  of  known  focal  distance  f,  and 
known  curvature  r,  is  pressed  against  a  drop  of  the  liquid 
in  question  on  a  glass  plate  (fig.  462).  The  liquid  forms 
thereby  a  plano-concave  lens,  whose  radius  of  curvature  is  r. 
The  focal  distance  F  of  the  whole  system  is  then  determined 
experimentally  ;  this  gives  the  focal  length  of  the  liquid  lens 
f  from  the  formula 

i   _  i  _  I 

T"7  7" 

while  from  the  formula  __  =  (»—  i)  —  we  get  the  value  of  n. 

563.  Laryngoscope. — As  an  application  of  lenses  may  be  adduced  the 
laryngoscope,   which    is   an   instrument   invented   to  facilitate   the  investi- 
gation of  the  larynx  and  the  other  cavities  of  the  mouth.     It  consists  of  a 
plane  convex  lens  L,  and  a  concave  reflector  M,  both  fixed  to  a  ring  which 
can  be  adjusted  to  any  convenient  lamp  (fig.  463).     The  flame  of  a  lamp  is 


Fig.  463. 

in  the  principal  focus  of  the  lens,  and  at  the  same  time  is  at  the  centre  of 
curvature  of  the  reflector.  Hence  the  divergent  pencil  proceeding  from  the 
lamp  to  the  lens  is  changed  after  emerging  into  a  parallel  pencil.  Moreover, 
the  pencil  from  the  lamp  impinging  upon  the  mirror,  is  reflected  to  the  focus 
of  the  lens,  and  traverses  the  lens  forming  a  second  parallel  pencil  which 
is  superposed  on  the  first.  This  being  directed  into  the  mouth  of  a  patient, 
its  condition  may  be  readily  observed. 


-564]  Decomposition  of  White  Light.  487 


CHAPTER   IV. 

DISPERSION   AND  ACHROMATISM. 

564.  Decomposition  of  wbite  light.  Solar  spectrum. — The  pheno- 
menon of  refraction  is  by  no  means  so  simple  as  we  have  hitherto  assumed  ; 
when  white  light,  or  that  which  reaches  us  from  the  sun,  passes  from  one 
medium  into  another,  //  is  decomposed  into  several  kinds  of  light,  a  phenor 
menon  to  which  the  name  dispersion  is  given. 

In  order  to  show  that  white  light  is  decomposed  by  refraction,  a  pencil  of 
solar  light  SA  (fig.  464)  is  allowed  to  pass  through  a  small  aperture  in  the 
window  shutter  of  a  dark 
chamber.  This  pencil 
tends  to  form  a  round 
and  colourless  image  of 
the  sun  at  K  ;  but  if  a 
flint  glass  prism,  ar- 
ranged horizontally,  be 
interposed  in  its  path, 
the  beam,  on  emerging 
from  the  prism,  becomes 
refracted  towards  its 
base,  and  produces  on 
a  distant  screen  a  ver- 
tical band  rounded  at 
the  ends,  coloured  in  all  Fig  464. 

the  tints  of  the  rainbow, 

which  is  called  the  solar  spectrum,  see  Plate  I.  In  this  spectrum  there  is, 
in  reality,  an  infinity  of  different  tints,  which  imperceptibly  merge  into  each 
other,  but  it  is  customary  to  distinguish  seven  principal  colours.  These  are 
violet,  indigo,  blue,  green,  yellow,  orange,  red ;  they  are  arranged  in  this 
order  in  the  spectrum,  the  violet  being  the  most  refrangible,  and  the  red  trie 
least  so.  They  do  not  all  occupy  an  equal  extent  in  the  spectrum,  violet 
having  the  greatest  extent  and  orange  the  least. 

With  transparent  prisms  of  different  substances,  or  with  hollow  glass 
prisms  filled  with  various  liquids,  spectra  are  obtained  formed  of  the  same 
colours,  and  in  the  same  order ;  but  when  the  deviation  produced  is  the 
same,  the  length  of  the  spectrum  varies  with  the  substance  of  which  the 
prism  is  made.  The  angle  of  separation  of  two  selected  rays  (say  in  the  red 
and  the  violet)  produced  by  a  prism  is  called  the  dispersion,  and  the  ratio  of 
this  angle  to  the  mean  deviation  of  the  two  rays  is  called  the  dispersive  power. 


488  On  Light.  [564- 

This  ratio  is  constant  for  the  same  substance  so  long  as  the  refracting  angle 
of  the  prism  is  small.  For  the  deviation  of  the  two  rays  is  proportional  to 
the  refracting  angle ;  their  difference  and  their  mean  vary  in  the  same 
manner,  and,  therefore,  the  ratio  of  their  difference  to  their  mean  is  constant. 
For  flint  glass  this  is  0*043  ;  f°r  crown  glass  it  is  0-0246  ;  for  the  dispersive 
power  of  flint  is  almost  double  that  of  crown  glass. 

The  spectra  which  are  formed  by  artificial  lights  rarely  contain  all  the 
colours  of  the  solar  spectrum  ;  but  their  colours  are  found  in  the  solar 
spectrum,  and  in  the  same  order.  Their  relative  intensity  is  also  modified. 
The  shade  of  colour  which  predominates  in  the  flame  predominates  also  in 
the  spectrum  :  yellow,  red,  and  green  flames  produce  spectra  in  which  the 
dominant  tint  is  yellow,  red,  or  green. 

565.  Production  of  a  pure  solar  spectrum. — In  the  above  experiment, 
when  the  light  is  admitted  through  a  wide  slit,  the  spectrum  formed  is  built 
up  of  a  series  of  overlapping  spectra,  and  the  colours  are  confused  and  indis- 
tinct.    In  order  to  obtain  a  pure  spectrum,  the  slit,  in  the  shutter  of  the  dark 
room  through. which  light  enters,  should  be  from  15  to  25  mm.  in  height  and 
from  i  to  2  mm.  in  breadth.     The  sun's  rays  are  directed  upon  the  slit  by  a 
mirror,  or  still  better  by  a  helibstat   (534).     An  achromatic  double  convex 
lens  is  placed  at  a  distance  from  the  slit  of  double  its  own  focal  length,  which 
should  be  about  a  metre,  and  a  screen  is  placed  at  the  same  distance  from 
the  lens.     An  image  of  the  slit  of  exactly  the  same  size  is  thus  formed  on  the 
screen  (561).     If  now  there  is  placed  near  the  lens,  between  it  and  the 
screen,  a  prism  with  an  angle  of  about  60°  and  with  its  refracting  edge 
parallel  to  the  slit,  a  very  beautiful,  sharp,  and  pure  spectrum  is  formed  on 
the  screen. 

The  prism  should  be  free  from  striae,  and  should  be  placed  so  that  it 
produces  the  minimum  deviation. 

566.  The  colours  of  the  spectrum  are  simple,  and  unequally  refran- 
gible.— If  one  of  the  colours  of  the  spectrum  be  isolated  by  intercepting  the 
others  by  means  of  a  screen  E,  as  shown  in  fig.  465,  and  if  the  light  thus  in- 
tercepted be  allowed  to 
pass    through   a   second 
prism,  B,  a  refraction  will 
be  observed,  but  the  light 
remains  unchanged ;  that 
is,  the  image  received  on 
the  screen  H  is  violet  if 
the    violet     pencil     has 

Fig  465.  been    allowed    to    pass, 

blue  if  the  blue   pencil, 

and  so  on.     Hence  the  colours  of  the  spectrum  are  simple ;    that  is,  they 
cannot  be  further  decomposed  by  the  prism. 

Moreover,  the  colours  of  the  spectrum  are  unequally  refrangible  ;  that 
is,  they  possess  different  refractive  indices.  The  elongated  shape  of  the 
spectrum  would  be  sufficient  to  prove  the  unequal  refrangibility  of  the  simple 
colours,  for  it  is  clear  that  the  violet,  which  is  most  deflected  towards  the 
base  of  the  prism,  is  also  most  refrangible,  and  that  red,  which  is  least  re- 
flected, is  least  refrangible.  But  the  unequal  refrangibility  of  simple  colours 


-566]  The  Colours  of  the  Spectrum  are  unequally  Refrangible.  489 

may  be  shown  by  numerous  experiments,  of  which  the  two  following  may  be 
adduced  : — 

i.  Two  narrow  strips  of  coloured  paper,  one  red  and  the  other  violet,  are 
fastened  close  to  each  other  on  a  sheet  of  black  paper.  On  looking  at  them 
through  a  prism,  they  are  seen  to  be  unequally  displaced,  the  red  band  to  a 
less  extent  than  the  violet ;  hence  the  red  rays  are  less  refrangible  than  the 
violet. 

ii.  The  same  conclusion  may  be  drawn  from  Newton's  experiment  with 
crossed  prisms.  On  a  prism,  A  (fig.  466),  in  a  horizontal  position,  a  pencil 


Fig.  466. 

of  white  light,  S,  is  received,  which,  if  it  had  merely  traversed  the  prism  A, 
would  form  the  spectrum  rz/,  on  a  distant  screen.  But  if  a  second  prism,  B. 
be  placed  in  a  vertical  position  behind  the  first,  in  such  a  manner  that  the 
refracted  pencil  passes  through  it,  the  spectrum  rv  becomes  deflected  towards 
the  base  of  the  vertical  prism  ;  but,  instead  of  being  deflected  in  a  direction 
parallel  to  jtself,  as  would  be  the  case  if  the  colours  of  the  spectrum  were 
equally  refracted,  it  is  obliquely  refracted  in  the  direction  r'l/^  proving  that 
from  red  to  violet  the  colours  are  more  and  more  refrangible. 

These  different  experiments  show  that  the  refractive  index  differs  in 
different  colours  ;  even  rays  which  are  to  perception  undistinguishable  have 
not  the  same  refractive  index.  In  the  red  band,  for  instance,  the  rays  at  the 


Fig.  467. 


468. 


extremity  of  the  spectrum  are  less  refracted  than  those  which  are  nearer  the 
orange  zone.  In  determining  indices  ol  refraction  (540),  it  is  usual  to  take, 
as  the  index  of  any  particular  substance,  the  refrangibility  of  the  yellow  ray 
in  a  prism  formed  of  that  substance. 


490 


On  Light. 


[567- 


567.  Decomposition  of  white  ligrlit.— Not  merely  can  white  light  be 
resolved  into  lights  of  various  colours,  but  by  combining  the  different  pencils 
separated  by  the  prism,  white  light  can  be  reproduced.  This  may  be  effected 
in  various  ways  : — 

i.  If  the  spectrum  produced  by  one  prism  be  allowed  to  fall  upon  a  second 
prism  of  the  same  material,  and  the  same  refracting  angle  as  the  first,  but 
inverted,  as  shown  in  fig.  468,  the  latter  reunites  the  different  colours  of 

the  spectrum,  and  it  is  seen  that  the  emer- 
gent pencil  E,  which  is  parallel  to  the  pencil 
S,  is  colourless. 

ii.  If  the  spectrum  falls  upon  a  double 
convex  lens  (fig.  467),  a  white  image  of  the 
sun  will  be  formed  on  a  white  screen  placed 
in   the   focus   of  the   lens  ;    a  glass   globe 
Figt  4&9  filled  with  water  produces  the  same  effect  as 

the  lens, 

iii.  When  the  spectrum  falls  upon  a  concave  mirror,  a  white  image  is 
formed  on  a  screen  of  ground  glass  placed  in  its  focus  (fig.  469). 

iv.  Light  may  be  recomposed  by  means  of  a  pretty  experiment,  which 
consists  in  receiving  the  seven  colours  of  the  spectrum  on  seven  small  glass 


Fig.  470. 

mirrors  with  plane  faces,  and  which  can  be  so  inclined  in  all  positions  that 
the  reflected  light  may  be  transmitted  in  any  given  direction  (fig.  470). 
When  these  mirrors  are  suitably  arranged,  the  seven  reflected  pencils  may 
be  caused  to  fall  on  the  ceiling  in  such  a  manner  as  to  form  seven  distinct 
images — red,  orange,  yellow,  &c.  When  the  mirrors  are  moved  so  that 
the  separate  images  become  superposed,  a  single  image  is  obtained,  which 
is  white. 

v.  By  means  of  Newtorts  disc,  fig.  471,  it  may  be  shown  that  the  seven 
colours  of  the  spectrum  form  white.  This  is  a  cardboard  disc  of  about  a 
foot  in  diameter ;  the  centre  and  the  edges  are  covered  with  black  paper, 
while  in  the  space  between  there  are  pasted  strips  of  paper  of  the  colours  of 
the  spectrum.  They  proceed  from  the  centre  to  the  circumference,  and  their 


-568]         Newton's  Tlieory  of  the  Composition  of  Light.  491 

relative  dimensions  and  tints  are  such  as  to  represent  five  spectra  T(fig.  472). 
When  this  disc  is  rapidly  rotated,  the  effect  is  the  same  as  if  the  retina  re- 
ceived simultaneously  the  impression  of  the  seven  colours. 

vi.  If  by  a  mechanical  arrangement,  a  prism,  on  which  the  sun's  light 
falls,  is  made  to  oscillate  rapidly,  so  that  the  spectrum  also  oscillates,  the 
middle  of  the  spectrum  appears  white. 

These  latter  phenomena  depend  on  the  physiological  fact,  that  sensation 
always  lasts  a  little  longer  than  the  impression  from  which  it  results.  If  a 
new  impression  is  allowed  to  act,  before  the  sensation  arising  from  the 
former  one  has  ceased,  a  sensation  is  obtained  consisting  of  two  impressions. 
And  by  choosing  the  time  short  enough,  three,  four,  or  more  impressions 
maybe  mixed  with  each  other.  With  a  rapid  rotation  the  disc  (fig.  471) 


Fig.  471. 

is  nearly  white.  It  is  not  quite  so,  for  the  colours  cannot  be  exactly  arranged 
in  the  same  proportion  as  those  in  which  they  exist  in  the  spectrum,  and 
pigment  colours  are  not  pure.  A  similar  explanation  applies  to  the  experi- 
ment of  the  oscillating  prism. 

568.  Newton's  theory  of  the  composition  of  light. — Newton  was  the 
first  to  decompose  white  light  by  the  prism,  and  to  recompose  it.  From  the 
various  experiments  which  we  have  described,  he  concluded  that  white  light 
was  not  homogeneous,  but  formed  of  seven  lights  unequally  refrangible, 
which  he  called  simple  or  primitive  lights.  Owing  to  the  difference  in  re- 
frangibility  they  become  separated  in  traversing  the  prism. 

The  designation  of  the  various  colours  of  the  spectrum  is  to  a  very  great 
extent  arbitrary' ;  for,  in  strict  accuracy7,  the  spectrum  is  made  up  of  an  infinite 
number  of  simple  colours,  which  pass  into  one  another  by  imperceptible 
gradations  of  colour  and  refrangibility. 


492  On  Light  [569- 

569.  Colour  of  bodies. — The  natural  colour  of  bodies  results  from  the 
fact    that  of  the  coloured  rays   contained   in  white   light,  one   portion  is 
absorbed  at  the  surface  of  the  body.     If  the  unabsorbed  portion  traverses 
the  body,  it  is  coloured  and  transparent ;  if,  on  the  contrary,  it  is  reflected, 
it   is   coloured   and   opaque.     In  both   cases   the  colour  results  from  the 
constituents   which    have   not    been   absorbed.      Those   which    reflect   or 
transmit  all  colours  in  the  proportion  in  which  they  exist  in  the  spectrum 
are  white ;   those   which   reflect   or  transmit   none   are   black.      Between 
these  two  limits  there  are  infinite  tints  according  to  the  greater  or  less 
extent  to  which  bodies  reflect  or  transmit  some  colours  and  absorb  others. 
Thus  a  body  appears  yellow,  because  it  absorbs  all  colours  with  the  ex- 
ception of  yellow.     In   like   manner,  a    solution  of  ammoniacal    oxide  of 
copper  absorbs  preferably  the  red  and  yellow  rays,  transmits  the  blue  rays 
almost  completely,  the  green  and  violet  less  so,  hence  the  light  seen  through 
it  is  blue. 

Hence  bodies  have  no  colour  of  their  own  ;  with  the  nature  of  the  in- 
cident light  the  colour  of  the  body  changes.  Thus,  if  in  a  dark  room  a  white 
body  be  successively  illuminated  by  each  of  the  colours  of  the  spectrum,  it 
has  no  special  colour,  but  appears  red,  orange,  green,  &c.,  according  to  the 
position  in  which  it  is  placed.  If  homogeneous  light  falls  upon  a  body,  it 
appears  brighter  in  the  colour  of  this  light,  if  it  does  not  absorb  this  colour  ; 
but  black  if  it  does  absorb  it.  In  the  light  of  a  lamp  fed  by  spirit  in  which 
some  common  salt  is  dissolved,  everything  white  and  yellow  seems  bright, 
while  other  colours,  such  as  vermilion,  ultramarine,  and  malachite,  are 
black.  This  is  well  seen  in  the  case  of  a  stick  of  red  sealing-wax  viewed 
in  such  a  light.  In  the  light  of  lamps  and  of  candles,  which  from  the  want 
of  blue  rays  appear  yellow,  yellow  and  white  appear  the  same,  and  blue  seems 
like  green.  In  bright  twilight  or  in  moonshine,  the  light  of  gas  has  a  reddish 
tint. 

570.  Mixed  colours.     Complementary  colours. — By  mixed  colours  we 
understand  the  impression  of  colour  which  results  from  the  coincident  action 
of  two  or  more  colours  on  the  same  position  of  the  retina.     This  new  im- 
pression is  single  ;  it  cannot  be  resolved  into 
its  components  ;  in  this  respect  it  differs  from 

P  y°'^  a  complex  sound,  in  which  the  ear,  by  practice, 

can  learn  to  distinguish  the  constituents.  Mixed 
colours   may  be   produced   by  looking  in   an 
oblique  direction  through  a  vertical  glass  plate 
^  P  (fig.  473)  at  a  coloured  wafer  b,  while,  at  the 

~F same  time,  a  wafer  of  another  colour  g  sends 
its  light  by  reflection  towards  the  observer's 
eye  ;  if  g  is  placed  in  a  proper  position  its  image  exactly  coincides  with 
that  of  b.  The  method  of  the  colour  disc  (567)  affords  another  means  of 
producing  mixed  colours. 

If  in  any  of  the  methods  by  which  the  impression  of  mixed  spectral 
colours  is  produced,  one  or  more  colours  be  suppressed,  the  residue  corre- 
sponds to  one  of  the  tints  of  the  spectrum  ;  and  the  mixture  of  the  colours 
taken  away  produces  the  impression  of  another  spectral  colour.  Thus,  if  in 
fig.  467  the  red  rays  are  cut  off  from  the  lens  L,  the  light  on  the  focus  is  no 


-571]  Spectral  Colours  and  Pigment  Colours.  493 

longer  white  but  greenish  blue.  In  like  manner  if  the  violet,  indigo,  and 
blue  of  the  colour  disc  be  suppressed,  the  rest  seems  yellow,  while  the 
mixture  of  that  which  has  been  taken  out  is  a  bluish  violet.  Hence  white 
can  always  be  compounded  of  two  tints  ;  and  two  tints  which  together  give 
white  are  called  complementary  colours.  Thus  of  spectral  tints  red  and 
greenish  yellow  are  complementary,  so  are  orange  and  Prussian  blue ; 
yellow  and  indigo  blue ;  greenish  yellow  and  violet. 

The  method  by  which  Helmholtz   investigated  the  mixture  of  spectral 
colours  is  as  follows  :— Two  very  narrow  slits,  A  and  B  (fig.  474),  at  right 


Fig.  474- 

angles  to  each  other  are  made  in  the  shutter  of  a  dark  room  ;  at  a  distance 
from  this  is  placed  a  powerfully  dispersing  prism  with  its  refracting  edge 
vertical.  When  this  is  viewed  through  a  telescope  the  slit  B  gives  the 
oblique  spectrum  LM,  while  the  slit  A  gives  the  spectrum  ST.  These  two 
spectra  partially  overlap,  and  where  this  is  the  case  two  homogeneous  spectral 
colours  mix.  Thus  at  I  the  red  of  one  spectrum  coincides  with  the  green  of 
the  other,  at  3  indigo  and  yellow  coincide,  and  so  forth. 

When  the  experiment  is  made  with  suitable  precautions,  the  colours  ob- 
tained by  mixing  the  spectral  colours  are  given  in  the  table  on  the  next  page, 
where  the  fundamental  spectra  to  be  mixed  are  given  in  the  first  horizontal 
and  vertical  column  and  the  resultant  colours  where  these  cross. 

The  mixture  of  mixed  colours  gives  rise  to  no  new  colours.  Only  the 
same  colours  are  obtained  as  a  mixture  of  the  primitive  spectral  colours  would 
yield,  except  that  they  are  less  saturated  as  it  is  called  ;  that  is,  more  mixed 
with  white. 

571.  Spectral  colours  and  pigment  colours. — A  distinction  must  be 
made  between  spectral  colours  and  pigment  colours.  Thus  a  mixture  of 
pigment  yellow  and  pigment  blue  produces  green  and  not  white,  as  is  the 
case  when  the  blue  and  yellow  of  the  spectrum  are  mixed.  The  reason  of 
this  is  that  in  the  mixture  of  pigments  we  have  a  case  of  subtraction  of 
colours,  and  not  of  addition.  For  in  the  mixture  the  pigment  blue  absorbs 
almost  entirely  the  yellow  and  red  light ;  and  the  pigment  yellow  absorbs 
the  blue  and  violet  light,  so  that  only  the  green  remains. 

In  the  above  series  are  two  spectral  colours  very  remote  in  the  spectrum 
which  have  nearly  the  same  complementary  tints  :  these  are  red,  the  com- 
plementary colour  to  which  is  greenish  blue  ;  and  violet,  whose  complementary 
colour  is  greenish  yellow.  Now  when  two  pairs  of  complementary  colours 
are  mixed  together,  they  must  produce  white  just  as  if  only  two  comple- 
mentary colours  were  mixed.  But  a  mixture  of  greenish  blue  and  of  greenish 
yellow  is  green.  Hence  it  follows  that  from  a  mixture  of  red,  green,  and 
violet,  white  must  be  formed.  This  may  easily  be  ascertained  to  be  the  case, 


494 


On  Light. 


[571- 


by  means  of  a  colour  disc  on  which  are  these  three  colours  in  suitable  pro- 
portions. 


Violet 

Blue 

Green 

Yellow 

Red 

Red 

Purple 

Rose 

Dull 
yellow 

Orange 

Red 

Yellow 

Rose 

White 

Yellowish 
green 

Yellow 

Green 

Pale  blue 

Bluish 
green 

Green 

Blue 

Indigo 

Blue 

Violet 

Violet 

From  the  above  facts  it  follows  that  from  a  mixture  of  red,  green,  and 
violet  all  possible  colours  may  be  constructed,  and  hence  these  three  spectral 
colours  are  called  the  fundamental  colours.  It  must  be  remarked  that  the 
tints  resulting  from  the.  mixture  of  these  three  have  never  the  saturation  of 
the  individual  spectral  colours. 

We  have  to  discriminate  three  points  in  regard  to  colour.  In  the  first 
place,  the  tint  or  colour  proper,  by  which  we  mean  that  special  property 
which  is  due  to  a  definite  refrangibility  of  the  rays  producing  it ;  secondly, 
the  saturation,  which  depends  on  the  greater  or  less  admixture  of  white  light 
with  the  colours  of  the  spectrum,  these  being  colours  which  are  fully  satu- 
rated ;  and  thirdly,  there  is  the  intensity  which  depends  on  the  amplitude  of 
vibration. 

572-  Homogeneous  light. — The  light  emitted  from  luminous  bodies  is 
seldom  or  never  quite  pure  ;  on  being  examined  by  the  prism  it  will  be  found 
to  contain  more  than  one  colour.  In  optical  researches  it  is  frequently  oi 
great  importance  to  procure  homogeneous  or  monochromatic  light.  Common 
salt  in  the  flame  of  a  Bunsen's  lamp  gives  a  yellow  of  great  purity.  For  red 
light,  ordinary  light  is  transmitted  through  glass  coloured  with  suboxide  of 
copper,  which  absorbs  nearly  all  the  rays  excepting  the  red.  A  very  pure 
blue  is  obtained  by  transmitting  ordinary  light  through  a  glass  trough  con- 
taining an  ammoniacal  solution  of  sulphate  of  copper,  and  a  nearly  pure 
red  by  transmitting  it  through  a  solution  of  sulphocyanide  of  iron. 

573.  Properties  of  the  spectrum. — Besides  its  luminous  properties,  the 
spectrum  is  found  to  produce  calorific  and  chemical  effects. 

Luminous  properties.  It  appears  from  the  experiments  of  Fraunhofer 
and  of  Herschel,  that  the  light  in  the  yellow  part  of  the  spectrum  has  the 
greatest  intensity,  and  that  in  the  violet  the  least. 

Heating  effects.  It  was  long  known  that  the  various  parts  of  the  spectrum 
differed  in  their  calorific  effects.  Leslie  found  that  a  thermometer  placed  in 


-573]  Chemical  Properties  of  the  Spectrum.  495 

different  parts  of  the  spectrum  indicated  a  higher  temperature  as  it  moved 
from  violet  towards  red.  Herschel  fixed  the  maximum  intensity  of  the 
heating  effects  just  outside  the  red;  Berard  in  the  red  itself.  Seebeck 
showed  that  those  different  effects  depend  on  the  nature  of  a  prism  :  with  a 
prism  of  water  the  greatest  calorific  effect  is  produced  in  the  yellow  ;  with 
one  of  alcohol  it  is  in  the  orange-yellow ;  and  with  a  prism  of  crown  glass 
it  is  in  the  middle  of  the  red. 

Melloni,  by  using  prisms  and  lenses  of  rock  salt,  and  by  availing  himself 
of  the  extreme  delicacy  of  the  thermo-electric  apparatus,  first  made  a  com- 
plete investigation  of  the  calorific  properties  of  the  thermal  spectrum.  This 
result  led,  as  we  have  seen,  to  the  confirmation  and  extension  of  Seebeck's 
observations. 

Chemical  properties.  In  numerous  phenomena,  light  acts  as  a  chemical 
agent.  For  instance,  chloride  of  silver  blackens  under  the  influence  of  light ; 
transparent  phosphorus  becomes  opaque  ;  vegetable  colouring  matters  fade  ; 
hydrogen  and  chlorine  gases,  when  mixed,  combine  slowly  in  diffused  light, 
and  with  explosive  violence  when  exposed  to  direct  sunlight.  The  chemical 
action  differs  in  different  parts  of  the  spectrum.  Scheele  found  that  when 
chloride  of  silver  was  placed  in  the  violet,  the  action  was  more  energetic 
than  in  any  other  part.  Wollaston  observed  that  the  action  extended  beyond 
the  violet,  and  concluded  that,  besides  the  visible  rays,  there  are  some 
invisible  and  more  highly  refrangible  rays.  These  are  the  chemical  or 
actinic  rays. 

The  most  remarkable  chemical  action  which  light  exerts  is  in  the  growth 
of  plant  life.  The  vast  masses  of  carbon  accumulated  in  the  vegetable 
world,  owe  their  origin  to  the  carbonic  acid  present  in  the  atmosphere. 
Under  the  influence  of  the  sun's  rays  the  chemical  attraction  which  holds 
together  the  carbon  and  oxygen  is  overcome  ;  the  carbon,  which  is  set  free, 
assimilates  at  that  moment  the  elements  of  water,  forming  cellulose  or 
woody  fibre,  while  the  oxygen  returns  to  the  atmosphere  in  the  gaseous  form. 

The  researches  of  Bunsen  and  Roscoe  show  that  whenever  chemical 
action  is  induced  by  light,  an  absorption  of  light  takes  place,  preferably  of 
the  more  refrangible  parts  of  the  spectrum.  Thus,  when  chlorine  and 
hydrogen  unite,  under  the  action  of  light,  to  form  hydrochloric  acid,  light  is 
absorbed,  and  the  quantity  of  chemically  active  rays  consumed  is  directly 
proportional  to  the  amount  of  chemical  action. 

There  is  a  curious  difference  in  the  action  of  the  different  spectral  rays. 
Moser  placed  an  engraving  on  an  iodised  silver  plate,  and  exposed  it  to  the. 
light  until  an  action  had  commenced,  and  then  placed  it  under  a  violet  glass 
in  the  sunlight.  After  a  few  minutes  a  picture  was  seen  with  great  distinct- 
ness, while  when  placed  under  a  red  or  yellow  glass  it  required  a  very  long 
time,  and  was  very  indistinct.  When,  however,  the  iodised  silver  plate  was 
first  exposed  in  a  camera  obscura  to  blue  light  for  two  minutes,  and  was  then 
brought  under  a  red  or  yellow  glass,  an  image  quickly  appeared,  but  not 
when  placed  under  a  green  glass.  It  appears  as  if  there  are  vibrations  of  a 
certain  velocity  which  could  commence  an  action,  and  that  there  are  others 
which  are  devoid  of  the  property  of  commencing,  but  can  continue  and 
complete  an  action  when  once  set  up.  Becquerel,  who  discovered  these 
properties  in  luminous  rays,  called  the  former  exciting  rays^  and  the  latter 


496  On  Light.  [573- 

continuing  or  phosphorogenic  rays.  The  phosphorogenic  rays,  for  instance, 
have  the  property  of  rendering  certain  objects  self-luminous  in  the  dark 
after  they  have  been  exposed  for  some  time  to  the  light.  Becquerel  found 
that  the  phosphorogenic  spectrum  extended  from  indigo  to  beyond  the 
violet. 

574.  Dark  lines  of  the  spectrum. — The  colours  of  the  solar  spectrum 
are  not  continuous.  For  several  grades  of  refrangibility  rays  are  wanting, 
and  in  consequence,  throughout  the  whole  extent  of  the  spectrum,  there 
are  a  great  number  of  very  narrow  dark  lines.  To  observe  them,  a  pencil 
of  solar  rays  is  admitted  into  a  darkened  room,  through  a  narrow  slit. 
At  a  distance  of  three  or  four  yards,  we  look  at  this  slit  through  a  prism 
of  flint  glass,  which  must  be  very  free  from  flaws,  taking  care  to  hold  its 
edge  parallel  to  the  slit.  We  then  observe  a  great  number  of  very  delicate 
dark  lines  parallel  to  the  edge  of  the  prism,  and  at  very  unequal  intervals. 

The  existence  of  the  dark  lines  was  first  observed  by  Wollaston  in  1 802  ; 
but  Fraunhofer,  a  celebrated  optician  of  Munich,  first  studied  and  gave  a 
detailed  description  of  them.  Fraunhofer  mapped  the  lines,  and  indicated 
the  most  marked  of  them  by  the  letters  A,  <z,  B,  C,  D,  E,  £,  F,  G,  H  ;  they 
are  therefore  generally  known  as  Fraunhofer's  lines. 

The  dark  line  A  (see  fig.  2  of  Plate  I.),  is  at  the  extremity  and  B  in  the 
middle  of  the  red  ray ;  C  at  the  boundary  of  the  red  and  orange  ray  ;  D  is 
in  the  yellow  ray  ;  E,  in  the  green  ;  F,  in  the  blue  ;  G,  in  the  indigo  ;  H,  in 
the  violet.  There  are  certain  other  noticeable  dark  lines,  such  as  a  in  the 
red,  and  b  in  the  green.  In  the  case  of  solar  light  the  positions  of  the  dark 
lines  are  fixed  and  definite  ;  on  this  account  they  are  used  for  obtaining  an 
exact  determination  of  the  refractive  index  (538)  of  each  colour  ;  for  example, 
the  refractive  index  of  the  blue  ray  is,  strictly  speaking,  that  of  the  dark  line 
F.  In  the  spectra  of  artificial  lights,  and  of  the  stars,  the  relative  positions 
of  the  dark  lines  are  changed.  In  the  electric  light  the  dark  lines  are  re- 
placed by  brilliant  lines.  In  coloured  flames — that  is  to  say,  flames  in  which 
certain  chemical  substances  undergo  evaporation — the  dark  lines  are  replaced 
by  very  brilliant  lines  of  light,  which  differ  for  different  substances.  Lastly, 
of  the  dark  lines,  some  are  constant  in  position  and  distinctness,  such  as 
Fraunhofer's  lines  ;  but  some  of  the  lines  only  appear  as  the  sun  nears  the 
horizon,  and  others  are  strengthened.  They  are  also  influenced  by  the  state 
of  the  atmosphere.  The  fixed  lines  are  due  to  the  sun  ;  the  variable  lines 
have  been  proved  by  Jannsen  and  Secchi  to  be  due  to  the  aqueous  vapour 
in  the  air,  and  are  called  atmospheric  or  telluric  lines. 

Fraunhofer  counted  in  the  spectrum  more  than  600  dark  lines,  more  or 
less  distinct,  distributed  irregularly  from  the  extreme  red  to  the  extreme 
violet  ray.  Brewster  counted  2,000.  By  causing  the  refracted  rays  to  pass 
successively  through  several  analysing  prisms,  not  merely  has  the  existence 
of  3,000  dark  lines  been  ascertained,  but  several  which  had  been  supposed 
single  have  been  shown  to  be  compound. 

575.  Applications  of  Fraunhofer's  lines. — Subsequently  to  Fraunhofer, 
several  physicists  studied  the  dark  lines  of  the  spectrum.  In  1822  Sir  J. 
Herschel  remarked  that  by  volatilising  substances  in  a  flame  a  very  delicate 
means  is  afforded  of  detecting  certain  ingredients  by  the  colours  they  impart 
to  certain  of  the  dark  lines  of  the  spectrum  ;  and  Fox  Talbot  in  1834  sug- 


-576] 


Spectroscope. 


497 


gested  optical  analysis  as  probably  the  most  delicate  means  of  detecting 
minute  portions  of  a  substance.  To  KirchhofT  and  Bunsen,  however,  is  really 
due  the  merit  of  basing  on  the  observation  of  the  lines  of  the  spectrum  a 
method  of  analysis.  They  ascertained  that  the  salts  of  the  same  metal,  when 
introduced  into  a  flame,  always  produced  lines  identical  in  colour  and  position, 
but  different  in  colour,  position,  or  number  for  different  metals,  and  finally 


that  an  exceedingly  small  quantity  of  a  metal  suffices  to  disclose  its  existence. 
Hence  has  arisen  a  new  method  of  analysis,  known  by  the  name  of  spectrum 
analysis. 

576.  Spectroscope. — The  name  of  spectroscope  has  been  given  to  the 
apparatus  employed  by  Kirchhoffand  Bunsen  for  the  study  of  the  spectrum. 
One  of  the  forms  of  this  apparatus  is  represented  in  fig.  475.  It  is  composed 
of  three  telescopes  mounted  on  a  common  foot,  and  whose  axes  converge 
towards  a  prism,  P,  of  flint-glass.  The  telescope  A  is  the  only  one  which 
can  turn  round  the  prism.  It  is  fixed  in  any  required  position  by  a  clamping 
screw  n.  The  screw-head,  /«,  is  used  to  focus  the  eyepiece.  The  screw- 
head  n  serves  to  change  the  inclination  of  the  axis. 

To  explain  the  use  of  the  telescopes  B  and  C,  we  must  refer  to  fig.  476, 
which  shows  the  passage  of  the  light  through  the  apparatus.  The  rays 
emitted  by  the  flame  G  fall  on  the  lens  #,  and  are  caused  to  converge  to  a 
point,  ^,  which  is  the  principal  focus  of  a  second  lens,  c.  Consequently  the 
pencil,  on  leaving  the  telescope  B,  is  formed  of  parallel  rays  (552).  This  pencil 
enters  the  prism  P.  On  leaving  the  prism,  the  light  is  decomposed,  and  in 
this  state  falls  on  the  lens  x.  By  this  lens  .r,  a  real  and  reversed  image  of 
the  spectrum  is  formed  at  /,  This  image  is  seen  by  the  observer  through  a 


On  Light. 


[576- 


magnifying  glass  which  forms  at  ss'  a  virtual  image  of  the  spectrum  magni- 
fied about  eight  times. 

The  telescope  C  serves  to  measure  the  relative  distances  of  the  lines  of 
the  spectrum.  For  this  purpose  there  is  placed  at  m  a  micrometer  divided 
into  25  equal  parts.  The  micrometer  is  formed  thus  : — A  scale  of  250 
millimetres  is  divided  with  great  exactness  into  25  equal  parts.  A  photo- 
graphic negative  on  glass  of  this  scale  is  taken,  reduced  to  15  millimetres. 
The  negative  is  taken  because  then  the  scale  is  light  on  a  dark  ground. 


Fig.  476. 

The  scale  is  then  placed  at  m  in  the  principal  focus  of  the  lens  e  ;  conse- 
quently, when  the  scale  is  lighted  by  the  candle  F,  the  rays  emitted  from  it 
leave  the  lens  e  in  parallel  pencils  ;  a  portion  of  these,  being  reflected  from 
a  face  of  the  prism,  passes  through  a  lens  x,  and  forms  a  perfectly  distinct 
image  of  the  micrometer  at  z,  thereby  furnishing  the  means  of  measuring 
exactly  the  relative  distances  of  the  different  spectral  lines. 

The  micrometric  telescope  C  (fig.  475)  is  furnished  with  several  adjusting 

screws,  z',  <9,  r :  of  these  i  adjusts  the 
focus ;  o  displaces  the  micrometer  in 
the  direction  of  the  spectrum  laterally  ; 
r  raises  or  lowers  the  micrometer,  which 
it  does  by  giving  different  inclinations 
to  the  telescope. 

The  opening  whereby  the  light  of  the 
flame  G  enters  the  telescope  B  consists 
of  a  narrow  vertical  slit,  which  can  be 
opened  more  or  less  by  causing  the 
moveable  piece  a  to  advance  or  recede 
by  means  of  the  screw  v  (fig.  477). 
When  for  purposes  of  comparison  the 
spectra  of  two  flames  are  to  be  examined 
simultaneously,  there  is  placed  over  the  upper  part  of  the  slit  a  small, 
prism,  whose  refracting  angle  is  60°,  Rays  from  one  of  the  flames,  H,  fall 
at  right  angles  on  one  face  of  the  prism  }  they  then  experience  total  reflection 


Fig  477. 


-577]  Direct  Vision  Spectroscopes.  499 

on  a  second  face,  and  leave  the  prism  by  the  third  face,  and  in  a  direction 
at  right  angles  to  that  face.  By  this  means  they  pass  into  the  telescope 
in  a  direction  parallel  to  its  axis,  without  in  any  degree  mixing  with  the  rays 
which  proceed  from  the  second  flame,  G.  Consequently,  the  two  pencils  of 
rays  traverse  the  prism  P  (fig.  476),  and  form  two  horizontal  spectra  which 
are  viewed  simultaneously  through  the  telescope  A.  In  the  flames  G  and  H 
are  platinum  wires,  *,  e'.  These  wires  have  been  dipped  beforehand  into 
solutions  of  the  salts  of  the  metals  on  which  experiment  is  to  be  made  ;  and 
by  the  vaporisation  of  these  salts  the  metals  modify  the  transmitted  light, 
and  give  rise  to  definite  lines. 

Each  of  the  flames  G  and  H  is  a  jet  of  ordinary  gas.  The  apparatus 
through  which  the  gas  is  supplied  is  known  as  a  Bunseris  burner.  The  gas 
comes  through  the  hollow  stem  k  (fig.  475).  At  the  lower  part  of  this  there 
is  a  lateral  orifice  which  admits  air  to  support  the  combustion  of  the  gas. 
This  orifice  can  be  more  or  less  closed  by  a  small  diaphragm,  which  acts  as 
a  regulator.  If  we  allow  a  moderate  amount  of  air  to  enter,  the  gas  burns 
with  a  luminous  flame,  and  the  lines  are  obscured.  But  if  a  strong  and 
steady  current  of  air  enters,  the  carbon  is  rapidly  oxidised,  the  flame  loses  its 
brightness,  and  burns  with  a  pale  blue  light,  but  with  an  intense  heat.  In 
this  state  it  no  longer  yields  a  spectrum.  If,  however,  a  metallic  salt  is  in- 
troduced either  in  a  solid  state  or  in  a  state  of  solution,  the  spectrum  of  the 
metal  makes  its  appearance,  and  in  a  fit  state  for  observation. 

There  are  three  chief  types  of  spectra  :  the  continuous  spectrum,  or 
those  furnished  by  ignited  solids  and  liquids  (fig.  I,  Plate  I.) ;  the  band  or 
line  spectrum,  consisting  of  a  number  of  bright  lines,  and  produced  by 
ignited  gases  or  vapours  ;  and  absorption  spectra,  or  those  furnished  by  the 
sun  or  fixed  stars.  For  an  explanation  of  these  see  art.  576.  Bodies  at  a 
red  heat  give  only  a  short  spectrum,  extending  at  most  to  the  orange  ;  as 
the  temperature  gradually  rises,  yellow,  green,  blue  and  violet  successively 
appear,  while  the  intensity  of  the  lower  colours  increases. 

Instead  of  the  prism  very  pure  spectra  may  also  be  obtained  by  means  of 
a  grating  (647).  For  more  detailed  investigations  of  the  spectral  lines  a  train 
of  prisms  is  used  ;  the  light  on  emerging  from  one  prism  passing  into  another. 
By  this  means  far  greater  dispersion  is  obtained,  though  at  the  same  time 
there  is  a  great  loss  of  light.  In  the  case  of  ten  prisms  it  has  been  found 
to  amount  to  ninety-nine  per  cent. 

Christie  has  used  with  advantage  a  semiprism  obtained  by  cutting  an 
isosceles  prism,  by  a  plane  at  right  angles  to  the  base.  These  have  the  ad- 
vantage that  they  produce  as  much  dispersion  as  with  several  prisms  without 
any  appreciable  loss  in  the  sharpness  of  the  images  ;  and  without  that  ab- 
sorption of  light  which  in  the  case  of  a  number  of  prisms  is  so  very  con- 
siderable. 

577.  Direct  vision  spectroscopes. — Prisms  may  be  combined  so  as  to 
get  rid  of  the  dispersion  without  entirely  destroying  the  refraction  (584)  ; 
they  may,  conversely,  be  combined  so  that  the  light  is  not  refracted,  but  is 
decomposed  and  produces  a  spectrum.  Combinations  of  prisms  of  this  kind 
are  used  in  what  are  called  direct  vision  spectroscopes.  Fig.  478  represents 
the  section  of  such  an  instrument  in  about  f  the  natural  size.  A  system  of 
two  flint  and  three  crown  glass  prisms  are  placed  in  a  tube  which  moves  in 


500  On  Light.  [577- 

a  second  one ;  at  the  end  of  this  is  an  aperture  0,  and  inside  it  a  slit  the 
width  of  which  can  by  a  special  arrangement  be  regulated  by  simply  turning 


Fig.  478. 

a  ring  r.  A  small  achromatic  lens  is  introduced  at  aa,  the  focus  of  which  is 
at  the  slit,  so  that  the  rays  pass  parallel  through  the  train  of  lenses,  and  the 
spectrum  is  viewed  at  e. 

578.  Experiments  with  the  spectroscope. — The  coloured  plate  at  the 
beginning  shows  certain  spectra  observed  by  means  of  the  spectroscope. 
No.  i  represents  the  continuous  spectrum. 

No.  2  shows  the  spectrum  of  sodium.  The  spectrum  contains  neither 
red,  orange,  green,  blue,  nor  violet.  It  is  marked  by  a  very  brilliant  yellow 
ray  in  exactly  the  same  position  as  Fraunhofer's  dark  line  D.  Of  all  metals 
sodium  is  that  which  possesses  the  greatest  spectral  sensibility.  In  fact,  it 
has  been  ascertained  that  one  two-hundred-millionth  of  a  grain  of  sodium  is 
enough  to  cause  the  appearance  of  the  yellow  line.  Consequently,  it  is 
very  difficult  to  avoid  the  appearance  of  this  line.  A  very  little  dust 
scattered  in  the  apartment  is  enough  to  produce  it — a  circumstance  which 
shows  how  abundantly  sodium  is  distributed  throughout  nature. 

No.  3  is  the  spectrum  of  lithium.  It  is  characterised  by  a  well-marked 
line  in  the  red  called  Lia,  and  by  the  feebler  orange  line  Li/3. 

Nos.  4  and  5  show  the  spectra  of  ccesium  and  rubidium,  metals  discovered 
by  Bunsen  and  Kirchhoff  by  means  of  spectrum  analysis.  The  former  is 
distinguished  by  two  blue  lines  Csa  and  Cs/3  ;  the  latter  by  two  very  brilliant 
dark  red  lines  Rby  and  RbS,  and  by  two  less  intense  violet  lines  Rba  and 
Rbj8.  A  third  metal,  thallium,  has  been  discovered  by  the  same  method 
by  Mr.  Crookes  in  England,  and  independently  by  M.  Lamy  in  France. 
Thallium  is  characterised  by  a  single  green  line.  Subsequently  to  this 
Richter  and  Reich  discovered  a  new  metal  associated  with  zinc,  and  which 
they  call  indium  from  a  couple  of  characteristic  lines  which  it  forms  in  the 
indigo  ;  and  quite  recently  Boisbaudran  has  discovered  a  new  metal  which 
he  calls  gallium  existing  in  zinc  in  very  minute  quantities. 

The  extreme  delicacy  of  the  spectrum  reactions,  and  the  ease  with  which 
they  are  produced,  constitute  them  a  most  valuable  help  in  the  qualitative 
analysis  of  the  alkalies  and  alkaline  earths.  It  is  sufficient  to  place  a  small 
portion  of  the  substance  under  examination  on  platinum  wire  as  represented 
in  fig.  477,  and  compare  the  spectrum  thus  obtained  either  directly  with  that 
of  another  substance,  or  with  the  charts  in  which  the  positions  of  the  lines 
produced  by  the  various  metals  are  laid  down. 

With  other  metals  the  production  of  their  spectra  is  more  difficult, 
especially  in  the  case  of  some  of  their  compounds.  The  heat  of  a  Bunsen's 
burner  is  insufficient  to  vaporise  the  metals,  and  a  more  intense  temperature 
must  be  used.  This  is  effected  by  taking  electric  sparks  between  wires  con- 
sisting of  the  metal  whose  spectrum  is  required,  and  the  electric  sparks  are 


-578]  Experiments  with  the  Spectroscope.  501 

most  conveniently  obtained  by  means  of  Ruhmkorflf's  coil  or  inductorium. 
Thus  all  the  metals  may  be  brought  within  the  sphere  of  spectrum  obser- 
vations. 

The  power  of  the  apparatus  has  great  influence  on  the  nature  of  the 
spectrum  ;  while  an  apparatus  with  one  prism  only  gives  in  a  sodium  flame 
the  well-known  yellow  line,  an  apparatus  with  more  prisms  resolves  it  into 
two  or  three  lines. 

It  has  been  observed  that  the  character  of  the  spectrum  changes  with  the 
temperature  ;  thus  chloride  of  lithium  in  the  flame  of  a  Bunsen's  burner  gives 
a  single  intense  peach-coloured  line  ;  in  a  hotter  flame,  as  that  of  hydrogen, 
it  gives  an  additional  orange  line  ;  while  in  the  oxy-hydrogen  jet  or  the 
voltaic  arc  a  broad  brilliant  blue  band  comes  out  in  addition.  The  sodium 
spectrum  produced  by  a  Bunsen's  burner  consists  of  a  single  yellow  line  ; 
if,  by  the  addition  of  oxygen,  the  heat  be  gradually  increased,  more  bright 
lines  appear  ;  and  with  the  aid  of  the  oxy-hydrogen  flame  the  spectrum  is 
continuous.  Sometimes  also,  in  addition  to  the  appearance  of  new  lines,  an 
increase  in  temperature  resolves  those  bands  which  exist  into  a  number  of 
fine  lines,  which  in  some  cases  are  more  and  in  some  less  refrangible  than  the 
bands  from  which  they  are  formed.  It  may  be  supposed  that  the  glowing 
vapour  found  at  the  low  temperature  consists  of  the  oxide  of  some  difficultly 
reducible  metal,  whereas  at  the  enormously  high  temperature  of  the  spark 
these  compounds  are  decomposed,  and  the  true  bright  lines  of  the  metal  are 
formed. 

The  delicacy  of  the  reaction  increases  very  considerably  with  the  tem- 
perature. With  the  exception  of  the  alkalies,  it  is  from  40  to  400  times  greater 
at  the  temperature  of  the  electric  spark  than  at  that  of  Bunsen's  burner. 

The  spectra  of  the  permanent  gases  are  best  obtained  by  taking  the 
electric  spark  of  a  RuhmkorfFs  coil,  or  Holtz's  apparatus,  through  glass 
tubes  of  a  special  construction,  provided  with  electrodes  of  platinum  and 
filled  with  the  gas  in  question  in  a  state  of  great  attenuation,  known  as 
Geissler's  tubes  ;  if  the  spark  be  passed  through  hydrogen,  the  light  emitted 
is  bright  red,  and  its  spectrum  consists  of  one  bright  red,  one  green,  and  one 
blue  line  No.  7,  the  first  two  of  which  appear  to  coincide  with  Fraunhofer's 
lines  C  and  F,  and  the  third  with  a  line  between  F  and  G.  No.  6  repre- 
sents the  spectrum  of  oxygen.  No.  8  is  the  spectrum  of  nitrogen.  The 
light  of  this  gas  in  a  Geissler's  tube  is  purple,  and  the  spectrum  very  com- 
plicated. 

If  the  electric  discharge  takes  place  through  a  compound  gas  or  vapour, 
the  spectra  are  those  of  the  elementary  constituents  of  the  gas.  It  seems  as 
if,  at  very  intense  temperatures,  chemical  combination  was  impossible,  and 
oxygen  and  hydrogen,  chlorine  and  the  metals,  could  coexist  in  a  separate 
form,  as  though  mechanically  mixed  with  each  other. 

The  nature  of  the  spectra  of  the  elementary  gases  is  very  materially  in- 
fluenced by  alterations  of  temperature  and  pressure.  Wiillner  made  a  series 
of  very  accurate  observations  on  the  gases  oxygen,  hydrogen,  and  nitrogen. 
He  not  only  used  gases  in  closed  tubes,  which  by  various  electrical  means 
he  raised  to  different  temperatures  ;  but  in  one  and  the  same  series  of  ex- 
periments, in  which  a  small  inductorium  was  used,  he  employed  pressures  vary- 
ing from  i oo  millimetres  to  a  fraction  of  a  millimetre  ;  while  in  another  series 


502  On  Light.  [578- 

in  which  a  larger  apparatus  was  used,  he  extended  the  pressure  to  2,000 
millimetres.  At  the  lowest  pressure  of  less  than  one  millimetre,  the  spectrum 
of  hydrogen  was  found  to  be  green,  and  consisting  of  six  splendid  groups  of 
lines,  which  at  a  higher  pressure  than  I  millimetre  changed  to  continuous 
bands ;  at  2  to  3  millimetres  the  spectrum  consisted  of  the  often-mentioned 
three  lines,  which  did  not  disappear  under  a  higher  pressure,  but  gradually 
became  less  brilliant  as  the  continuous  spectrum  increased  in  extent  and 
lustre.  From  this  point  the  light,  and  therefore  the  spectrum,  became 
feebler.  Using  the  larger  apparatus,  the  band  spectrum  appeared  only 
under  a  higher  pressure  ;  at  the  highest  pressure  of  2,000  millimetres  it  gave 
place  to  the  continuous  spectrum,  since  the  bright  lines  continually  extended 
and  ultimately  merged  into  each  other. 

579.  Explanation  of  the  dark  lines  of  the  solar  spectrum. — It  has 
been  already  seen  that  incandescent  sodium  vapour  gives  a  bright  yellow 
line  corresponding  to  the  dark  line  D  of  the  solar  spectrum.  Kirchhoff 
found  that,  when  the  brilliant  light  produced  by  incandescent  lime  passes 
through  a  flame  coloured  by  sodium  in  the  usual  manner,  a  spectrum  is  pro- 
duced in  which  is  a  dark  line  coinciding  with  the  dark  line  D  of  the  solar 
spectrum ;  what  would  have  been  a  bright  yellow  line  becomes  a  dark  line 
when  formed  on  the  background  of  the  lime  light.  By  allowing  in  a  similar 
manner  the  lime  light  to  traverse  vapours  of  potassium,  barium,  strontium,  &c., 
the  bright  lines  which  they  would  have  formed  were  found  to  be  converted 
into  dark  lines  :  such  spectra  are  called  absorption  spectra. 

It  appears,  then,  that  the  vapour  of  sodium  has  the  power  of  absorbing 
rays  of  the  same  refrangibility  as  that  which  it  emits.  And  the  same  is  true 
of  the  vapours  of  potassium,  barium,  strontium,  &c.  This  absorptive  power 
is  by  no  means  an  isolated  phenomenon.  These  substances  share  it,  for  ex- 
ample, with  the  vapour  of  nitrous  acid,  which  Brewster  found  to  possess  the 
following  property  : — when  a  tube  filled  with  this  vapour  is  placed  in  the  path 
of  the  light  either  of  the  sun  or  of  a  gas  flame,  and  the  light  is  subsequently 
decomposed  by  a  prism,  a  spectrum  is  produced  which  is  full  of  dark  lines 
(No.  9,  Plate  I.) ;  and  Miller  showed  that  iodine  and  bromine  vapour  pro- 
duced analogous  effects. 

Hence  the  origin  of  the  above  phenomenon  is,  doubtless,  the  absorption 
by  the  sodium  vapour  of  rays  of  the  same  kind — that  is,  having  the  same  refran- 
gibility— as  those  which  it  has  itself  the  power  of  emitting.  Other  rays  it 
allows  to  pass  unchanged,  but  these  it  either  totally  or  in  great  part  suppresses. 
Thus  the  particular  lines  in  the  spectrum  to  which  these  rays  would  converge 
are  illuminated  only  by  the  feebly  luminous  sodium  flame,  and  accordingly 
appear  dark  by  contrast  with  the  other  portions  of  the  spectrum  which 
receive  light  from  the  powerful  flame  behind. 

By  replacing  one  of  the  flames,  G  or  H  (fig.  477),  by  a  ray  of  solar  light 
reflected  from  a  heliostat,  Kirchhoff  ascertained  by  direct  comparison  that 
the  bright  lines  which  characterise  iron  correspond  to  dark  lines  in  the  solar 
spectrum.  He  also  found  the  same  to  be  the  case  with  sodium,  magnesium, 
calcium,  nickel,  and  some  other  metals. 

From  these  observations  we  may  draw  important  conclusions  with  re- 
spect to  the  constitution  of  the  sun.  Since  the  solar  spectrum  has  dark  lines 
where  sodium,  iron,  &c.,  give  bright  ones  (No.  1 1,  Plate  I.),  it  is  probable 


-579]   Explanation  of  Uie  Dark  Lines  of  the  Solar  Spectrum.  503 

that  around  the  solid,  or  more  probably  liquid,  body  of  the  sun,  which  throws 
out  the  light,  there  exists  a  vaporous  envelope  which,  like  the  sodium  flame 
in  the  experiment  described  above,  absorbs  certain  rays  ;  namely,  those  which 
the  envelope  itself  emits.  Hence  those  parts  of  the  spectrum  which,  but  for 
this  absorption,  would  have  been  illuminated  by  these  particular  rays,  appear 
feebly  luminous  in  comparison  with  the  other  parts,  since  they  are  illumi- 
nated only  by  the  light  emitted  by  the  envelope,  and  not  by  the  solar 
nucleus  ;  and  we  are  at  the  same  time  led  to  conclude  that  in  this  vapour 
there  exist  the  metals  sodium,  iron,  &c. 

Huggins  and  Miller  applied  spectrum  analysis  to  the  investigation  of  the 
heavenly  bodies.  The  spectra  of  the  moon  and  planets,  whose  light  is  re- 
flected from  the  sun,  give  the  same  lines  as  those  of  the  sun.  Uranus  proves 
an  exception  to  this,  and  is  probably  still  in  a  self-luminous  condition.  The 
spectra  of  the  fixed  stars  contain,  however,  dark  lines  differing  from  the  solar 
lines,  and  from  one  another.  Four  distinct  types  of  spectra  are  distinguished 
by  Secchi.  The  first  embraces  the  white  stars  and  includes  the  well-known 
Sirius  and  a  Lyrae.  Their  spectra  (No.  12,  Plate  I.)  usually  contain  a  number 
of  very  fine  lines,  and  always  contain  four  broad  dark  lines  which  coincide 
with  the  bright  lines  of  hydrogen.  Out  of  346  stars  164  were  found  to  belong 
to  this  group.  The  second  group  embraces  those  having  spectra  intersected 
by  numerous  fine  lines  like  those  of  our  sun.  About  140  stars,  among  them 
Pollux,  Capella,  $  Aquilas,  belong  to  this  group.  The  third  group  embraces 
the  red  and  orange  stars,  such  as  a  Orionis,  3  Pegasi  ;  the  spectra  of  these 
(Nos.  13,  14,  Plate  I.)  are  divided  into  eight  or  ten  parallel  columnar  clusters 
of  dark  and  bright  bands  increasing  in  intensity  to  the  red.  Group  four  is 
made  up  of  small  red  stars  with  spectra,  and  is  constructed  of  three  bright 
zones  increasing  in  intensity  towards  the  violet.  It  would  thus  appear  that 
these  fixed  stars,  while  differing  from  one  another  in  the  matter  of  which  they 
are  composed,  are  constructed  on  the  same  general  plan  as  our  sun. 
Huggins  has  observed  a  striking  difference  in  the  spectra  of  the  nebulae ; 
where  they  can  at  all  be  observed,  they  are  found  to  consist  generally  of 
bright  lines,  like  the  spectra  of  the  ignited  gases,  instead  of  like  the  spectra 
of  the  sun  and  stars  consisting  of  a  bright  ground  intersected  by  dark  lines. 
It  is  hence  probable  that  the  nebulae  are  masses  of  glowing  gas,  and  do  not 
consist,  like  the  sun  and  stars,  of  a  photosphere  surrounded  by  a  gaseous 
atmosphere. 

One  of  the  most  interesting  triumphs  of  spectrum  analysis  has  been  the 
discover)'  of  the  true  nature  of  the  protuberances,  which  appear  during  a  solar 
eclipse  as  mountains  or  cloud-shaped  luminous  objects  varying  in  size,  and 
surrounding  the  moon's  disc. 

During  the  eclipse  of  1868  it  had  been  ascertained  by  Jannsen  that  pro- 
tuberances emitted  certain  bright  lines  coinciding  with  those  of  hydrogen. 
They  have,  however,  been  fully  understood  only  since  Lockyer  and  Jannsen 
have  discovered  a  method  of  investigating  them  at  any  time.  The  principle 
of  this  method  is  as  follows  : — When  a  line  of  light  admitted  through  a  slit  is 
decomposed  by  a  prism,  the  length  of  the  spectrum  may  be  increased  by 
passing  it  through  two  or  more  prisms  ;  as  the  quantity  of  light  is  the  same, 
it  is  clear  that  the  intensity  of  the  spectrum  will  be  diminished.  This  is  the 
case  with  the  ordinary  sources  of  light,  such  as  the  sun ;  if  the  light  be 


504  On  Light.  [579^ 

homogeneous,  it  will  be  merely  deviated,  and  not  reduced  in  intensity,  by 
dispersion.  And  if  the  source  of  light  emit  lights  of  both  kinds,  the  image 
of  the  slit  of  light  of  a  definite  refrangibility,  which  the  mixture  may  contain, 
will  stand  out  by  its  superior  intensity  on  the  weaker  ground  of  the  con- 
tinuous spectrum.  This  is  the  case  with  the  spectrum  of  the  protuberances. 
Viewed  through  an  ordinary  spectroscope,  the  light  they  emit  is  overshadowed 
by  that  of  the  sun  ;  but  by  using  prisms  of  great  dispersive  power  the  sun's 
light  becomes  weakened,  and  the  spectrum  of  the  protuberances  may  be 
observed.  Lockyer's  researches  leave  no  doubt  that  they  are  ignited  gas 
masses,  principally  of  hydrogen.  By  altering  the  position  of  the  slit  a  series 
of  sections  of  the  prominences  are  obtained,  by  collating  which  the  form  of 
the  prominence  may  be  inferred.  They  are  thus  found  to  enclose  the  sun 
usually  to  a  depth  of  about  5,000  miles,  but  sometimes  in  enormous  local 
accumulations,  which  reach  the  height  of  70,000  miles.  Lockyer  has  not 
merely  examined  these  phenomena  right  on  the  edge  of  the  sun  ;  but  he  has 
been  able  to  observe  them  on  the  disc  itself.  He  has  shown  that  some  of 
these  protuberances  are  the  results  of  sudden  outbursts  or  storms,  which 
move  with  the  enormous  velocity  of  120  miles  in  a  second. 

For  a  fuller  account  of  this  branch  of  Physics,  which  is  incompatible  with 
the  limits  of  this  work,  the  reader  is  referred  to  Roscoe's  '  Lectures  on  Spec- 
trum Analysis,'  and  to  the  same  writer's  articles  in  Watts's  '  Dictionary  of 
Chemistry,'  or  to  Schellen's  '  Spectrum  Analysis,'  translated  by  Lassell,  or 
to  Lockyer  '  On  the  Spectroscope.' 

580.  Uses  of  tne  spectroscope. — When  a  liquid  placed  in  a  glass  tube 
or  in  a  suitable  glass  cell  is  interposed  between  a  source  of  light  and  the 
slit  of  the  spectroscope,  on  looking  through  the  telescope  the  spectrum  ob- 
served will  in  many  cases  be  found  to  be  traversed  by  dark  bands.     No.  10, 
Plate    I,  represents   the  appearance  of  the   spectrum  when  a  solution  of 
chlorcphylle,  the  green  colouring  matter  of  plants,  is  thus  interposed.     Both 
in  the  red,  the  yellow,  and  the  violet  parts,  dark  bands  are  formed,  and  the 
blue  gives  way  to  a  reddish  shimmer.     If,  instead  of  chlorophylle,  arterial 
blood  greatly  diluted  be  used,  the  red  of  the  spectrum  appears  brighter,  but 
green  and  violet  are   nearly  extinguished.     As  these  bands  thus  differ  in 
different  liquids  as  regards  position,  breadth,  and  intensity,  in  many  cases 
they   afford   the   most   suitable   means  of  identifying   bodies.     Sorby  and 
Browning  have  devised  a  combination  of  the  microscope  and  spectroscope, 
called  the  microspectroscope,  which  renders  it  possible  to  examine  even  very 
minute  traces  of  substances. 

This  application  of  the  spectroscope  has  been  very  useful  in  investigating 
substances  which  have  special  importance  in  physiology  and  pathology  ; 
thus  in  examining  normal  and  diseased  blood,  in  detecting  albumen  in  urine, 
and  in  ascertaining  the  rate  at  which  certain  substances  pass  into  the  various 
fluids  of  the  system.  The  characteristic  absorption  bands  which  certain 
liquids,  such  as  wine,  beer,  &c.,  present  in  their  normal  state,  compared  with 
those  yielded  by  adulterated  substances,  furnishes  a  delicate  and  certain 
mean  of  detecting  the  latter. 

581.  Abnormal  dispersion. — A  remarkable  exception  to  the  ordinary 
law  of  dispersion  was  discovered  by  Christiansen,  and  subsequently  confirmed 
and  extended  by  Soret  and  Kundt,  that  the  solutions  of  certain  substances, 


-5  8  2]  Fluorescence.  505 

such  as  indigo  and  permanganate  of  potassium,  give  spectra  in  which  the 
order  of  the  colours  is  not  the  same  as  in  the  prismatic  spectrum.  Thus  when 
a  hollow  glass  prism  is  filled  with  an  alcoholic  solution  of  fuchsine,  the  order 
of  the  colours  in  the  spectrum  which  it  yields  is  as  follows.  Violet  is  least 
refracted,  then  red,  and  then  yellow,  which  is  most  refracted.  It  we  imagine 
that  the  central  green  of  an  ordinary  spectrum  is  removed,  and  then  the 
position  of  the  rest  is  interchanged,  we  get  an  idea  of  the  abnormal  spectrum 
of  fuchsine.  Kundt  examined  a  great  number  of  substances  in  this  direc- 
tion, mostly  the  colours  derived  from  aniline,  and  found  that  the  abnormal 
dispersion  is  exhibited  by  all  substances  with  surface  colour.  These  bodies 
have  the  peculiarity  that  when  viewed  in  diffused  light  they  exhibit  a 
different  colour  to  that  which  they  transmit.  Thus  a  thin  flake  of  fuchsine 
appears  green  in  diffused,  but  red  in  transmitted  light. 

The  substances  in  solution  are  examined  by  placing  them  in  hollow  glass 
prisms  ;  if  the  solutions  are  weak,  the  abnormal  dispersion  of  the  substance 
is  concealed  by  that  of  the  solvent,  while  stronger  solutions  absorb  so  much 
light  as  to  be  almost  opaque,  and  prisms  of  very  small  refracting  angle  have 
to  be  used.  Soret  gets  rid  of  this  difficulty  by  immersing  the  prism  contain- 
ing the  solution  in  glass  vessels  with  parallel  sides  filled  with  the  solvent. 
The  dispersion  due  to  the  solvent  is  thereby  eliminated,  and  only  that  of  the 
substance  comes  into  play.  Cyanine  gives  a  well-marked,  abnormal  spec- 
trum, the  order  of  the  colours  being  the  following :  green,  light  blue,  dark 
blue,  a  dark  space,  red  and  traces  of  orange,  the  green  being  the  colour  which 
is  least  diffused. 

The  same  explanation  cannot  be  given  of  this  as  of  the  ordinary  colour 
of  bodies  (569),  but  must  be  ascribed  to  the  fact  that  the  bodies  in  question 
totally  reflect  light  of  certain  wave  lengths  (637)  at  almost  all  incidences, 
and  that  these  colours  are  reflected  on  the  surface.  Hence  it  follows  that 
the  colour  of  these  bodies  in  diffused  light,  must  be  almost  complementary 
to  the  transmitted  light — a  prevision  which  experiment  confirms. 

582.  Fluorescence. — Stokes  made  the  remarkable  discovery  that  under 
certain  circumstances  the  rays  of  light  are  capable  of  undergoing  a  change 
of  refrangibility.  The  discovery  originated  in  the  study  of  a  phenomenon 
observed  by  Sir  J.  Herschel,  that  certain  solutions  when  looked  at  by  trans- 
mitted light  appear  colourless,  but  when  viewed  in  reflected  light  present  a 
bluish  appearance.  Stokes  has  found  that  this  property,  which  he  calls 
fluorescence,  is  characteristic  of  a  large  class  of  bodies. 

The  phenomenon  is  best  seen  when  a  solution  of  sulphate  of  quinine, 
contained  in  a  trough  with  parallel  sides,  is  placed  in  different  positions  in 
the  solar  spectrum.  No  change  is  observed  in  the  upper  part  of  the  spec- 
trum, but  from  about  the  middle  of  the  lines  G  and  H  (coloured  Plate)  to 
some  distance  beyond  the  extreme  range  of  the  violet,  rays  of  a  beautiful 
sky-blue  colour  are  seen  to  proceed.  These  invisible  ultra-violet  rays  also 
become  visible  when  the  spectrum  is  allowed  to  fall  on  paper  impregnated 
with  a  solution  of  asculine  (a  substance  extracted  from  horse-chestnut),  an 
alcoholic  solution  of  stramonium,  or  a  plate  of  canary  glass  (which  is  coloured 
by  means  of  uranium).  This  change  arises  from  a  diminution  in  the  re- 
frangibility of  those  rays  outside  the  violet,  which  are  ordinarily  too  refran- 
gible to  affect  the  eye. 


506  On  Light.  [582- 

Glass  appears  to  absorb  many  of  these  more  refrangible  rays,  which  is 
not  the  case  nearly  to  the  same  extent  with  quartz.  When  a  prism  and 
trough  formed  of  plates  of  quartz  are  used,  and  the  spectrum  is  received 
on  a  sheet  of  paper  on  which  a  wash  of  solution  of  sulphate  of  quinine  has 
been  made,  two  juxtaposed  spectra  can  be  obtained.  That  which  is  on  the 
part  coated  with  sulphate  of  quinine  extends  beyond  the  line  H  to  an  extent 
equal  to  that  of  the  visible  spectrum.  In  the  spectrum,  thus  made  visible, 
dark  lines  may  be  seen  like  those  in  the  ordinary  spectrum. 

The  phenomena  may  be  observed  without  the  use  of  a  prism.  When  an 
aperture  in  a  dark  room  is  closed  by  means  of  a  piece  of  blue  glass,  and  the 
light  is  allowed  to  fall  upon  a  piece  of  canary  glass,  it  instantly  appears  self- 
luminous  from  the  emission  of  the  altered  rays.  If  a  test  tube  be  half  filled 
with  a  solution  of  sulphate  of  quinine  and  on  it  be  poured  an  ethereal  solu- 
tion of  chlorophylle,  the  respective  layers  appear  colourless,  and  green  in 
transmitted,  and  sky-blue  and  blood-red  in  reflected  light. 

In  most  cases  it  is  the  violet  and  ultra-violet  rays  which  undergo  an 
alteration  of  refrangibility,  but  the  phenomenon  is  not  confined  to  them.  A 
decoction  of  madder  in  alum  gives  yellow  and  violet  light  from  about  the 
line  D  to  beyond  the  violet ;  an  alcoholic  solution  of  chlorophylle  gives  red 
light  from  the  line  B  to  the  limit  of  the  spectrum.  In  these  cases  the  yellow, 
the  green,  and  the  blue  rays  experience  diminution  of  refrangibility ;  the 
change  produces  more  highly  refrangible  rays.  An  exception  to  this  rule 
is  met  with  in  the  case  of  Magdala  red.  If  on  a  solution  of  this  substance 
contained  in  a  rectangular  glass  vessel  a  solar  spectrum  be  allowed  to  fall, 
an  orange  yellow  fluorescence  is  found  even  in  the  red  part  of  the  spectrum. 
The  electric  light  gives  a  very  remarkable  spectrum.  With  quartz  ap- 
paratus Stokes  obtained  a  spectrum  six  or  eight  times  as  long  as  the  ordinary 
one.  Several  flames  of  no  great  illuminating  power  emit  very  peculiar 
light.  Characters  traced  on  paper  with  solution  of  stramonium,  which  are 
almost  invisible  in  daylight,  appear  instantaneously  when  illuminated  by  the 
flame  of  burning  sulphur  or  of  bisulphide  of  carbon.  Robinson  has  found 
that  the  light  of  the  aurora  is  peculiarly  rich  in  rays  of  high  refrangibility. 

583.  Chromatic  aberration. — The  various  lenses  hitherto  described 
(5 51)  possess  the  inconvenience  that,  when  at  a  certain  distance  from  the 

eye,  they  give  images  with  co- 
loured edges.  This  defect, 
which  is  most  observable  in 
condensing  lenses,  is  due  to  the 
unequal  refrangibility  of  the 
simple  colours  (564),  and  is 
called  chromatic  aberration. 

For,  as  a  lens  may  be  com- 
Fig  4?9  pared    to   a    series   of    prisms 

with  infinitely  small  faces,  and 

united  at  their  bases,  it  not  only  refracts  light,  but  also  decomposes  it  like 
a  prism.  On  account  of  this  dispersion,  therefore,  lenses  have  really  a 
distinct  focus  for  each  colour.  In  condensing  lenses,  for  example,  the  red 
rays,  which  are  the  least  refrangible,  form  their  focus  at  a  point,  R,  on  the 
axis  of  the  lens  (fig.  479) ;  while  the  violet  rays,  which  are  most  refrangible, 


-584] 


Achromatism. 


507 


coincide  in  the  nearer  point,  V.  The  foci  of  the  orange,  yellow,  green,  blue, 
and  indigo  are  between  these  points.  The  chromatic  aberration  is  more 
perceptible  in  proportion  as  the  lenses  are  more  convex,  and  as  the  point 
at  which  the  rays  are  incident  is  farther  from  the  axis  ;  for  then  the  de- 
viation, and  therefore  the  dispersion,  are  increased. 

If  a  pencil  of  rays  which  has  passed  through  a  condensing  lens  be 
received  on  a  screen  placed  at  mm  within  the  focal  distance,  a  bright  spot  is 
seen  with  a  red  border ;  if  it  is  placed  at  ss,  the  bright  spot  has  a  violet 
border. 

The  inequality  in  the  refraction  of  the  blue  and  red  rays  may  be  demon- 
strated by  closing  a  small  aperture,  half  with  red  and  half  with  blue  glass 
(fig.  480) ;  on  each  half  a  black  arrow  is  painted,  and  a  lamp  is  placed 
behind  it.  By  means  of  a  lens  of  60  cm.  focus  an  image  is  formed  on  a 
screen  at  a  distance  of  about  2  .metres.  If,  the  screen  be 
placed  so  that  a  sharp  image  is  obtained  of  the  black  object 
on  the  blue  ground,  the  outlines  of  the  other  are  confused. 
To  get  a  sharp  image  of  the  arrow  on  the  red  ground 
the  screen  must  be  moved  farther  away. 

584.  Achromatism.  —  By  combining  prisms  which 
have  different  refracting  angles  (544),  and  are  formed  of 
substances  of  unequal  dispersive  powers  (564),  white  light  F»&-  480 

may  be  refracted  without  being  dispersed.  The  same  result  is  obtained  by 
combining  lenses  of  different  substances,  the  curvatures  of  which  are 
suitably  combined.  The  images  of  objects  viewed  through  such  lenses  do 
not  appear  coloured,  and  they  are  accordingly  called  achromatic  lenses  ; 
achromatism  being  the  term  applied  to  the  phenomenon  of  the  refraction 
of  light  without  decomposition. 

By  observing  the  phenomenon  of  the  dispersion  of  colours  in  prisms  of 
water,  of  oil  of  turpentine,  and  of  crown  glass,  Newton  was  led  to  suppose 
that  dispersion  was  proportional  to  refraction.     He  concluded  that  there 
could  be  no  refraction  without  dispersion,  and, 
therefore,   that    achromatism   was    impossible. 
Almost  half  a  century  elapsed  before  this  was 
found  to  be  incorrect.     Hall,  an  English  philo- 
sopher, in  1733,  was  the  first  to  construct  achro- 
matic lenses,  but  he  did  not  publish  his   dis- 
covery.   It  is  to  Dollond,  an  optician  in  London, 
that  we  owe  the  greatest  improvement  which 
has  been   made  in    optical    instruments.      He 
showed  in  1757  that  by  combining  two  lenses — 
one  a  double  convex   crown   glass  lens,  the  other  a  concavo-convex   lens 
of  flint  glass  (fig.  482) — a  lens  is  obtained  which  is  virtually  achromatic. 

To  explain  this  result,  let  two  prisms  BFC  and  CDF,  be  joined  and 
turned  in  a  contrary  direction,  as  shown  in  fig.  481.  Let  us  suppose,  in  the 
first  case,  that  both  prisms  are  of  the  same  material,  but  that  the  refracting 
angle  of  the  second,  CDF,  is  less  than  the  refracting  angle  of  the  first; 
the  two  prisms  will  produce  the  same  effect  as  a  single  prism,  BAF  ;  that  is 
to  say,  that  white  light  which  traverses  it  will  not  only  be  refracted,  but  also 
decomposed.  If,  on  the  contrary,  the  first  prism  BCF  were  of  crown 

z  2 


Fig  481. 


508  On  Light.  [584- 

glass,  and  the  other  CFD  of  flint  glass,  the  dispersion  might  be  destroyed 
without  destroying  the  refraction.  For  as  flint  glass  is  more  dispersive  than 
crown,  and  as  the  dispersion  produced  by  a  prism  diminishes  with  its  re- 
fracting angle  (564),  it  follows  that  by  suitably  lessening  the  refracting 
angle  of  the  flint  glass  prism  CFD,  as  compared  with  the  refracting  angle 
of  the  crown  glass  prism  BCF,  the  dispersive  power  of  these  prisms  may 
be  equalised ;  and  as,  from  their  position,  the  dispersion  takes  place  in  a 
contrary  direction,  it  is  neutralised  ;  that  is,  the  emergent  rays  EO  are 
parallel,  and  therefore  give  white  light.  Nevertheless,  the  ratio  of  the  angles 
BCF  and  CFD,  which  is  suitable  for  the  parallelism  of  the  red  rays  and 
violet  rays,  is  not  so  for  the  intermediate  rays,  and,  consequently,  only  two 
of  the  rays  of  the  spectrum  can  be  exactly  combined,  and  the  achromatism 
is  not  quite  perfect.  To  obtain  perfect  achromatism,  several  prisms  would 
be  necessary,  of  unequally  dispersive  materials,  and  the  angles  of  which  were 
suitably  combined. 

The  refraction  is  not  destroyed  at  the  same  time  as  the  dispersion  ;  that 
could  only  happen  if  the  refracting  power  of  a  body  varied  in  the  same  ratio 
as  its  dispersive  power,  which  is  not  the  case.     Consequently, 
the  emergent  ray  EO  is  not  exactly  parallel  to  the  incident  ray, 
and  there  is  a  refraction  without  appreciable  decomposition. 

Achromatic  lenses  are  made  of  two  lenses  of  unequal  dis- 
persive materials  ;  one,  A,  of  flint  glass,  is  a  diverging  concavo- 
convex  (fig.  482) ;  the  other,  B,  of  crown  glass,  is  double  convex, 
and  one  of  its  faces  may  exactly  coincide  with  the  concave  face 
of  the  first.     As  with  prisms,  several  lenses  would  be  necessary 
Fig.  482.      to  obtain  perfect  achromatism  ;  but  for  optical  instruments  two 
are  sufficient,  their  curvatures  being  such  as  to  combine  not  the 
extreme  red  and  violet,  but  the  blue  and  orange  rays,  while  at  the  same  time 
regard  is  had  to  the  correction  for  spherical  aberration. 


-586]  The  Simple  Microscope.  509 


CHAPTER  V. 

OPTICAL  INSTRUMENTS. 

585.  Tbe  different  kinds  of  optical  instruments. — By  the  term  optical 
instrument  is  meant  any  combination  of  lenses,  or  of  lenses  and  mirrors. 
Optical  instruments  may  be  divided   into  three  classes,  according  to  the 
ends  they  are  intended  to  answer,  viz.  : — i.  Microscopes,  which  are  designed 
to  obtain  a  magnified  image  of  any  object  whose  real  dimensions  are  too 
small  to  admit  of  its  being  seen  distinctly  by  the  naked  eye.     ii.   Telescopes, 
by   which   very   distant   objects,   whether  celestial  or  terrestrial,   may   be 
observed,     iii.  Instruments  designed  to  project  on  a  screen  a  magnified  or 
diminished  image  of  any  object  which  can  thereby  be  either  depicted  or 
rendered  visible  to  a   crowd  of  spectators ;    such   as   the  camera  lucida, 
the  camera  obscura,  photographic  apparatus,  the  magic  lantern,  the  solar 
microscope,  the  photo-electric  microscope,  &c.     The  two  former  classes  yield 
virtual  images  ;  the  last,  with  the  exception  of  the  camera  lucida,  yield  real 
images. 

MICROSCOPES. 

586.  Tbe  simple  microscope. — The  simple  microscope,  or  magnifying 
glass,  is  merely  a  convex  lens  of  short  focal  length,  by  means  of  which  we 
look  at  objects  placed  between  the  lens  and  its  principal  focus.     Let  AB 
(fig.  483)  be  the  object  to  be  observed,  placed   between  the  lens  and  its 
principal     focus,     F. 

Draw  the  secondary 
axes  AO  and  BO,  and 
also  from  A  and  B 
rays  parallel  to  th« 
axis  of  the  lens  FO. 
Now  these  rays,  on 
passing  out  of  the 
lens,  tend  to  pass 
through  the  second 
principal  focus  F'  ; 
consequently  they  are 
divergent  with  refe-  Fis-  483- 

rence  to  the  second- 
ary axes,  and  therefore,  when  produced,  will  cut   those  axes  in  A'  and  B 
respectively.     These  points  are  the  virtual  foci  of  A  and    B  respectively. 
The  lens  therefore  produces  at  A'B'  an  erect  and  magnified  virtual  image  of 
the  object  AB. 

The  position  and  magnitude  of  this  image  depend  on  the  distance  of  the 


5io 


On  Light. 


object  from  the  focus.  Thus,  if  AB  is  moved  to  ab  nearer  the  lens,  the 
secondary  axes  will  contain  a  greater  angle,  and  the  image  will  be  formed  at 
a'b',  and  will  be  much  smaller,  and  nearer  the  eye.  On  the  other  hand,  if 
the  object  is  moved  farther  from  the  lens,  the  angle  between  the  secondary 
axes  is  diminished,  and  their  intersection  with  the  prolongation  of  the  re- 
fracted rays  taking  place  beyond  A'B',  the  image  is  formed  farther  from  the 
lens,  and  is  larger. 

In  a  simple  microscope  both  chromatic  aberration  and  spherical  aberra- 
tion increase  with  the  degree  of  magnification.     We  have  already  seen  that 

the  former  can  be  corrected 
by  using  achromatic  lenses 
(584),  and  the  latter  by  using 
stops,  which  allow  the  pas- 
sage of  such  rays  only  as 
Fig.  484.  are  nearly  parallel  to  the 

axis,  the  spherical  aberration 

of  these  rays  being  nearly  inappreciable.  Spherical  aberration  may  be  still 
further  corrected  by  using  two  plano-convex  lenses,  instead  of  one  very 
convergent  lens.  When  this  is  done,  the  plane  face  of  each  lens  is  turned 
towards  the  object  (fig.  484).  Although  each  lens  is  less  convex  than  the 
simple  lens  which  together  they  replace,  yet  their  joint  magnifying  power  is 
as  great,  and  with  a  less  amount  of  spherical  aberration,  since  the  first  lens 

draws  towards  the  axis  the  rays  which 
fall  on  the  second  lens.  This  combination 
of  lenses  is  known  as  Wollastoris  doublet. 
There  are  many  forms  of  the  simple 
microscope.  One  of  the  best  is  that  re- 
presented in  fig.  485.  On  a  horizontal 
support,  E,  which  can  be  raised  and 
lowered  by  a  rack  K  and  pinion  D,  there 
is  a  black  eyepiece,  m,  in  the  centre  of 
which  is  fitted  a  small  convex  lens.  Below 
this  is  the  stage  b,  which  is  fixed,  and  on 
which  the  object  is  placed  between  glass 
plates.  In  order  to  illuminate  the  object 
powerfully,  diffused  light  is  reflected  from 
a  concave  glass  mirror,  M,  so  that  the 
reflected  rays  fall  upon  the  object.  In 
using  this  microscope  the  eye  is  placed 
very  near  the  lens,  which  is  lowered  or 

raised  until  the  position  is  found  at  which  the  object  appears  in  its  greatest 
distinctness. 

587.  Conditions  of  distinctness  of  the  images. — In  order  that  objects 
looked  at  through  a  microscope  should  be  seen  with  distinctness,  they  must 
•have -a  strong  light  thrown  upon  them,  but  this  is  by  no  means  enough.  It 
is  necessary  that  the  image  be  formed  at  a  determinate  distance  from  the 

eye.  :  In  fact,  there  is  for  each  person  a  distance  of  most  distinct  vision a 

distance,  that  is  to  say,  at  which  an  object  must  be  placed  from  an  observer's 
.eye,  in  order  to  be  seen  with  greatest  distinctness.  This  distance  is  different 


Fig.  485. 


-588] 


Apparent  Magnitude  of  an  Object. 


5  L 


for  different  observers,  but  ordinarily  is  between  10  and  12  inches.  It  is, 
therefore,  at  this  distance  from  the  eye  that  the  image  ought  to  be  formed. 
Moreover,  this  is  why  each  observer  has  to  focus  the  instrument ;  that  is,  te 
adapt  the  microscope  to  his  own  distance  of  most  distinct  vision.  This  is 
effected  by  slightly  varying  the  distance  from  the  lens  to  the  object,  for  we 
have  seen  above  that  a  slight  displacement  of  the  object  causes  a  great  dis- 
placement of  the  image.  With  a  common  magnifying  glass,  such  as  is  held 
in  the  hand,  the  adjustment  is  effected  by  merely  moving  it  nearer  to  or 
farther  from  the  object.  In  the  microscope  the  adjustment  is  effected  by 
means  of  a  rack  and  pinion,  which  in  the  case  of  the  instrument  shown  in 
fig.  485  moves  the  instrument,  but  moves  the  object  in  the  case  of  the 
instrument  depicted  in  fig.  489.  What  has  been  said  about  focussing  the 
microscope  applies  equally  to  telescopes.  In  the  latter  instrument  the  eye- 
piece is  generally  adjusted  with  respect  to  the  image  formed  in  the  focus  of 
the  object-glass. 

In  respect  of  the  distinctness  of  the  image  the  general  rules  for  convex 
lenses  apply. 

In  order  to  lessen  the  dispersion  lenses  have  been  constructed  of  diamond, 
of  ruby,  and  of  other  precious  stones,  which  for  a  small  amount  of  dispersion 
have  a  great  degree  of  refrangibility.  Drops  of  water  or  of  Canada  Balsam 
in  minute  apertures  in  a  thin  piece  of  wood  or  of  metal  act  as  microscopes. 

588.  Apparent  magnitude  of  an  object. — The  apparent  magnitude  or 
apparent  diameter  of  a  body,  is  the  angle  it  subtends  at  the  eye  of  the 


Fig.  487. 


observer.  Thus,  if  AB  is  the  object,  and  O  the  observer's  eye  (figs.  486,  487), 
the  apparent  magnitude  of  the  object  is  the  angle  AOB  contained  by  two 
visual  rays  drawn  from  the  centre  of  the  pupil  to  the  extremities  of  the 
object. 

In  the  case  of  objects  seen  through  optical  instruments,  the  angles 
which  they  subtend  are  so  small  that  the  arcs  which  measure  the  angles  do 
not  differ  sensibly  from  their  tangents.  The  ratio  of  two  such  angles  is 
therefore  the  same  as  that  of  their  tangents.  Hence  we  deduce  the  two 
following  principles  : — 


512  On  Light.  [588- 

I.  When  the  same  object  is  seen  at  unequal  distances,  the  apparent  diameter 
varies  inversely  as  the  distance  from  the  observer's  eye. 

II.  In  the  case  of  two  objects  seen  at  the  same  distance,  the  ratio  of  the 
apparent  diameters  is  the  same  as  that  of  their  absolute  magnitudes. 

These  principles  may  be  proved  as  follows  :—  i.  in  fig.  486,  let  AB  be  the 
object  in  its  first  position,  and  ab  the  same  object  in  its  second  position. 
For  the  sake  of  distinctness  these  are  represented  in  such  positions  that  the 
line  OC  passes  at  right  angles  through  their  middle  points  C  and  c  respec- 
tively. It  is,  however,  sufficient  that  ab  and  AB  should  be  the  bases  of 
isosceles  triangles  having  a  common  vertex  at  O.  Now  by  what  has  been 
said  above,  AB  is  virtually  an  arc  of  a  circle  described  with  centre  O  and 
radius  OC  ;  likewise  ab  is  virtually  an  arc  of  a  circle  whose  centre  is  O  and 
radius  Qc.  Therefore, 

A-§:-f*-JL:  JL. 
OC     Oc    OC     Qc 

Therefore,  AOB  varies  inversely  as  OC. 

ii.  Let  AB  and  A/B/  be  two  objects  placed  at  the  same  perpendicular 
distance,  OC,  from  the  eye,  O,  of  the  observer  (fig.  487).  Then  they  are 
virtually  arcs  of  a  circle  whose  centre  is  O  and  radius  OC.  Therefore, 

AOB  :  A'OB'-        :  ~-AB  :  A'B, 


a  proportion  which  expresses  the  second  principle. 

589.  Measure  of  magnification.  —  In  the  simple  microscope  the  mea- 

sure of  the  magnification  produced,  is  the  ratio  of  the  apparent  diameter  of 

the  image  to  that  of 
the  object,  both  being 
at  the  distance  of  most 
distinct  vision.  The 
same  rule  holds  good 
for  other  microscopes. 
It  is,  however,  import- 
ant to  obtain  an  ex- 
pression for  the  mag- 
nification depending 
on  data  that  are  of 
easier  determination. 

In  fig.  488  let  AB  be 
F»e-  488.  the  object,  and  A'B'  its 

image   formed   at   the 

distance  of  most  distinct  vision.     Let  a'b'  be  the  projection  of  AB  on  A/B/. 

Then,   since   the   eye   is   very    near  the   glass,   the   magnification   equals 

^25',  or  ^?-';  that  is,  ^?'.     But  since  the   triangles  A'OB'  and  AOB 
a'  Ob'  a'b  AB 

are  similar,  A'B'  :  AB  =  DO  :  CO.  Now  DO  is  the  distance  of  most  distinct 
vision,  and  CO  is  very  nearly  equal  to  FO,  the  focal  length  of  the  lens. 
Therefore,  the  magnification  equals  the  ratio  of  the  distance  of  most  distinct 
vision  to  the  focal  length  of  the  lens.  Hence  we  conclude  that  the  magni- 
fication is  greater  :  ist,  as  the  focal  length  of  the  lens  is  smaller,  in  other 


-591]  Principle  of  the  Compound  Microscope.  513 

words,  as  the  lens  is  more  convergent ;  2ndly,  as  the  observer's  distance  of 
most  distinct  vision  is  greater. 

A  simpler  and  more  general  definition  of  the  measure  of  magnification 
may  be  stated  thus  : — Let  a  be  the  angular  magnitude  of  the  object  as  seen 
by  "the  naked  eye,  0  the  angular  magnitude  of  the  image,  whether  real  or 
virtual,  actually  present  to  the  eye,  then  the  magnification  is  $+a.  This 
rule  applies  to  telescopes. 

By  changing  the  lens  the  magnification  can  be  increased,  but  only 
within  certain  limits  if  we  wish  to  obtain  a  distinct  image.  By  means  of 
a  simple  microscope  distinct  magnification  may  be  obtained  up  to  120 
diameters. 

The  magnification  we  have  here  considered  is  linear  magnification. 
Superficial  magnification  equals  the  square  of  the  linear  magnification  :  for 
instance,  the  former  will  be  1,600  when  the  latter  is  40. 

590.  Principle  of  the  compound  microscope. — The  compound  micro- 
scope in  its  simplest  form  consists  of  two  condensing  lenses  :  one,  with  a 
short  focus,  is  called  the  object-glass  or  objective,  because  it  is  turned  towards 
the  object  ;  the  other  is  less  condensing,  and  is  called  the  eyepiece  or  power, 
because  it  is  close  to  the  observers  eye. 

Fig.  489  represents  the  path  of  the  luminous  rays,  and  the  formation  of 
the  image  in  the  simplest  form  of  a  compound  microscope.  An  object  AB, 
being  placed  very 
near  the  principal 
focus  of  the  object- 
glass,  M,  but  a  little 
farther  from  the  glass, 
a  real  image,  ab,  in- 
verted and  somewhat 
magnified,  is  formed  Fig.  489. 

on  the  other  side  of 

the  object-glass  (556).  Now  the  distance  of  the  two  lenses,  M  and  N,  is 
such  that  the  position  of  the  image,  ab,  is  between  the  eyepiece,  N,  and  its 
focus,  F.  From  this  it  follows  that  for  the  eye  at  E,  looking  at  the  image 
through  the  eyepiece,  this  glass  produces  the  same  effect  as  a  simple  micro- 
scope, and  instead  of  this  image,  ab,  another  image,  a'b',  is  seen,  which  is 
virtual,  and  still  more  magnified.  This  second  image,  although  erect  as 
regards  the  first,  is  inverted  in  reference  to  the  object.  It  may  thus  be 
said,  that  the  compound  microscope  is  in  effect  a  simple  microscope  ap- 
plied not  to  the  object,  but  to  its  image  already  magnified  by  the  first 
lens. 

591.  Compound  microscope. — The  principle  of  the  compound  micro- 
scope has  been  already  (590)  explained  ;  the  principal  accessories  to  the 
instrument  remain  to  be  described. 

Fig.  490  represents  a  perspective  view,  and  fig.  491  a  section  of  a  com- 
pound microscope.  The  body  of  the  microscope  consists  of  a  series  of  brass 
tubes,  DD',  H,  and  I  ;  in  the  former  of  these  is  fitted  the  eyepiece  O,  and  in 
the  lower  part  of  the  latter  the  object-glass  o.  The  tube  I  moves  with  gentle 
friction  in  the  tube  DD',  which  in  turn  can  also  be  moved  in  a  larger  tube 
fixed  in  the  ring  E.  This  latter  is  fixed  to  a  piece  BB',  which  by  means  of  a 

23 


5*4 


On  Light. 


[591- 


very  fine  screw,  worked  by  the^milled  head  T,  can  be  moved  up  and  down 
an  inner  rod,  c,  not  represented  in  the  figure.  The  whole  body  of  the  micro- 
scope is  raised  and  lowered  with-  the  piece  BB',  so  that  it  can  be  placed 
near  or  far  from  the  object  to  be  examined.  Moreover,  the  rod  c,  and  all 
the  other  pieces  of  the  apparatus,  rest  on  a  horizontal  axis,  A,  with  which 
they  turn  under  so  much  friction  as  to  remain  fixed  in  any  position  in  which 
they  may  be  placed. 

The  objects  to  be  observed  are  placed  between  two  glass  plates,  V,  on 
a  stagey  R.     This  is  perforated  in  the  centre  so  that  light  can  be  reflected 

OK 


Fig.  491 


Fig.  490. 

upon  it  by  a  concave  reflecting  glass  mirror,  M.  The  mirror  is  mounted  on 
an  articulated  support,  so  that  it  can  be  placed  in  any  position  whatever, 
so  as  to  reflect  to  the  object  either  the  diffused  light  of  the  atmosphere, 
or  that  from  a  candle  or  lamp.  Between  the  reflector  and  the  stage  is  a 
diaphragm  or  stop,  K,  perforated  by  four  holes  of  different  sizes,  any  one 
of  which  can  be  placed  over  the  perforation  in  the  stage,  and  thus  the  light 
falling  on  the  object  maybe  regulated  ;  the  light  can,  moreover,  be  regulated 
by  raising,  by  a  lever  n,  the  diaphragm,  K,  which  is  moveable  in  a  slide. 


-591]  Compound  Microscope.  5 1 5 

Above  the  diaphragm  is  a  piece,  ;//,  to  which  can  be  attached  either  a  very 
small  stop,  so  that  only  very  little  light  can  reach  the  object,  or  a  condensing 
lens,  which  illuminates  it  strongly,  or  an  oblique  prism,  represented  at  X. 
The  rays  from  the  reflector  undergo  two  total  reflections  in  this  prism,  and 
emerge  by  a  lenticular  face  that  concentrates  them  on  the  object,  but  in  an 
oblique  direction,  which  in  some  microscopic  observations  is  an  advantage. 
Objects  are  generally  so  transparent  that  they  can  be  lighted  from  below  ; 
but  where,  owing  to  their  opacity,  this  is  not  possible,  they  are  lighted  from 
above  by  means  of  a  condensing  lens  mounted  on  a  jointed  support,  and  so 
placed  that  they  receive  the  diffused  light  of  the  atmosphere. 

Fig.  491  shows  the  arrangement  of  the  lenses  and  the  path  of  the  rays  in 
the  microscope.  At  o  is  the  object-glass,  consisting  of  three  small  con- 
densing lenses,  represented  on  a  larger  scale  at  L,  on  the  right  of  the  figure. 
The  effects  of  these  lenses  being  added  to  each  other  they  act  like  a  single 
very  powerful  condensing  lens.  The  object  being  placed  at  *',  a  very  little 
beyond  the  principal  focus  of  the  system,  the  emerging  rays  fall  upon  a 
fourth  condensing  lens,  «,  the  use  of  which  will  be  seen  presently  (592,  593). 
Having  become  more  convergent,  owing  to  their  passage  through  the  lens, 
//,  the  rays  form  at  aa'  a  real  and  amplified  image  of  the  object  /.  This 
image  is  between  a  fifth  condensing  lens,  O,  and  the  principal  focus  of  this 
lens.  Hence,  on  looking  through  this,  it  acts  as  a  magnifier  (556),  and  gives 
at  AA',  a  virtual  and  highly  magnified  image  of  aa',  and  therefore  of  the 
object.  The  two  glasses,  n  and  O,  constitute  the  eyepiece  in  the  same  man- 
ner as  the  three  glasses,  o,  constitute  the  object-glass. 

The  first  image,  aa',  must  not  merely  be  formed  between  the  glass,  O, 
and  its  principal  focus,  but  at  such  a  distance  from  this  glass  that  the  second 
image,  AA',  is  formed  at  the  observer's  distance  of  distinct  vision.  This 
result  is  obtained  in  moving,  by  the  hand,  the  body,  DH,  of  the  microscope 
in  the  larger  tube  fixed  to  the  ring,  E,  until  a  tolerably  distinct  image  is 
obtained  ;  then  turning  the  milled  head,  T,  in  one  direction  or  the  other, 
the  piece,  BB',  and  with  it  the  whole  microscope,  are  moved  until  the  image 
AA'  attains  its  greatest  distinctness,  which  is  the  case  when  the  image  aa' 
is  formed  at  the  distance  of  distinct  vision  :  a  distance  which  can  always  be 
ultimately  obtained,  for  as  the  object-glass  approaches  or  recedes  from  the 
object,  the  image  aa'  recedes  from  or  approaches  the  eyepiece,  and  at  the 
same  time  the  image  AA'. 

This  operation  is  called  the  focussing.  In  the  microscope,  where  the 
distance  from  the  object-glass  to  the  eyepiece  is  constant,  it  is  effected  by 
altering  their  distance  from  the  object.  In  telescopes,  where  the  objects 
are  inaccessible,  the  object  is  effected  by  varying  the  distance  of  the  eye- 
piece and  the  object-glass. 

The  microscope  possesses  numerous  eyepieces  and  object-glasses,  by 
means  of  which  a  great  variety  of  magnifying  power  is  obtained.  A  small 
magnifying  power  is  also  obtained  by  removing  one  or  two  of  the  lenses  of 
the  object-glass. 

The  above  contains  the  essential  features  of  the  microscope  ;  it  is  made 
in  a  great  variety  of  forms,  which  differ  mainly  in  the  construotion  of  the 
stand,  the  arrangement  of  the  lenses,  and  in  the  illumination.  For  descrip- 
tions of  these,  the  student  is  referred  to  special  works  on  the  Microscope. 


On  Light. 


[592 


502.  Achromatism  of  the  microscope.  Campani's  eyepiece. — When 
a  compound  microscope  consists  of  two  single  lenses,  as  in  fig.  490,  not  only 
is  the  spherical  aberration  uncorrected,  but  also  the  chromatic  aberration, 
the  latter  defect  causing  the  images  to  be  surrounded  by  fringes  of  the 
prismatic  colours,  these  fringes  being  larger  as  the  magnification  is  greater. 
It  is  with  a  view  to  correcting  these  aberrations  that  the  object-glass  (see 
fig.  491)  is  composed  of  three  achromatic  lenses,  and  the  eyepiece  of  two 
lenses,  n  and  #z,  for  the  first  of  these,  «,  would  be  enough  to  produce  colour 
unless  the  magnifying  power  were  low. 

The  effect  of  this  eyepiece  in  correcting  the  colour  may  be  explained  as 
follows  : — It  will  be  borne  in  mind  that  with  respect  to  red  rays  the  focal 
length  of  a  lens  is  greater  than  the  focal  length  of  the  same  lens  with 
reference  to  the  violet  rays. 

-D 

In  fact,  if  in  the  equation  (4)  (559),  we  write  R'  =  oo ,  we  obtain /= 


which  gives  the  focal  length  of  a  plano-convex  lens  whose  refractive  index 
is  n.  Now,  in  flint  glass,  and  for  the  red  ray,  n  —  i  equals  0*63,  and  for  the 
violet  ray  n  —  i  equals  0-67. 

Let  ab  be  the  object,  O  the  object-glass  which  is  corrected  for  colour. 
Consequently,  a  pencil  of  rays  falling  from  a  on  O  would  converge  to  the 


Fig.  492. 


focus,  A,  without  any  separation  of  colours  ;  but  falling  on  ^^.field-glass  C 
the  red  rays  would  converge  to  r,  the  violet  rays  to  v,  and  intermediate 
colours  to  intermediate  points.  In  like  manner  the  rays  from  £,  after 
passing  through  the  field-glass,  would  converge  to  r\  or  ?/,  and  intermediate 
points.  So  that  on  the  whole  there  would  be  formed  a  succession  of 
coloured  images  of  ab  ;  viz.  a  red  image  at  rr' ,  a  violet  image  at  vv',  and 
between  them  images  of  intermediate  colours.  Let  d  be  the  point  of  the 
object  which  is  situated  on  the  axis.  The  rays  from  d  will  converge  to  R, 
V,  and  intermediate  points.  Now  suppose  the  eye-glass  O'  to  be  placed  in 
such  a  manner  that  R  is  the  principal  focus  of  O'  for  the  red  rays,  then  V 
will  be  its  principal  focus  for  the  violet  rays.  Consequently,  the  red  rays, 
after  emerging  from  O  ,  will  be  parallel  to  the  axis,  and  so  will  the  violet 
rays  emerging  from  V,  and  so  of  any  other  colour.  Consequently,  the 
colours  of  d,  which  are  separated  by  C,  are  again  combined  by  O'.  The 
same  is  very  nearly  true  of  r  and  v,  and  of  r'  and  v'.  Hence  a  combination 
of  lenses  C  and  O'  corrects  the  chromatic  aberration  that  would  be  produced 
by  the  use  of  a  single  eye-glass.  Moreover,  by  drawing  the  rays  towards  the 
axis,  it  diminishes  the  spherical  aberration,  and,  as  we  shall  see  in  the  next 
article,  enlarges  the  field  of  view. 

In   all   eyepieces  consisting  of  two    lenses  the  lens  to  which  the  eye  is 
applied  is  called  the  eye-lens,  the  one  towards  the  object-glass  is  called  the 


-594] 


Magnifying  Power.     Micrometer. 


517 


field-lens.  The  eyepiece  above  described  was  invented  by  Huyghens,  who 
was  not,  however,  aware  of  its  property  of  achromatism.  He  designed  it  for 
use  with  the  telescope.  It  was  applied  to  the  microscope  by  Campani.  The 
relation  between  the  focal  lengths  of  the  lenses  is  as  follows  : — The  focal 
length  of  the  field-glass  is  three  times  that  of  the  eye-lens,  and  the  distance 
between  their  centres  is  half  the  sum  of  the  focal  length.  It  easily  follows 
from  this  that  the  image  of  the  point  d  would,  but  for  the  interposition  of  the 
field-lens,  be  formed  at  D,  which  is  so  situated  that  CD  is  three  times  DO', 
then  the  mean  of  the  coloured  images  would  be  formed  midway  between  C 
and  O'. 

593.  Field  of  view. — By  the  field  of  view  of  an  optical  instrument  is 
meant  all  those  points  which  are  visible  through  the  eyepiece.  The  advan- 
tage obtained  by  the  use  of  an  eyepiece  in  enlarging  the  field  of  view  will  be 
readily  understood  by  an  inspection  of  the  accompanying  figure.  As  before, 
O  is  the  object-glass,  C  the  field-lens,  O'the  eye-lens,  and  E  the  eye  placed 
on  the  axis  of  the  instrument.  Let  a  be  a  point  of  the  object ;  if  we  suppose 
the  field-lens  removed,  the  pencil  of  rays  from  a  would  be  brought  to  a 
focus  at  A,  and  none  of  them  would  fall  on  the  eye-lens  O',  nor  pass  into  the 


O' 


Fig.  493 


eye  E.  Consequently,  a  is  beyond  the  field  of  view.  But  when  the  field- 
glass  C  is  interposed,  the  pencil  of  rays  is  brought  to  a  focus  at  A',  and 
emerges  from  O'  into  the  eye.  Consequently,  a  is  now  within  the  field  of 
view.  It  is  in  this  manner  that  the  substitution  of  an  eyepiece  for  a  single 
eye-lens  enlarges  the  field  of  view. 

594.  Magrnifyinff  power.  Micrometer. — The  magnifying  power  of  any 
optical  instrument  is  the  ratio  of  the  magnitude  of  the  image  to  the  mag- 
nitude of  the  object.  The  magnifying  power  in  a 
compound  microscope  is  the  product  of  the  respec- 
tive magnifying  powers  of  the  object-glass  and  of 
the  eyepiece  ;  that  is,  if  the  first  of  these  magnifies 
20  times,  and  the  other  10,  the  total  magnifying 
power  is  200.  The  magnifying  power  depends  on 
the  greater  or  less  convexity  of  the  object-glass 
and  of  the  eyepiece,  as  well  as  on  the  distance  be- 
tween these  two  glasses,  together  with  the  distance 
of  the  object  from  the  object-glass.  A  magnifying 
power  of  1,500  and  even  upwards  has  been  ob- 
tained ;  but  the  image  then  loses  in  sharpness 
what  it  gains  in  extent.  To  obtain  precise  and 


Fig.  494. 


well-illuminated  images,  the  magnifying  power  ought  not  to  exceed  500  to 
600  diameters,  which  gives  a  superficial  enlargement  250,000  to  360,000 
times  that  of  the  object. 


5t8  On  Light.  [594- 

The  magnifying  power  is  determined  experimentally  by  means  of  the 
micrometer ;  this  is  a  small  glass  plate,  on  which,  by  means  of  a  diamond, 
a  series  of  lines  is  drawn  at  a  distance  from  each  other  of  i  or  T|^  of  a 
millimetre.  The  micrometer  is  placed  in  front  of  the  object-glass,  and 
.then  instead  of  viewing  directly  the  rays  emerging  from  the  eyepiece, 
O,  they  are  received  on  a  piece  of  glass,  A  (fig.  494),  inclined  at  an 
angle  of  45°,  and  the  eye  is  placed  above  so  as  to  see  the  image  of  the 
micrometer  lines,  which  is  formed  by  reflection  on  a  screen,  E,  on  which  is  a 
scale  divided  into  millimetres.  By  counting  the  number  of  divisions  of  this 
scale  corresponding  to  a  certain  number  of  lines  of  the  image,  the  magni- 
fying power  may  be  deduced.  Thus,  if  the  image  occupies  a  space  of  45 
millimetres  on  the  scale  and  contains  15  lines  of  the  micrometer,  the  distance 
between  each  of  which  shall  be  assumed  at  T^  millimetre,  the  absolute 
magnitude  of  the  object  will  be  ~  millimetre  ;  and  as  the  image  occupies  a 
space  of  45  millimetres,  the  magnification  will  be  the  quotient  of  45  by  ~,  or 
300.  The  eye  in  this  experiment  ought  to  be  at  such  a  distance  from  the 
screen,  E,  that  the  screen  is  distinctly  visible  :  this  distance  varies  with 
different  observers,  but  is  usually  10  to  12  inches.  The  magnifying  power 
of  the  microscope  can  also  be  determined  by  means  of  the  camera  lucida. 

When  once  the  magnifying  power  is  known,  the  absolute  magnitude  of 
objects  placed  before  the  microscope  is  easily  deduced.  For,  as  the  magni- 
fying power  is  the  quotient  of  the  size  of  the  image  by  the  size  of  the  object, 
it  follows  that  the  size  of  the  image  divided  by  the  magnifying  power  gives 
the  size  of  th,e  object ;  in  this  manner  the  diameters  of  all  microscopic 
objects  are  determined. 

TELESCOPES. 

595.  Astronomical  telescope. — The  astronomical  telescope  is  used  for 
observing  the  heavenly  bodies  ;  like  the  microscope,  it  consists  of  a  con- 
densing eyepiece  and  object-glass.     The  object-glass,  M  (fig.  495),  forms  be- 
tween  the  eyepiece,   N, 
and  its   principal  focus, 
an   inverted  image  of  the 
heavenly  body,  and  this 
eyepiece,  which  acts  as 
a  magnifying  glass,  then 
F;g.  495.  gives  a  virtual  and  highly 

magnified  image,  a'b\  of 

the  image  ab.  The  astronomical  telescope  appears,  therefore,  analogous  to 
the  microscope  ;  but  the  two  instruments  differ  in  this  respect ;  that  in  the 
microscope,  the  object  being  very  near  the  object-glass,  the  image  is  formed 
much  beyond  the  principal  focus,  and  is  greatly  magnified,  so  that  both  the 
object-glass  and  the  eyepiece  magnify  ;  while  in  the  astronomical  telescope, 
the  heavenly  body  being  at  a  great  distance,  the  incident  rays  are  parallel, 
and  the  image  formed  in  the  principal  focus  of  the  object-glass  is  much 
smaller  than  the  object.  There  is,  therefore,  no  magnification  except  by 
the  eyepiece,  and  this  ought,  therefore,  to  be  of  very  short  focal  length. 

Fig.  496  shows  an  astronomical  telescope  mounted  on  its  stand.  Above 
it  there  is  a  small  telescope  which  is  called  the  fender.  Telescopes  with 


-596]  Terrestrial  Telescope.  519 

a  large  magnifying  power  are  not  convenient  for  finding  a  star,  as  they  have 
but  a  small  field  of  view  :  the  position  of  the  star  is,  accordingly,  first 
sought  by  the  finder,  which  has  a  much  larger  field  of  view  ;  that  is,  takes  in 
a  far  greater  extent  of  the  heavens  :  it  is  then  viewed  by  means  of  the 
telescope. 


The  magnification  (589)   equals  (fig.  495)  ;  that  is,  it  equals 

a  (Jo  0OC, 

f  F* 
and  therefore  is  approximately  equal  to  —  -  -  ,  F  being  the  focus  of  the  object- 

glass,  M,  and  being  supposed  very  nearly  to  coincide  with  the  focus  of  the 


Fig.  496- 

eyepiece,  N  ;  it  may,  therefore,  be  concluded  that  the  magnifying  power  is 
greater  in  proportion  as  the  object-glass  is  less  convergent,  and  the  eyepiece 
more  so. 

When  the  telescope  is  used  to  make  an  accurate  observation  of  the  stars, 
for  example,  the  zenith  distance,  or  their  passage  over  the 
meridian,  a  cross  wire  is  added.  This  consists  of  two  very 
fine  metal  wires  or  spider  threads  stretched  across  a  circular 
aperture  in  a  small  metal  plate  (fig.  497).  The  wires  ought  to 
be  placed  in  the  position  where  the  inverted  image  is  pro- 
duced by  the  object-glass,  and  the  point  where  the  wires  cross 
ought  to  be  on  the  optical  axis  of  the  telescope,  which  thus 
becomes  the  line  of  sight  or  collimation. 

596.  Terrestrial  telescope. — The  terrestrial  telescope  differs  from  the 
astronomical  telescope  in  producing  images  in  their  right  positions.  This  is 
effected  by  means  of  two  condensing  glasses,  P  and  Q  (fig.  498),  placed 
between  the  object-glass,  M,  and  the  eyepiece,  R.  The  object  being  sup- 
posed to  be  at  AB,  at  a  greater  distance  than  can  be  shown  in  the  drawing, 


Fig.  497. 


520 


On  Light. 


[596- 


an  inverted  and  much  smaller  image  is  formed  at  ba  on  the  other  side  of  the 
object-glass.  But  the  second  lens,  P,  is  at  such  a  distance  that  its  principal 
focus  coincides  with  the  image  ab  ;  from  which  it  follows  that  the  luminous 
rays  which  pass  through  b,  for  example,  after  traversing  the  lens,  P,  take  a 
direction  parallel  to  the  secondary  axis,  bO  (552).  Similarly  the  rays  passing 
by  a  take  a  direction  parallel  to  the  axis  aO.  After  crossing  in  H,  these 
various  rays  traverse  a  third  lens  Q,  whose  principal  focus  coincides  with 
the  point  H.  The  pencil  B^H  converges  towards  b',  on  a  secondary  axis, 
O'£',  parallel  to  its  direction;  the  pencil  A^H  converging  in  the  same  manner 
at  a',  an  erect  image  of  the  object,  AB,  is  produced  at  a'b'.  This  image  is 
viewed,  as  in  the  astronomical  telescope,  through  a  condensing  eyepiece,  R, 
so  placed  that  it  acts  as  a  magnifying  glass  ;  that  is,  its  distance  from  the 
image,  a'b\  is  less  than  the  principal  focal  distance  ;  hence,  there  is  formed, 
at  a"b",  a  virtual  image  of  a'b',  erect,  and  much  magnified.  The  lenses  P 


Fig.  498. 

and  O,  which  only  serve  to  rectify  the  position  ol  the  image,  are  fixed  in  a 
brass  tube,  at  a  constant  distance,  which  is  equal  to  the  sum  of  their  principal 
focal  distances.  The  object-glass,  M,  moves  in  a  tube,  and  can  be  moved 
to  or  from  the  lens  P,  so  that  the  image,  ab,  is  always  formed  in  the  focus  of 
the  lens,  whatever  be  the  distance  of  the  object.  The  distance  of  the  lens, 
R,  may  also  be  varied,  so  that  the  image  a"b"  may  be  formed  at  the  dis- 
tance of  distinct  vision. 

This  instrument  may  also  be  used  as  an  astronomical  telescope  by  using 
a  different  eyepiece  ;  this  must  have  a  much  greater  magnifying  power  than 
in  the  former  case. 

In  the  terrestrial  telescope  the  magnifying  power  is  the  same  as  in  the 
astronomical  telescope,  provided  always  that  the  correcting  glasses,  P  and 
Q,  have  the  same  convexity. 

597.  Galileo's  telescope — Galileo's  Telescope  is  the  simplest  of  all 
telescopes,  for  it  only  consists  of  two  lenses  ;  namely,  an  object-glass,  M,  and 

a  diverging  or  double  con- 
cave eyepiece,  R  (fig.  499), 
and  it  gives  at  once  an  erect 
image.  Opera-glasses  are 
constructed  on  this  prin- 
ciple. 

Fig.  499.  If  the  object  be    repre- 

sented by  the  right  line  AB, 

a  real  but  inverted  and  smaller  image  would  be  formed  at  ba  ;  but  in 
traversing  the  eyepiece,  R,  the  rays  emitted  from  the  points  A  and  B  are 
refracted,  and  diverge  from  the  secondary  axe?  £O'  and  aO',  which  corre- 
spond to  the  points  b  and  a  of  the  image.  Hence,  these  rays  produced 


-599]  The  Gregorian  Telescope.  521 

backward  meet  their  axes  in  a '  and  b' ;  the  eye  which  receives  them  sees 
accordingly  an  erect  and  magnified  image  in  a'b',  which  appears  nearer 
because  it  is  seen  under  an  angle,  a'Q'b',  greater  than  the  angle,  AOB, 
under  which  the  object  is  seen. 

The  magnifying  power  is  equal  to  the  ratio  of  the  angle  a'Q'b'  to  the 
angle  AOB,  and  is  usually  from  2  to  4. 

The  distance  of  the  eyepiece  R  from  the  image  ab  is  pretty  nearly  equal 
to  the  principal  focal  distance  of  this  eyepiece  ;  it  follows,  therefore,  that  the 
distance  between  the  two  lenses  is  the  distance  between  their  respective 
focal  distances  ;  hence,  Galileo's  telescope  is  very  short  and  portable.  It 
has  the  advantage  of  showing  objects  in  their  right  position  ;  and,  further, 
as  it  has  only  two  lenses,  it  absorbs  very  little  light :  in  consequence,  how- 
ever, of  the  divergence  of  the  emergent  rays,  it  has  only  a  small  field  of  view, 
and  in  using  it  the  eye  must  be  placed  very  near  the  eyepiece.  The  eye- 
piece can  be  moved  to  or  from  the  object-glass,  so  that  the  image  a'  b'  is 
always  formed  at  the  distance  of  distinct  vision. 

The  opera-glass  is  usually  double,  so  as  to  produce  an  image  in  each  eye, 
by  which  greater  brightness  is  attained. 

The  time  at  which  telescopes  were  invented  is  not  known.  Some  at- 
tribute their  invention  to  Roger  Bacon  in  the  I3th  century7 ;  others  to 
J.  B.  Porta  at  the  end  of  the  i6th  ;  others,  again,  to  a  Dutchman,  Jacques 
Metius,  who,  in  1609,  accidentally  found  that  by  combining  two  glasses,  one 
concave  and  the  other  convex,  distant  objects  appeared  nearer  and  much 
larger. 

Galileo's  was  the  first  telescope  directed  towards  the  heavens.  By  its 
means  Galileo  discovered  the  mountains  of  the  moon,  Jupiter's  satellites,  and 
the  spots  on  the  sun. 

598.  Reflecting:  telescopes. — The  telescopes  previously  described  are 
refracting  or  diopttic  telescopes.     It  is,  however,  only  in  recent  times  that 
it  has  been  possible  to  construct  achromatic  lenses  of  large  size  ;  before  this, 
a  concave  metallic  mirror  was  used  instead  of  the  object-glass.     Telescopes 
of  this  kind  are  called  reflecting  or  catoptric  telescopes.     The  principal  forms 
are  those  devised  by  Gregory,  Newton,  Herschel,  and  Cassegrain. 

599.  The    Gregorian    telescope. — Figure    50x3    is   a   representation    of 
Gregory's  telescope  ;  it  is  mounted  on  a  stand,  about  which  it  is  moveable, 
and  can  be  inclined  at  any  angle.     This  mode  of  mounting  is  optional ;  it 
may  be  equatorially  mounted.     Fig.  501   gives  a  longitudinal  section.     It 
consists  of  a  long  brass  tube  closed  at  one  end  by  a  concave  metallic  mirror, 
M,  which  is  perforated  in  the  centre  by  a  round  aperture  through  which 
rays  reach  the  eye.     There  is  a  second  concave  metal  mirror,  N,  near  the 
end  of  the  tube  :  it  is  somewhat   larger  than  the  central  aperture  in   the 
large  mirror,  and  its  radius  of  curvature  is  much  smaller  than  that  of  the 
large  mirror.     The  axes  of  both  mirrors  coincide  with  the  axis  of  the  tube. 
As  the  centre  of  curvature  of  the  large  mirror  is  at  O,  and  its  focus  at  ab, 
rays,  such  as  SA,  emitted  from  a  heavenly  body,  are  reflected   from  the 
mirror,  M,  and  form  at  ab  an  inverted  and  very  small  image  of  the  heavenly 
body.     The  distance  of  the  mirrors  and  their  curvatures  is  so  arranged  that 
the  position  of  this  image  is  between  the  centre,  0,  and  the  focus,/  of  the  small 
mirror ;  hence  the  rays,  after  being  reflected  a  second  time  from  the  mirror 


522 


On  Light. 


[599- 


N,  form  at  a'b'  a  magnified  and  inverted  image  of  ab,  and  therefore  in  the 
true  position  of  the  heavenly  body.  This  image  is  viewed  through  an  eye- 
piece, P,  which  may  either  be 
simple  or  compound,  its  object 
being  to  magnify  it  again  so  that 
it  is  seen  at  a"b". 

As  the  objects  viewed  are  not 
always  at  the  same  distance,  the 
focus  of  the  large  mirror,  and  there- 
fore that  of  the  small  one,  vary  in 
position. 

And  as  the  distance  of  distinct 
vision  is  not  the  same  with  all  eyes, 
the  image  a"b"  ought  to  be  formed 
at  different  distances.  The  required 
adjustments  may  be  obtained  by 
bringing  the  small  mirror  nearer  to 
or  farther  from  the  larger  one  ;  this 
is  effected  by  means  of  a  milled 
head,  A  (fig.  500),  which  turns  a 
rod,  and  this  by  a  screw  moves  a 
piece  to  which  the  mirror  is  fixed. 

600.  The  Newtonian  tele- 
scope.— This  instrument  does  not 


Fig.  500. 


differ  much  from  that  of  Gregory  ;  the  large  mirror  is  not  perforated,  and 
there  is  a  small  plane  mirror  inclined  at  an  angle  of  45°  towards  an  eyepiece 
placed  in  the  side  of  the  telescope. 


Fig.  501. 

The  difficulty  of  constructing  metallic  mirrors  caused  telescopes  of 
Gregorian  and  Newtonian  construction  to  fall  into  disuse.  Of  late,  how- 
ever, the  process  of  silvering  glass  mirrors  has  been  carried  to  a  high  state 
of  perfection,  and  Foucault  applied  these  mirrors  to  Newtonian  telescopes 
with  great  success.  His  first  mirror  was  only  four  inches  in  diameter,  but 
he  has  successively  constructed  mirrors  of  8,  12,  and  13  inches,  and  at  the 
time  of  his  death  had  completed  one  of  32  inches  in  diameter. 

Fig.  503  represents  a  Newtonian  telescope  mounted  on  an  equatorial 
stand,  and  fig.  502  gives  a  horizontal  section  of  it.  This  section  shows  how 
the  luminous  rays  reflected  from  the  parabolic  mirror,  M,  meet  a  small 
rectangular  prism,  ;;*«,  which  replaces  the  inclined  plane  mirror  used  in  the 
old  form  of  Newtonian  telescope.  After  undergoing -a  total  reflection  from 


-600]  The  Newtonian  Telescope.  523 

mn,  the  rays  form  at  ab  a  very  small  image  of  the  heavenly  body.  This 
image  is  viewed  through  an  eyepiece  with  four  lenses  placed  on  the  side  of 
the  telescope,  and  magnifying  from  50  to  800  times,  according  to  the  size  of 
the  silvered  mirror. 

In  reflectors  the  mirror  acts  as  object-glass,  but  there  is,  of  course,  no 
chromatic  aberration.     The  spherical  aberration  is  corrected  by  the  form 


given  to  the  reflector,  which  is  paraboloid,  but  slightly  modified  by  trial  to 
suit  the  eyepiece  fitted  to  the  telescope. 

The  mirror  when  once  polished  is  immersed  in  a  silvering  liquid,  which 
consists  essentially  of  ammoniacal  solution  of  nitrate  of  silver,  to  which  some 
reducing  agent  is  added.  When  a  polished  glass  surface  is  immersed  in 
this  solution,  silver  is  deposited  on  the  surface  in  the  form  of  a  brilliant 
metallic  layer,  which  adheres  so  firmly  that  it  can  be  polished  with  rouge  in 
the  usual  manner.  These  new  telescopes  with  glass  mirrors  have  the  ad- 
vantage over  the  old  ones  that  they  give  purer  images,  they  weigh  less,  and 
are  much  shorter,  their  focal  distance  being  only  about  six  times  the  diameter 
of  the  mirror. 

These  details  known,  the  whole  apparatus  remains  to  be  described.'  The 
body  of  the  telescope  (fig.  503)  consists  of  an  octagonal  wooden  tube.  The 
end  G  is  open  ;  the  mirror  is  at  the  other  end.  At  a  certain  distance  from 
this  end,  two  axles  are  fixed,  which  rest  on  bearings  supported  by  two  wooden 
uprights  A  and  B.  These  are  themselves  fixed  to  a  table,  PQ,  which  turns 
on  a  fixed  plate,  RS,  placed  exactly  parallel  to  the  equator.  On  the  circum- 
ference of  the  turning  table  there  is  a  brass  circle  divided  into  360  degrees, 
and  beneath  it,  but  also  fixed  to  the  turning  table,  there  is  a  circular  toothed 
wheel,  in  which  an  endless  screw,  V,  works.  By  moving  this  in  either 
direction  by  means  of  the  handle  ;«,  the  table  PQ,  and  with  it  the  telescope, 
can  be  turned.  A  vernier,  x,  fixed  to  the  plate  RS,  gives  the  fractions  of  a 
degree.  On  the  axis  of  the  motion  of  the  telescope  there  is  a  graduated 
circle,  O,  which  serves  to  measure  the  declination  of  the  star— that  is,  its 
angular  distance  from  the  equator  ;  while  the  degrees  traced  round  the  table, 
RS,  serve  to  measure  the  right  ascension — that  is,  the  angle  which  the  de- 
clination circle  of  the  star  makes  with  the  declination  circle  passing  through 
the  first  point  of  Aries. 

In  order  to  fix  the  telescope  in  declination,  there  is  a  brass  plate,  E,  fixed 
to  the  upright  ;  it  is  provided  with  a  clamp,  in  which  the  limb  O  works,  and 
which  can  be  screwed  tight  by  means  of  a  screw  with  a  milled  head  r.  On 
the  side  of  the  apparatus  there  is  the  eyepiece,  o,  which  is  mounted  on  a 
sliding  copper  plate,  on  which  there  is  also  the  small  prism  mn,  represented 


524 


On  Light. 


[600- 


in  section  in  fig.  502.  To  bring  the  image  to  the  right  place,  this  plate  may 
be  moved  by  means  of  a  rack  and  a  milled  head  a.  The  handle,  #,  serves  to 
clamp  or  unclamp  the  screw,  V.  The  drawing  was  one  taken  from  a  tele- 
scope, the  mirror  of  which  is  only  6£  inches  in  diameter,  and  which  gives  a 
magnifying  power  of  1 50  to  2co. 


Fig.  503. 

601.  The  Herscbelian  telescope. — Sir  W.  Herschel's  telescope,  which 
until  recently  was  the  most  celebrated  instrument  of  modern  times,  was  con- 
structed on  a  method  differing  from  those  described.  The  mirror  was  so  in- 
clined that  the  image  of  the  star  was  formed  at  ab  on  the  side  of  the  telescope 
near  the  eyepiece,  o  ;  hence  it  is  termed  the  front  view  telescope.  As  the 
rays  in  this  telescope  only  undergo  a  single  reflection,  the  loss  of  light  is  less 


-602] 


Camera  Obscura. 


525 


than  in  either  of  the  preceding  cases,  and  the  image  is  therefore  brighter. 
The  magnifying  power  is  the  quotient  of  the  principal  focal  distance  of  the 
mirror  by  the  focal  distance  of  the  eyepiece. 

Herschel's  great  telescope  was  constructed  in  1789  ;  it  was  40  feet  in 
length,  the  great  mirror  was  50  inches  in  diameter.  The  quantity  of  light 
obtained  by  this  instru- 
ment was  so  great  as  to 
enable  its  inventor  to 
use  magnifying  powers 
far  higher  than  anything 
which  had  hitherto  been 
attempted. 

Herschel's  telescope 

has  been   exceeded   by  F,g.  504> 

one  constructed  by  the 

late  Earl  of  Rosse.  This  magnificent  instrument  has  a  focal  distance  of  53 
feet,  the  diameter  of  the  spectrum  being  six  feet.  It  is  at  present  used  as 
a  Newtonian  telescope,  but  it  can  also  be  arranged  as  a  front  view  tele- 
scope. 


INSTRUMENTS   FOR   FORMING   PICTURES   OF  OBJECTS. 

602.  Camera  obscura. — The  camera  obscura  (dark  chamber)  is,  as  its 
name  implies,  a  closed  space  impervious  to  light.  There  is,  however,  a  small 
aperture  by  which  luminous  rays  enter,  as  shown  in  fig.  505.  The  rays,  pro- 


ceeding from  external  objects,  and  entering  by  this  aperture,  form  on  the 
opposite  side  an  image  of  the  object  in  its  natural  colours,  but  of  reduced 
dimensions,  and  in  an  inverted  position. 


526 


On  Light. 


[602- 


Porta,  a  Neapolitan  physician,  the  inventor  of  this  instrument,  found  that 
by  fixing  a  double  convex  lens  in  the  aperture,  and  placing  a  white  screen  in 
the  focus,  the  image  was  much  brighter  and  more  definite. 

Fig.  505  represents  a  camera  obscura,  such  as  is  used  for  drawing.  It 
consists  of  a  rectangular  wooden  box,  formed  of  two  parts  which  slide  in  and 
out.  The  luminous  rays,  R,  pass  into  the  box  through  a  lens  B,  and  form  an 
image  on  the  opposite  side,  O,  which  is  at  the  focal  distance  of  the  lens. 
But  the  rays  are  reflected  from  a  glass  mirror,  M,  inclined  at  an  angle  of  45°, 
and  form  an  image  on  the  ground-glass  plate,  N.  When  a  piece  of  tracing 
paper  is  placed  on  this  screen,  a  drawing  of  the  image  is  easily  made.  A 
wooden  door,  A,  cuts  off  extraneous  light. 

The  box  is  formed  of  two  parts,  sliding  one  within  the  other,  like  the 
joints  of  a  telescope,  so  that,  by  elongating  it  more  or  less,  the  reflected 

image  may  be  made  to  fall  exactly 
on  the  screen,  N,  at  whatever  dis- 
tance the  object  may  be  situated. 

Fig.  506  shows  another  kind  of 
camera  obscura  which  is  occasionally 
erected  in  summer-houses.  In  a 
brass  case,  A,  there  is  a  triangular 
prism,  P  (fig.  507),  which  acts  both 
as  condensing  lens  and  as  mirror. 
One  of  its  faces  is  plane,  but  the 
others  have  such  curvatures  that  the 
combined  refractions  on  entering 
and  emerging  from  the  prism  pro- 
duce the  effect  of  a  meniscus  lens. 
Hence  rays  from  an  object,  AB, 
after  passing  into  the  prism  and  un- 
dergoing total  reflection  from  the 
face,  cd,  form  at  ab  a  real  image  of 
AB. 

In  fig.  506,  the  small  table  B 
corresponds  to  the  focus  of  the  prism 
in  the  case,  A,  and  an  image  forms 
on  a  piece  of  paper  placed  on  the 
table.  The  whole  is  surrounded  by 

a  black  curtain,  so  that  the  observer  can  place  himself  in  complete  dark- 
ness.    . 

603.  Camera  luclda. — The  camera  lucida  is  a  small  instrument  depend- 
ing on  internal  reflection,  and  serves  for  taking  an  outline  of  any  object.  It 
was  invented  by  Wollaston  in  1804.  It  consists  of  a  small  four-sided  glass 
prism,  of  which  fig.  508  gives  a  section  perpendicular  to  the  edges.  A  is  a 
right  angle,  and  C  an  angle  of  135°  ;  the  other  angles,  B  and  D,  are  67^°. 
The  prism  rests  on  a  stand,  on  which  it  can  be  raised  or  lowered,  and  turned 
more  or  less  about  an  axis  parallel  to  the  prismatic  edges.  When  the  face 
AB  is  turned  towards  the  object,  the  rays  from  the  object  fall  nearly  per- 
pendicular on  this  face,  pass  into  the  prism  without  any  appreciable  refrac- 
tion, and  are  totally  reflected  from  BC  ;  for  as  the  line  ab  is  perpendicular  to 


-604] 


Magic  Lantern. 


527 


Fig.  507. 


BC,  and  nL  to  AB,  the  angle  anL  will  equal  the  angle  B  ;  that  s,  it  will  con- 
tain 67  £°,  and  this  being  greater  than  the  critical  angle  of  glass  (540),  the  ray 
Ln  will  undergo  total  reflection.  The  rays  are  again 
totally  reflected  from  0,  and  emerge  near  the  summit,  A 

D,  in  a  direction  almost  perpendicular  to  the  face     I 

DA,  so  that  the  eye  which  receives  the  rays  sees  at  K~ 
L'  an  image  of  the  object  L.  If  the  outlines  of  the 
image  are  traced  with  a  pencil,  a  very  correct  design 
is  obtained  ;  but  unfortunately  there  is  a  great  diffi- 
culty in  seeing  both  the  image  and  the  point  of  the 
pencil,  for  the  rays  from  the  object  give  an  image 
which  is  farther  from  the  eye  than  the  pencil.  This 
is  corrected  by  placing  between  the  eye  and  prism  a 
lens,  I,  which  gives  to  the  rays  from  the  pencil  and 
those  from  the  object  the  same  divergence.  In  this  case,  however,  it  is 
necessary  to  place  the  eye  very  near  the  edge  of  the  prism,  so  that  the  aper- 
ture of  the  pupil  is  divided  into  two  parts,  one  of  which  sees  the  image  and 
the  other  the  pencil. 

Amici's  camera  lucida,  represented  in  fig.  509,  is  preferable  to  that  of 
\Vollaston,  inasmuch  as  it  allows  the  eye  to  change  its  position  to  a  con- 
siderable extent,  without  ceasing  to  see  the  image  and  the  pencil  at  the 
same  time.  It  con- 
sists of  a  rectangular 
glass  prism,  ABC, 
having  one  of  its  per- 
pendicular faces  turn- 
ed towards  the  object 
to  be  depicted,  while 
the  other  is  at  right 
angles  to  an  inclined 
plate  of  glass,  inn. 


The    rays,    LI,    pro- 
ceeding from  the  ob 


Fig.  508.  Fig.  509. 

ject,  and  entering  the  prism,  are  totally  reflected  from  its  base  at  D,  and 
emerge  in  the  direction  KH.  They  are  then  partially  reflected  from  the 
glass  plate  mn  at  H,  and  form  a  vertical  image  of  the  object,  L,  which  is 
seen  by  the  eye  in  the  direction  OL'.  The  eye  at  the  same  time  sees 
through  the  glass  the  point  of  the  pencil  applied  to  the  paper,  and  thus 
the  outline  of  the  picture  may  be  traced  with  great  exactness. 

604.  Magric  lantern. — This  is  an  apparatus  by  which  a  magnified  image 
of  small  objects  may  be  projected  on  a  white  screen  in  a  dark  room.  It 
consists  of  a  tin-plate  box,  in  which  there  is  a  lamp  placed  in  the  focus  of  a 
concave  mirror,  A  (fig.  511).  The  reflected  rays  fall  upon  a  condensing  lens,  B, 
(fig.  510),  which  concentrates  them  on  the  figure  painted  on  a  glass  plate,  V. 
There  is  a  double  convex  lens,  C,  at  a  distance  from  V  of  rather  more  than 
its  focal  distance,  and,  consequently,  a  real  and  very  much  magnified  image 
of  the  figure  on  the  glass  is  produced  on  the  screen  (556). 

Dissolving  views  are  obtained  by  arranging  two  magic  lanterns,  which 
are  quite  alike,  with  different  pictures,  in  such  a  manner  that  both  pictures 


528 


On  Light. 


[604- 


are  produced  on  exactly  the  same  part  of  a  screen.  The  object-glasses  of 
both  lanterns  are  closed  by  shades,  which  are  so  arranged  that  according  as 
one  is  raised  the  other  is  lowered,  and  vice  versa.  In  this  way  one  picture  is 
gradually  seen  to  change  into  the  other. 

The  magnifying  power  of  the  magic  lantern  is  obtained  by  dividing  the 
distance  of  the  lens  C  from  the  image  by  its  distance  from  the  object.     If 

Fig.  510. 


Fig.  511. 

the  image  is  100  or  1,000  times  farther  from  the  lens  than  the  object,  the 
image  will  be  100  or  1,000  times  as  large.  Hence  a  lens  with  a  very  short 
focus  can  produce  a  very  large  image,  provided  the  screen  is  sufficiently 
large. 

605.  Solar  microscope. — The  solar  microscope  is  in  reality  a  magic 
lantern  illuminated  by  the  sun's  rays  ;  it  serves  to  produce  highly  magnified 


Fig.  512. 

images  ot  very  small  objects.  It  is  worked  in  a  dark  room  ;  fig.  512  re- 
presents it  fitted  in  the  shutter  of  a  room,  and  fig.  513  gives  the  internal 
details.  •  -  -  • 


-606] 


Photo-electric  Microscope. 


529 


The  sun's  rays  fall  on  a  plane  mirror,  M,  placed  outside  the  room,  and 
are  reflected  towards  a  condensing  lens,  /,  and  from  thence  to  a  second  lens, 
0  (fig-  5r3)»  by  which  they  are  concentrated  at  its  focus.  The  object  to  be 
magnified  is  at  this  point ;  it  is  placed  between  two  glass  plates,  which,  by 
means  of  a  spring,  «,  are  kept  in  a  firm  position  between  two  metal  plates, 
;//.  The  object  thus  strongly  illuminated  is  very  near  the  focus  of  a 
system  of  three  condensing  lenses,  JT,  which  forms  upon  a  screen  at  a 
suitable  distance  an  inverted  and  greatly  magnified  image,  ab.  The  distance 
of  the  lenses,  o  and  x,  from  the  object  is  regulated  by  means  of  screws,  C 
and  D. 

As  the  direction  of  the  sun's  light  is  continually  varying,  the  position  of 
the  mirror  outside  the  shutter  must  also  be  changed,  so  that  the  reflection  is 


Fig.  513- 

ahvays  in  the  direction  of  the  axis  of  the  microscope.  The  most  exact 
apparatus  for  this  purpose  is  the  heliostat  (534) ;  but  as  this  instrument  is 
very  expensive,  the  object  is  usually  attained  by  inclining  the  mirror  to  a 
greater  or  less  extent  by  means  of  an  endless  screw  B,  and  at  the  same  time 
turning  the  mirror  itself  round  the  lens,  /,  by  a  knob,  A,  which  moves  in  a 
fixed  slide. 

The  solar  microscope  labours  under  the  objection  of  concentrating  great 
heat  on  the  object,  which  soon  alters  it.  This  is  partially  obviated  by 
interposing  a  layer  of  a  saturated  solution  of  alum,  which,  being  a  power- 
fully athermanous  substance  (434),  cuts  off  a  considerable  portion  of  the  heat. 

The  magnifying  power  of  the  solar  microscope  may  be  deduced  experi- 
mentally by  substituting  for  the  object  a  glass  plate  marked  with  lines  at  a 
distance  of  r\  or  ^  of  a  millimetre.  Knowing  the  distance  of  these  lines  on 
the  image,  the  magnifying  power  may  be  calculated.  The  same  method  is 
used  with  the  photo-electric  light.  According  to  the  magnifying  power  which 
it  is  desired  to  obtain,  the  objective  x  is  formed  of  one,  two,  or  three  lenses, 
which  are  all  achromatic. 

The  solar  microscope  furnishes  the  means  of  exhibiting  to  a  large  audience 
many  curious  phenomena,  such,  for  instance,  as  the  circulation  of  blood  in 
the  smaller  animals,  the  crystallisation  of  salts,  the  occurrence  of  animalculae 
in  water,  vinegar,  &c.  &c. 

606.  Photo-electric  microscope. — This  is  nothing  more  than  the  solar 
microscope,  which  is  illuminated  by  the  electric  light  instead  of  by  the  sun's 

A  A 


530 


On  Light. 


[606- 


rays.  The  electric  light,  by  its  intensity,  its  steadiness,  and  the  readiness 
with  which  it  can  be  procured  at  any  time  of  the  day,  is  far  preferable  to  the 
solar  light.  The  photo-electric  microscope  alone  will  be  described  here  : 
the  electric  light  will  be  considered  under  the  head  of  Galvanism. 

Fig.  514  represents  the  arrangement  devised  by  Duboscq.  A  solar 
microscope,  ABD,  identical  with  that  already  described,  is  fixed  on  the 
outside  of  a  brass  box.  In  the  interior  are  two  charcoal  points  which  do 
not  quite  touch,  the  space  between  them  being  exactly  on  the  axis  of  the 
lenses.  The  electricity  of  one  end  of  a  powerful  battery  reaches  the  charcoal 


Fig   514- 

a,  by  means  of  a  copper  wire,  K  ;  while  the  electricity  from  the  opposite  end 
of  the  battery  reaches  c  by  a  second  copper  wire  H. 

During  the  passage  of  the  electricity,  a  luminous  arc  is  formed  between 
the  two  ends  of  the  carbons,  which  gives  a  most  brilliant  light,  and  power- 
fully illuminates  the  microscope.  This  is  effected  by  placing  at  D  in  the 
inside  of  the  tube  a  condensing  lens,  whose  principal  focus  corresponds  to 
the  space  between  the  two  charcoals.  In  this  manner  the  luminous  rays, 
which  enter  the  tubes,  D  and  B,  are  parallel  to  their  axis,  and  the  same 
effects  are  produced  as  with  the  ordinary  solar  microscope  ;  a  magnified 


-607] 


Lighthouse  Lenses. 


531 


image  of  the  object  placed  between  two  plates  of  glass  is  produced  on  the 
screen. 

In  continuing  the  experiment,  the  two  carbons  become  consumed,  and 
to  an  unequal  extent,  a  more  quickly  than  c.  Hence,  their  distance  increasing, 
the  light  becomes  weaker,  and  is  ultimately  extinguished.  In  speaking 
afterwards  of  the  electric  light,  the  working  of  the  apparatus,  P,  which  keeps 
these  charcoals  at  a  constant  distance,  and  thus  ensures  a  constant  light, 
will  be  explained. 

The  part  of  the  apparatus,  MN,  may  be  considered  as  a  universal  photo- 
genic apparatus.  The  microscope  can  be  replaced  by  the  head-pieces  of  the 
phantasmagoria,  the  polyorama,  the  megascope,  by  polarising  apparatus,  &c., 
and  in  this  manner  is  admirably  adapted  for  exhibiting  optical  phenomena 
to  a  large  auditory.  Instead  of  the  electric  light,  we  may  use  with  this 
apparatus  the  oxy-hydrogen  or  Drummond's  light,  which  is  obtained  by 
heating  a  cylinder 
of  lime  in  the  flame 
produced  by  the 
combustion  of  a 
mixture  of  hydro- 
gen or  of  coal  gas 
with  oxygen  gab. 

607.  !•  i  gr  n  t- 
house  lenses.  — 
Lenses  of  large 
dimensions  are 
very  difficult  of 
construction ;  they 
further  produce  a 
considerable  sphe- 
rical aberration, 
and  their  thick- 
ness causes  the 
loss  of  much  light. 
In  order  to  avoid 
these  inconveni- 
ences, echelon  len- 
ses have  been  con- 
structed. They 
consist  of  a  plano- 
convex lens,  C 
(figs.  515  and  516), 
surrounded  by  a 
series  of  annular 
and  concentric 
segments,  A,  B, 

each  of  which  has  a  plane  face  on  the  same  side  as  the  plane  face  of  the 
central  lens,  while  the  faces  on  the  other  side  have  such  a  curvature  that  the 
foci  of  the  different  segments  coincide  in  the  same  point.  These  rings  form, 
together  with  the  central  lens,  a  single  lens,  a  section  of  which  is  represented 

A  A  2 


532  On  Light.  [607- 

in  fig.  516.  The  drawing  was  made  from  a  lens  of  about  2  feet  in  diameter, 
the  segments  of  which  are  formed  of  a  single  piece  of  glass  ;  but  with  larger 
lenses,  each  segment  is  likewise  formed  of  several  pieces. 

Behind  the  lens  there  is  a  support  fixed  by  three  rods,  on  which  a  body 
can  be  placed  and  submitted  to  the  sun's  rays.  As  the  centre  of  the  support 
coincides  with  the  focus  of  the  lens,  the  substances  placed  there  are  melted 
and  volatilised  by  the  high  temperature  produced.  Gold,  platinum,  and 
quartz  are  melted.  The  experiment  proves  that  heat  is  refracted  in  the  same 
way  as  light  :  for  the  position  of  the  calorific  focus  is  identical  with  that  of 
the  luminous  focus. 

Formerly  parabolic  mirrors  were  used  in  sending  the  light  of  beacons 
and  lighthouses  to  great  distances,  but  they  have  been  supplanted  by  the  use 
of  lenses  of  the  above  construction.  In  most  cases,  oil  is  used  in  a  lamp  of 
peculiar  construction,  which  gives  as  much  light  as  20  moderators.  The 
light  is  placed  in  the  principal  focus  of  the  lens  so  that  the  emergent  rays 
form  a  parallel  beam  (fig.  450),  which  loses  intensity  only  by  passing  through 
the  atmosphere,  and  can  be  seen  at  a  distance  of  above  40  miles.  In  order 
that  all  points  of  the  horizon  may  be  successively  illuminated,  the  lens 
is  continually  moved  round  the  lamp  by  a  clockwork  motion,  the  rate 
of  which  varies  with  different  lighthouses.  Hence,  in  different  parts, 
the  light  alternately  appears  and  disappears  after  equal  intervals  of  time. 
These  alternations  serve  to  distinguish  lighthouses  from  an  accidental 
fire  or  a  star.  By  means,  too,  of  the  number  of  times  the  light  disap- 
pears in  a  given  time,  and  by  the  colour  of  the  light,  sailors  are  enabled 
to  distinguish  the  lighthouses  from  one  another,  and  hence  to  know  their 
position. 

Of  late  years  the  use  of  the  electric  light  has  been  substituted  for  that  of 
oil  lamps  ;  a  description  of  the  apparatus  will  be  given  in  a  subsequent 
chapter. 

PHOTOGRAPHY. 

608.  Photography  is  the  art  of  fixing  the  images  of  the  camera  obscura 
on  substances  sensitive  to  light.  The  various  photographic  processes  may 
be  classed  under  three  heads  :  photography  on  metal,  photography  on  paper, 
and  photography  on  glass. 

Wedgwood  was  the  first  to  suggest  the  use  of  chloride  of  silver  in  fixing 
the  image,  and  Davy,  by  means  of  the  solar  microscope,  obtained  images  of 
small  objects  on  paper  impregnated  with  chloride  of  silver  ;  but  no  method 
was  known  of  preserving  the  images  thus  obtained,  by  preventing  the  further 
action  of  light.  Niepce,  in  1814,  obtained  permanent  images  of  the  camera 
by  coating  glass  plates  with  a  layer  of  a  varnish  composed  of  bitumen  dis- 
solved in  oil  of  lavender.  This  process  was  tedious  and  inefficient,  and  it 
was  not  until  1839  that  the  problem  was  solved.  In  that  year,  Daguerre 
described  a  method  of  fixing  the  images  of  the  camera,  which,  with  the  sub- 
sequent improvements  of  Talbot  and  Archer,  has  rendered  the  art  of  photo- 
graphy one  of  the  most  marvellous  discoveries  ever  made,  either  as  to  the 
beauty  and  perfection  of  the  results,  or  as  to  the  celerity  with  which  they  are 
produced. 


-608] 


PhotograpJiy. 


S33 


In  Daguerre's  process,  the  Dagucrrotype,  the  picture  is  produced  on  a 
plate  of  copper  coated  with  silver.  This  is  first  very  carefully  polished— an 
operation  on  which  much  of  the  success  of  the  subsequent  operations  depends. 
It  is  then  rendered  sensitive  by  exposing  it  to  the  action  of  iodine  vapour, 
which  forms  a  thin  layer  of  iodide  of  silver  on  the  surface.  The  plate  is  now 
fit  to  be  exposed  in  the  camera ;  it  is  sensitive  enough  for  views  which  re- 
quire an  exposure  of  ten  minutes  in  the  camera,  but  when  greater  rapidity  is 
required,  as  for  portraits,  &c.,  it  is  further  exposed  to  the  action  of  an  accele- 
rator, such  as  bromine  or  hypobromite  of  calcium.  All  the  operations  must 
be  performed  in  a  room  lighted  by  a  candle,  or  by  the  daylight  admitted 
through  yellow  glass,  which  cuts  off  all  chemical  rays.  The  plate  is  preserved 
from  the  action  of  light  by  placing  it  in  a  small  wooden  case  provided  with 
a  slide  on  the  sensitive  side. 

The  third  operation  consists  in  exposing  the  sensitive  plate  to  the  action 
of  light,  placing  it  in  that  position  in  the  camera  where  the  image  is  produced 
with  greatest  delicacy.  For 

photographic      purposes      a  I9Q1  \. 

camera  obscura  of  peculiar 
construction  is  used.  The 
brass  tube  A  (fig.  517),  con- 
tains an  achromatic  con- 
densing lens,  which  can  be 
moved  by  means  of  a  rack- 
work  motion,  to  which  is 
fitted  a  milled  head,  D.  At 
the  opposite  end  of  the  box 
is  a  ground-glass  plate,  E, 
which  slides  in  a  groove,  B, 
in  which  the  case  containing 
the  plate  also  fits.  The 
camera  being  placed  in  a 
proper  position  before  the  object,  the  sliding  part  of  the  box  is  adjusted 
until  the  image  is  produced  on  the  glass  with  the  utmost  sharpness  ;  this  is 
the  case  when  the  glass  slide  is  exactly  in  the  focus.  The  final  adjustment 
is  made  by  means  of  the  milled  head,  D. 

The  glass  slide  is  then  replaced  by  the  case  containing  the  sensitive  plate  ; 
the  slide  which  protects  it  is  raised  ;  and  the  plate  exposed  for  a  time,  the 
duration  of  which  varies  in  different  cases,  and  can  only  be  hit  exactly 
by  great  practice.  The  plate  is  then  removed  to  a  dark  room.  No  change 
is  perceptible  to  the  eye,  but  those  parts  on  which  the  light  has  acted  have 
acquired  the  property  of  condensing  mercury  :  the  plate  is  next  placed 
in  a  box  and  exposed  to  the  action  of  mercurial  vapour  at  60  or  70  de- 
grees. 

The  mercury  is  deposited  on  the  parts  affected,  in  the  form  of  globules 
imperceptible  to  the  naked  eye.  The  shadows,  or  those  parts  on  which 
the  light  has  not  acted,  remain  covered  with  the  layer  of  iodide  of  silver. 
This  is  removed  by  treatment  with  hyposulphite  of  sodium,  which  dis- 
solves iodide  of  silver  without  affecting  the  rest  of  the  plate.  The  plate  is 
next  immersed  in  a  solution  of  chloride  of  gold  in  hyposulphite  of  sodium 


Fig.  517- 


534 


On  Light. 


[608- 


which  dissolves  the  silver,  while  some  gold  combines  with  the  mercury 
and  silver  of  the  parts  attacked,  and  greatly  increases  the  intensity  of  the 
lustre. 

Hence  the  light  parts  of  the  image  are  those  on  which  the  mercury 
has  been  deposited,  and  the  shaded  those  on  which  the  metal  has  retained 
its  reflecting  lustre. 

Fig.  518  represents  a  section  of  the  camera  and  the  object-glass.  At  first 
it  consisted  of  a  double  convex  lens,  but  now  double  achromatic  lenses,  LL', 


Fig.  518. 

are  used  as  object-glasses.  They  act  more  quickly  than  objectives  with  a 
single  lens,  have  a  shorter  focus,  and  can  be  more  easily  focussed  by  moving 
the  lens,  L',  by  means  of  the  rack  and  pinion,  D. 

609.  Photographs  on  paper. — In  Daguerre's  process,  which  has  just 
been  described,  the  images  are  produced  directly  on  metal  plates.  With 
paper  and  glass,  photographs  of  two  kinds  may  be  obtained  :  those  in  which 
an  image  is  obtained  with  reversed  tints,  so  that  the  lightest  parts  have  be- 
come the  darkest  on  paper,  and  vice  versa  ;  and  those  in  which  the  lights 
and  shades  are  in  their  natural  position.  The  former  are  called  negative, 
and  the  latter  positive  pictures. 

A  negative  may  be  taken  either  on  glass  or  on  paper  ;  it  serves  to  produce 
a  positive  picture. 

Negatives  on  glass. — A  glass  plate  of  the  proper  size  is  carefully  cleaned 
and  coated  with  a  uniformly  thick  layer  of  collodion  impregnated  with  iodide 
of  potassium.  The  plate  is  then  immersed  for  about  a  minute  in  a  bath  of 
nitrate  of  silver  containing  30  grains  of  the  salts  in  an  ounce  of  water.  This 
operation  must  be  performed  in  a  dark  room.  The  plate  is  then  removed, 
allowed  to  drain,  and  when  somewhat  dry,  placed  in  a  closed  flame,  and 
afterwards  exposed  in  the  camera,  for  a  shorter  time  than  in  the  case  of  a 
Daguerrotype.  On  removing  the  plate  to  a  dark  room,  no  change  is  visible, 
but  on  pouring  over  it  a  solution  called  the  developer,  an  image  gradually 
appears.  The  principal  substances  used  for  developing  are  protosulphate 
of  iron  and  pyrogallic  acid.  The  action  of  light  on  iodide  of  silver  appears 
to  produce  some  molecular  change,  or  else  some  actual  chemical  decom- 
position, in  virtue  of  which  the  developers  have  the  property  of  reducing 
to  the  metallic  state  those  parts  of  the  iodide  of  silver  which  have  been  most 
acted  upon  by  the  light.  When  the  picture  is  sufficiently  brought  out,  water 
is  poured  over  the  plate,  in  order  to  prevent  the  further  action  of  the  deve- 


-611]  Photographs  on  Albumenised  Paper  and  Glass.         535 

loper.  The  parts  on  which  light  has  not  acted  are  still  covered  with  iodide 
of  silver,  which  would  be  affected  if  the  plate  were  now  exposed  to  the  light. 
It  is,  accordingly,  washed  with  solution  of  hyposulphite  of  sodium,  which 
dissolves  the  iodide  of  silver  and  leaves  the  image  unaltered.  The  picture 
is  then  coatecl  with  a  thin  layer  of  spirit  varnish,  to  protect  it  from  mechanical 
injury. 

When  once  the  negative  is  obtained,  it  may  be  used  for  printing  an  in- 
definite number  of  positive  pictures.  For  this  purpose  paper  is  impregnated 
with  chloride  of  silver,  by  immersing  it  first  in  solution  of  nitrate  of  silver  and 
then  in  one  of  chloride  of  sodium ;  chloride  of  silver  is  thus  formed  on  the 
paper  by  double  decomposition.  The  negative  is  placed  on  a  sheet  of  this 
paper  in  a  copying  frame,  and  exposed  to  the  action  of  light  for  a  certain 
time.  The  chloride  of  silver  becomes  acted  upon — the  light  parts  of  the 
negative  being  most  affected,  and  the  dark  parts  least  so.  A  copy  is  thus 
obtained,  on  which  the  lights  of  the  negative  are  replaced  by  shades,  and 
inversely.  In  order  to  fix  the  picture,  it  is  washed  in  a  solution  of  hyposul- 
phite of  sodium,  which  dissolves  the  unaltered  chloride  of  silver.  The 
picture  is  afterwards  immersed  in  a  bath  of  chloride  of  gold,  which  gives  it 
tone. 

6 10.  Positives  on  glass. — Very  beautiful  positives  are  obtained  by  pre- 
paring the  plates  as  in  the  preceding  cases  ;  the  exposure  in  the  camera, 
however,  is  not  nearly  so  long  as  for  the  negatives.  The  picture  is  then 
developed  by  pouring  over  it  a  solution  of  protosulphate  of  iron,  which  pro- 
duces a  negative  image  ;  and  by  afterwards  pouring  a  solution  of  cyanide  of 
potassium  over  the  plate,  this  negative  is  rapidly  converted  into  a  positive. 
It  is  then  washed  and  dried,  and  a  coating  of  varnish  poured  over  the 
picture. 

6n.  Photographs  on  albumenised  paper  and  glass. — In  some  cases, 
paper  impregnated  with  a  solution  of  albumen  containing  iodide  of  potassium 
is  used  instead  of  collodion,  over  which  it  has  the  advantage  that  it  can  be 
prepared  for  some  time  before  it  is  used,  and  that  it  produces  certain  effects 
in  the  middle  tints.  It  has  the  disadvantage  of  not  being  nearly  so  sensitive. 
It  requires,  therefore,  longer  exposure  and  is  unsuitable  for  portraits,  but  in 
some  cases  can  be  advantageously  used  for  views. 


536 


On  Light. 


[612- 


CHAPTER   VI. 

THE   EYE  CONSIDERED   AS   AN   OPTICAL    INSTRUMENT. 

6 1 2.  Structure  of  the  human  «jye. — The  eye  is  the  organ  of  vision  ; 
that  is  to  say,  of  the  phenomenon  by  virtue  of  which  the  light  emitted 
or  reflected  from  bodies  excites  in  us  the  sensation  which  reveals  their  pre- 
sence. 

The  eye  is  placed  in  a  bony  cavity  called  the  orbit ;  it  is  maintained 
in  its  position  by  the  muscles  which  serve  to  move  it,  by  the  optic  nerve, 

the  conjunctiva,  and  the  eyelids. 
Its  size  is  much  the  same  in  all 
persons  :  it  is  the  varying  aper- 
ture of  the  eyelids  that  makes 
the  eye  appear  larger  or  smaller. 
Fig.  519  represents  a  trans- 
verse section  of  the  eye  from 
back  to  front.  The  general 
shape  is  that  of  a  spheroid,  the 
curvature  of  which  is  greater  in 
the  anterior  than  in  the  posterior 
part.  It  is  composed  of  the 
following  parts  :  the  cornea,  the 
sclerotica,  the  iris,  the  pttpil, 
the  aqueotis  humour,  the  crys- 
talline, the  vitreous  body,  the 
hyaloid  membrane,  the  choroid,  the  retina,  and  the  optic  nerve. 

Cornea. — The  cornea,  a,  is  a  transparent  membrane  situated  in  front  of 
the  ball  of  the  eye.  In  shape  it  resembles  a  small  watch-glass,  and  it  fits 
into  the  sclerotica,  i ;  in  fact,  these  membranes  are  so  connected  that  some 
anatomists  have  considered  them  as  one  and  the  same,  and  have  distin- 
guished them  by  calling  the  cornea  the  transparent,  and  the  sclerotica  the 
opaque  cornea. 

Sclerotica. — The  sclerotica,  i,  or  sclerotic  coat,  is  a  membrane  which, 
together  with  the  cornea,  envelopes  all  parts  of  the  eye.  In  front  there  is 
an  almost  circular  aperture  into  which  the  cornea  fits  ;  a  perforation  behind 
gives  passage  to  the  optic  nerve. 

Iris. — The  iris,  d,  is  an  annular,  opaque  diaphragm,  placed  between  the 
cornea  and  the  crystalline  lens.  It  constitutes  the  coloured  part  of  the  eye, 
and  is  perforated  by  an  aperture  called  \he  pupil,  which  in  man  is  circular. 
In  some  animals,  especially  those  belonging  to  the  genus  felts,  it  is  narrow 
and  elongated  in  a  vertical  direction  ;  in  the  ruminants  it  is  elongated  in  a 


-612]  Structure  of  the  Human  Eye.  537 

transverse  direction.  It  is  a  contractile  membrane,  and  its  diameter  varies 
in  the  same  individual  between  0-12  and  0*28  of  an  inch;  but  these  limits 
may  be  exceeded.  The  luminous  rays  pass  into  the  eye  through  the  pupil. 
The  pupil  enlarges  in  darkness,  but  contracts  under  the  influence  of  a  bright 
light.  These  alterations  of  contraction  and  enlargement  take  place  with 
extreme  rapidity  ;  they  are  very  frequent,  and  play  an  important  part  in  the 
act  of  vision.  The  movements  of  the  iris  are  involuntary. 

It  appears  from  this  description  that  the  iris  is  a  screen  with  a  variable 
aperture,  whose  function  is  to  regulate  the  quantity  of  light  which  penetrates 
into  the  eye  ;  for  the  size  of  the  pupil  diminishes  as  the  intensity  of  light 
increases.  The  iris  serves  also  to  correct  the  spherical  aberration,  as  it 
prevents  the  marginal  rays  from  passing  through  the  edges  of  the  crystalline 
lens.  It  thus  plays  the  same  part  with  reference  to  the  eye  that  a  stop  does 
in  optical  instruments  (558). 

Aqueous  humour. — Between  the  posterior  part  of  the  cornea  and  the 
front  of  the  crystalline  there  is  a  transparent  liquid  called  the  aqueous  hu- 
mour. The  space,  ^,  occupied  by  this  humour  is  divided  into  two  parts  by 
the  iris  :  the  part  <£,  between  the  cornea  and  the  iris,  is  called  the  anterior 
chamber ;  the  part  c,  which  is  between  the  iris  and  the  crystalline,  is  the 
posterior  chamber. 

Crystalline  lens. — This  is  a  double  convex  transparent  body  placed  im- 
mediately behind  the  iris ;  the  inner  margin  of  which  is  in  contact  with 
its  anterior  surface,  though  not  attached  to  it.  The  lens  is  enclosed  in  a 
transparent  membrane,  called  its  capsule }  it  is  less  convex  on  its  anterior 
than  on  its  posterior  surface,  and  is  composed  of  almost  concentric  layers, 
which  decrease  in  density  and  refracting  power  from  the  centre  to  the  cir- 
cumference. 

To  the  anterior  surface  of  the  capsule,  near  its  margin,  is  fixed  a  firm 
transparent  membrane,  which  is  attached  behind  to  the  front  of  the  hyaloid 
membrane,  and  is  known  as  the  suspensory  ligament.  This  ligament  exerts 
attraction,  all  round,  on  the  front  surface  of  the  lens,  and  renders  it  less 
convex  than  it  would  otherwise  be,  and  its  relaxation  plays  an  important 
part  in  the  adaptation  of  the  eye  for  sight  at  different  distances. 

Vitreous  body.  Hyaloid  membrane. — The  vitreous  body,  or  vitreous 
humour,  is  a  transparent  mass  resembling  the  white  of  an  egg,  which  occu- 
pies all  the  part  of  the  ball  of  the  eye  //,  behind  the  crystalline.  The  vitreous 
humour  is  surrounded  by  the  hyaloid  membrane,  /,  which  lines  the  posterior 
face  of  the  crystalline  capsule,  and  also  the  interior  face  of  another  mem- 
brane called  the  retina. 

Retina.  Optic  neme. — The  retina,  m,  is  a  membrane  which  receives  the 
impression  of  light,  and  transmits  it  to  the  brain  by  the  intervention  of  a 
nerve,  «,  called  the  optic  nerve,  which,  proceeding  from  the  brain,  pene- 
trates into  the  eye,  and  extends  over  the  retina  in  the  form  of  a  nervous 
network.  The  nerve-fibres  themselves  are  not  sensitive  to  light,  but  are 
only  stimulated  by  it  indirectly  through  the  intervention  of  certain  structures 
called  the  rods  and  cones.  Where  the  optic  nerve  enters,  there  are  no  rods 
or  cones  ;  this  part  of  the  retina  therefore  is  insensitive  to  light  and  is  called 
the  punctum  cacum. 

The  only  property  of  the  retina  and  optic  nerve  is  that  of  receiving  and 

A  A  3 


538  On  Light.  [612- 

transmitting  to  the  brain  the  impression  of  objects.  These  organs  have  been 
cut  and  pricked  without  causing  any  pain  to  the  animals  submitted  to  these 
experiments  ;  but  there  is  reason  to  believe  that  irritation  of  the  optic  nerve 
causes  the  sensation  of  a  flash  of  light. 

Choroid, — The  choroid,  k,  is  a  membrane  between  the  retina  and  the 
sclerotica.  It  is  completely  vascular,  and  is  covered  on  the  internal  face 
by  a  black  substance  which  resembles  the  colouring  matter  of  a  negro's 
skin,  and  which  absorbs  all  rays  not  intended  to  co-operate  in  producing 
vision. 

The  choroid  elongates  in  front,  and  forms  a  series  of  convoluted  folds, 
called  ciliary  processes,  which  penetrate  between  the  iris  and  the  crystalline 
capsule,  to  which  they  adhere,  forming  round  it  a  disc,  resembling  a  radiated 
flower.  By  its  vascular  tissue,  the  choroid  serves  to  carry  the  blood  into 
th'e  interior  of  the  eye,  and  especially  to  the  ciliary  processes. 

613.  Refractive  indices  of  the  transparent  media  of  the  eye. — The 
refractive  indices  from  air  into  the  transparent  parts  of  the  eye  were  deter- 
mined by  Brewster.     His  results  are  contained  in  the  following  table,  com- 
pared with  water  as  a  standard  : — 

Water  .         .         .         .  .         .         .         .         .         .  1*3358 

Aqueous  humour  .         .         .         .         .         .         .         .         .  1*3366 

Vitreous  humour i'3394 

Exterior  coating  of  the  crystalline        .....  1*3767 

Centre  of  the  crystalline i'399o 

Mean  refraction  of  the  crystalline 1*3839 

614.  Curvatures  and  dimensions  of  various  parts  of  the  human  eye. 

Radius  of  curvature  of  the  sclerotica 0-40  to  0-44  in. 

„                   „                    cornea 0*28  to  0-32  „ 

„                  „                    anterior  face  of  the  crystalline    .  0*28  to  0-40  „ 

„                  „                    posterior  face  of  the  crystalline  .  0*20  to  0*24  ,, 

Diameter  of  the  iris 0-44  to  0*48  „ 

„          „         pupil 0-12  to  0*28  „ 

„          „         crystalline    . 0*40  „ 

Thickness  of  the  crystalline .         .         .         .         .         .         .  0*20  „ 

Distance  from  the  pupil  to  the  cornea 0*08  „ 

Length  of  the  axis  of  the  eye 0*88  to  0*96  „ 

615.  Path  of  rays  in  the  eye. — From  what  has  been  said  as  to  the 
structure  of  the  eye,  it  may  be  compared  to  a  camera  obscura  (602),  of  which 
the  pupil  is  the  aperture,  the  crystalline  is  the  condensing  lens,  and  the 
retina  is  the  screen  on  which  the  image  is  formed.     Hence,  the  effect  is  the 
same  as  when  the  image  of  an  object  placed  in  front  of  a  double  convex  lens 
is  formed  in  its  conjugate  focus.     Let  AB  (fig.   520)  be  an  object  placed 
before  the  eye,  and  let  us  consider  the  rays  emitted  from  any  point  of  the 
object,  A.     Of  all  these  rays,  those  which  are  directed  towards  the  pupil  are 
the  only  ones  which  penetrate   the  eye,  and  are   operative  in  producing 
vision.     These  rays,  on  passing  into  the  aqueous  humour,  experience  a  first 
refraction  which  brings  them  near  the  secondary  axis  Aa,  drawn  through 


-617] 


Optic  Axis,  Optic  Angle,  Visual  Angle. 


539 


the  optic  centre  of  the  crystalline  ;  they  then  traverse  the  crystalline,  which 
again  refracts  them  like  a  double  convex  lens,  and,  having  experienced  a 


Fig.  520. 

final  refraction  by  the  vitreous  humour,  they  meet  in  a  point,  «,  and  form 
the  image  of  the  point,  A.  The  rays  issuing  from  the  point  B  form  in  like 
manner  an  image  of  it  at  the  point  b,  so  that  a  very  small,  real,  and  inverted 
image  is  formed  exactly  on  the  retina,  provided  the  eye  is  in  its  normal 
condition. 

6 1 6.  Inversion  of  images. — In  order  to  show  that  the  images  formed 
on  the  retina  are  really  inverted,  the  eye  of  an  albino  or  any  animal  with 
pink  eyes  may  be  taken  ;  this  has  the  advantage  that,  as  the  choroid  is 
destitute  of  pigment,  light  can  traverse  it  without  loss.  This  is  then  deprived 
at  its  posterior  part  of  the  cellular  tissue  surrounding  it,  and  fixed  in  a  hole 
in  the  shutter  of  a  dark  room ;  by  means  of  a  lens  it  may  be  seen  that  the 
inverted  images  of  external  objects  are  depicted  on  the  retina. 

The  inversion  of  images  in  the  eye  has  greatly  occupied  both  physicists 
and  physiologists,  and  many  theories  have  been  proposed  to  explain  how  it 
is  that  we  do  not  see  inverted  images  of  objects.  The  chief  difficulty  seems 
to  have  arisen  from  the  conception  of  the  mind  or  brain  as  something 
behind  the  eye,  locking  into  it,  and-  seeing  the  image  upon  the  retina ; 
whereas  really  this  image  simply  causes  a  stimulation  of  the  optic  nerve, 
which  produces  some  molecular  change  in  some  part  of  the  brain,  and  it  is 
only  of  this  change,  and  not  of  the  image,  as  such,  that  we  have  any  con- 
sciousness. The  mind  has  thus  no  direct  cognisance  of  the  image  upon  the 
retina,  nor  of  the  relative  positions  of  its  parts,  and,  sight  being  supple- 
mented by  touch  in  innumerable  cases,  it  learns  from  the  first  to  associate 
the  sensations  brought  about  by  the  stimulation  of  the  retina  (although  due 
to  an  inverted  image)  with  the  correct  position  of  the  object  as  taught  by  touch. 

617.  Optic  axis,  optic  angle,  visual  angle. — The  principal  optic  axis 
of  an  eye  is  the  axis  of  its  figure  ;  that  is  to  say,  the  straight  line  in  reference 


Fig.  511. 

to  which  it  is  symmetrical.     In  a  well-shaped   eye  it  is  the  straight  line 
passing  through  the  centre  of  the  pupil  and  of  the  crystalline,  such  as  the 


540  On  Light.  [617- 

line  O<?  (fig.  520).  The  lines  A«,  B£,  which  are  almost  rectilinear,  are 
secondary  axes.  The  eye  sees  objects  most  distinctly  in  the  direction  of  the 
principal  optic  axis. 

The  optic  angle  is  the  angle  BAG  (fig.  521),  formed  between  the 
principal  optic  axis  of  the  two  eyes  when  they  are  directed  towards  the 
same  point.  This  angle  is  smaller  in  proportion  as  the  objects  are  more 
distant. 

The  visual  angle  is  the  angle  AOB  (fig.  522),  under  which  an  object  is 
seen  ;  that  is  to  say,  the  angle  formed  by  the  secondary  axes  drawn  from 


the  optic  centre  of  the  crystalline  to  the  opposite  extremities  of  the  object. 
For  the  same  distance,  this  angle  increases  with  the  magnitude  of  the 
object,  and  for  the  same  object  it  decreases  as  the  distance  increases,  as  is 
the  case  when  the  object  passes  from  AB  to  A'B'.  It  follows,  therefore, 
that  objects  appear  smaller  in  proportion  as  they  are  more  distant ;  for  as 
the  secondary  axes,  AO,  BO,  cross  in  the  centre  of  the  crystalline,  the  size 
of  the  image  projected  on  the  retina  depends  on  the  size  of  the  visual  angle, 
AOB. 

618.  Estimation  of  the  distance  and  size  of  objects. — The  estimation 
of  distance  and  of  size  depends  on  numerous  circumstances  ;  these  are — the 
visual  angle,  the  optic  angle,  the  comparison  with  objects  whose  size  is 
familiar  to  us  ;  to  these  must  be  added  the  effect  of  what  is  called  aerial 
perspective  ;  that  is,  a  more  or  less  vaporous  medium  which  enshrouds  the 
distant  objects,  and  thereby  diminishes  not  only  the  sharpness  of  the  out- 
lines, but  also  softens  the  contrast  between  light  and  shade,  which  close  at 
hand  are  marked. 

When  the  size  of  an  object  is  known,  as  the  figure  of  a  man,  the  height 
of  a  tree  or  of  a  house,  the  distance  is  estimated  by  the  magnitude  of  the 
visual  angle  under  which  it  is  seen.  If  its  size  is  unknown,  it  is  judged 
relatively  to  that  of  objects  which  surround  it. 

A  colonnade,  an  avenue  of  trees,  the  gas-lights  on  the  side  of  a  road, 
appear  to  diminish  in  size  in  proportion  as  their  distance  increases,  because 
the  visual  angle  decreases  ;  but  the  habit  of  seeing  the  columns,  trees,  &c., 
in  their  proper  height,  leads  our  judgment  to  rectify  the  impression  produced 
by  vision.  Similarly,  although  distant  mountains  are  seen  under  a  very 
small  angle,  and  occupy  but  a  small  space  in  the  field  of  view,  our  familiarity 
with  the  effects  of  aerial  perspective  enables  us  to  form  a  correct  idea  of 
their  real  magnitude. 

The  optic  angle  is  also  an  essential  element  in  appreciating  distance. 
This  angle  increasing  or  diminishing  according  as  objects  approach  or 
recede,  we  move  our  eyes  so  as  to  make  their  optic  axes  converge  towards 
the  object  which  we  are  looking  at,  and  thus  obtain  an  idea  of  its  distance. 
Nevertheless,  it  is  only  by  long  custom  that  we  can  establish  a  relation 


-620]  Distance  of  Distinct  Vision.  541 

between  our  distance  from  the  objects  and  the  corresponding  motion  of  the 
eyes.  It  is  a  curious  fact  that  persons  born  blind,  and  whose  sight  has  been 
restored  by  the  operation  for  cataract,  imagine  at  first  that  all  objects  are  at 
the  same  distance. 

Vertical  distances  are  estimated  too  low  compared  with  horizontal  ones  ; 
on  high  mountains  and  over  large  surfaces  of  water,  distances  are  estimated 
too  low  owing  to  the  want  of  intervening  objects.  A  room  filled  with  furni- 
ture appears  larger  than  an  empty  room  of  the  same  size. 

We  cannot  recognise  the  true  form  of  an  object  if  with  moderate  illumina- 
tion the  visual  angle  is  less  than  half  a  minute.  A  white  square,  a  metre  in 
the  side,  appears  at  a  distance  of  about  5  miles  under  this  angle  as  a  bright 
spot  which  can  scarcely  be  distinguished  from  a  circle  of  the  same  size. 

A  very  bright  object,  however,  such  as  an  incandescent  platinum  wire,  is 
seen  in  a  dark  ground  under  an  angle  of  2  seconds.  So  too  a  small  dark 
object  is  seen  against  a  bright  ground  ;  thus  a  hair  held  against  the  sky  can 
be  seen  at  a  distance  of  I  or  2  metres. 

619.  Distance  of  distinct  vision. — The  distance  of  distinct  vision,  as 
already  stated,  is  the  distance  at  which  objects  must  be  placed  so  as  to  be 
seen  with  the  greatest  distinctness.     It  varies  in  different  individuals,  and  in 
the  same  individual  it  is  often  different  in  the  two  eyes.     For  small  objects, 
such  as  print,  it  is  from  10  to  12  inches  in  normal  cases. 

In  order  to  obtain  an  approximate  measurement  of  the  least  distance  of 
distinct  vision,  two  small  parallel  slits  are  made  in  a  card  at  a  distance  of 
0*03  of  an  inch.  These  apertures  are  held  close  before  the  eye,  and  when  a 
fine  slit  in  another  card  is  held  very  near  these  apertures,  the  slit  is  seen 
double,  because  the  rays  of  light  which  have  traversed  both  apertures  do  not 
intersect  each  other  on  the  retina,  but  behind  it.  But,  if  the  latter  card  is 
gradually  removed,  the  distance  is  ultimately  reached  at  which  both  images 
coincide  and  form  one  distinct  image.  This  is  the  distance  of  distinct 
vision.  Stampfer  constructed  an  optometer  on  the  principle  of  this  experi- 
ment. 

Persons  who  see  distinctly  only  at  a  very  short  distance  are  called 
myoptic,  or  short-sighted^  and  those  who  see  only  at  a  long  distance  are 
presbyoptic,  or  long-sighted. 

Sharpness  of  sight  may  be  compared  by  reference  to  that  of  a  normal 
eye  taken  as  a  unit.  Such  a  standard  eye,  according  to  Snellen,  recog- 
nises quadrangular  letters  when  they  are  seen  under  an  angle  of  5' ;  if,  for 
instance,  such  letters  are  i^™"1  high  at  a  distance  of  10  metres.  The  sharp- 
ness of  vision  of  one  who  recognises  these  letters  at  a  distance  of  3  metres 

is  then   ^ 
10 

620.  Accommodation. — By  this  term  is  meant  the  changes  which  occur 
in  the  eye  to  fit  it  for  seeing  distinctly  objects  at  different  distances  from  it. 

If  the  eye  be  supposed  fixed  and  its  parts  immoveable,  it  is  evident  that 
there  could  only  be  one  surface  whose  image  would  fall  exactly  upon  the 
retina  :  the  distance  of  this  surface  from  the  eye  being  dependent  on  the 
refractive  indices  of  the  media  and  the  curvatures  of  the  refracting  surfaces 
of  the  eye.  The  image  of  any  point  nearer  the  eye  than  this  distinctly  seen 
surface  would  fall  behind  the  retina  ;  the  image  of  any  more  distant  point 


542  On  Light.  [620- 

would  be  formed  in  front  of  it  :  in  each  case  the  section  of  a  luminous  cone 
would  be  perceived  instead  of  the  image  of  the  point,  and  the  latter  would 
appear  diffused  and  indistinct. 

Experience,  however,  shows  us  that  a  normal  eye  can  see  distinct  images 
of  objects  at  very  different  distances.  We  can,  for  example,  see  a  distant 
tree  through  a  window,  and  also  a  scratch  on  the  pane,  though  not  both  dis- 
tinctly at  the  same  moment ;  for  when  the  eye  is  arranged  to  see  one  clearly, 
the  image  of  the  other  does  not  fall  accurately  upon  the  retina.  An  eye 
completely  at  rest  seems  adapted  for  seeing  distant  objects  ;  the  sense  of 
effort  is  greater  in  a  normal  eye  when  a  near  object  is  looked  at,  after  a 
distant  one,  than  in  the  reverse  case  ;  and  in  paralysis  of  the  nerves  govern- 
ing the  accommodating  apparatus  the  eye  is  persistently  adapted  for  distant 
sight.  There  must,  therefore,  be  some  mechanism  in  the  eye  by  which  it 
can  be  voluntarily  altered,  so  that  the  more  divergent  rays  proceeding  from 
near  objects  shall  come  to  a  focus  upon  the  retina.  There  are  several  con- 
ceivable methods  by  which  this  might  be  effected  ;  it  is  actually  brought 
about  by  a  drawing  forwards  of  the  crystalline  lens  and  a  greater  convexity 
of  its  anterior  surface. 

This  is  shown  by  the  following  experiment : — If  a  candle  be  placed  on  one 
side  of  the  eye  of  a  person  looking  at  a  distant  object,  and  his  eye  be  observed 
from  the  other  side,  three  distinct  images  of  the  flame  will  be  seen  ;  the  first, 
virtual  and  erect,  is  reflected  from  the  anterior  surface  of  the  cornea  ;  the 
next,  erect  and  less  bright,  is  reflected  from  the  anterior  surface  of  the  lens  ; 
the  third,  inverted  and  brilliant,  is  formed  on  the  posterior  surface  of  the  lens. 
If  now  the  person  look  at  a  near  object,  no  change  is  observed  in  the  first 
and  third  images,  but  the  second  image  becomes  smaller  and  approaches  the 
first  ;  which  shows  that  the  anterior  surface  of  the  crystalline  lens  becomes 
more  convex  and  approaches  the  cornea.  In  place  of  the  candle,  Helmholtz 
throws  light  through  two  holes  in  the  screen  upon  the  eye,  and  observes  the 
distance  on  the  eye  between  the  two  shining  points,  instead  of  the  size  of  the 
flame  of  the  candle. 

This  change  in  the  lens  is  effected  chiefly  by  means  of  a  circular  muscle 
(ciliary  muscle),  the  contraction  of  which  relaxes  the  suspensory  ligament, 
and  so  allows  the  front  surface  of  the  lens  to  assume  more  or  less  of  that 
greater  convexity  which  it  would  normally  exhibit  were  it  not  for  the  drag 
exercised  upon  it  by  the  ligament.  Certain  other  less  important  changes 
tending  to  make  the  lens  more  convex  and  to  push  it  forwards  occur,  which 
cannot,  however,  be  explained  without  entering  into  minute  anatomical 
details.  When  the  eye  is  accommodated  for  near  vision,  the  pupil  contracts 
and  so  partially  remedies  the  greater  spherical  aberration. 

The  range  of  accommodation,  called   by  Bonders  — ,  is   measured  by 

A 

first  of  all  determining  the  greatest  distance,  R,  at  which  a  person  can 
read  without  spectacles,  and  then  the  smallest,  P,  at  which  he  can  read ; 

i-l-Jr 

621.  Binocular  vision. — A  single  eye  sees  most  distinctly  any  point 
situated  on  its  optical  axis,  and  less  distinctly  other  points  also,  towards 
which  it  is  not  directly  looking,  but  which  still  are  within  its  circle  of  vision. 


-622]  The  Principle  of  the  Stereoscope.  543 

It  is  able  to  judge  of  the  direction  of  any  such  point,  but  unable  by  itself 
to  estimate  its  distance.  Of  the  distance  of  an  object  it  may,  indeed,  learn 
to  judge  by  such  criteria  as  loss  of  colour,  indistinctness  of  outline,  decrease 
in  magnitude,  &c.  ;  but  if  the  object  is  near,  the  single  eye  is  not  infallible, 
even  with  these  aids. 

When  the  two  eyes  are  directed  upon  a  single  point,  we  then  gain  the 
power  of  judging  of  its  distance  as  compared  with  that  of  any  other  point, 
and  this  we  seem  to  gain  by  the  sense  of  greater  or  less  effort  required  in 
causing  the  optical  axis  to  converge  upon  the  one  point  or  upon  the  other. 
Now  a  solid  object  may  be  regarded  as  composed  of  points  which  are  at  dif- 
ferent distances  from  the  eye.  Hence  in  looking  at  such  an  object,  the  axes 
of  the  two  eyes  are  rapidly  and  insensibly  varying  their  angle  of  convergence, 
and  we  as  rapidly  are  gaining  experience  of  the  difference  in  distance  of  the 
various  points  of  which  the  object  is  composed,  or,  in  other  words,  an  assur- 
ance of  its  solidity.  Such  kind  of  assurance  is  necessarily  unattainable  in 
monocular  vision. 

622.  The  principle  of  the  stereoscope. — Let  any  solid  object,  such  as 
a  small  box,  be  supposed  to  be  held  at  some  short  distance  before  the  two 


eyes.  On  whatever  point  of  it  they  are  fixed,  they  will  see  that  point  the 
most  distinctly,  and  other  points  more  or  less  clearly.  But  it  is  evident  that, 
as  the  two  eyes  see  from  different  points  of  view,  there  will  be  formed  in  the 
right  eye  a  picture  of  the  object  different  from  that  formed  in  the  left ;  and 
it  is  by  the  apparent  union  of  these  two  dissimilar  pictures  that  we  see  the 
object  in  relief.  If,  therefore,  we  delineate  the  object,  first  as  seen  by  the 
right  eye,  and  then  as  seen  by  the  left,  and  afterwards  present  these  dis- 
similar pictures  again  to  the  eyes,  taking  care  to  present  to  each  eye  that 
picture  which  was  drawn  from  its  point  of  view,  there  would  seem  to  be  no 
reason  why  we  should  not  see  a  representation  of  the  object,  as  we  saw  the 
object  itself,  in  relief.  Experiment  confirms  the  supposition.  If  the  object 
held  before  the  eyes  were  a  truncated  pyramid,  r,  and  /,  fig.  523,  would  re- 
present its  principal  lines,  as  seen  by  the  right  and  left  eyes  respectively.  If 
a  card  be  held  between  the  figures,  and  they  are  steadily  looked  at,  r  by  the 
right  eye,  and  /  simultaneously  by  the  left,  for  a  few  seconds,  there  will 
be  seen  a  single  picture  having  the  unmistakable  appearance  of  relief. 
Even  without  a  card  interposed,  the  eye,  by  a  little  practice,  may  soon  be 
taught  so  to  combine  the  two  as  to  form  this  solid  picture.  Three  pictures 


544 


On  Light. 


[622- 


will  in  that  case  be  seen,  the  central  being  solid,  and  the  two  outside  ones 
plane.  Fig.  524  will  explain  this.  Let  r  and  /  be  any  two  correspond- 
ing points,  say  the  points  marked  by  a  large  dot 
in  the  figures  drawn  above  ;  R  and  L  the  positions 
of  the  right  and  left  eyes  ;  then  the  right  eye  sees 
the  point  r  in  the  direction  R#,  and  the  left  eye  the 
point  /  in  the  direction  L<?,  and  accordingly  each 
by  itself  judging  only  by  the  direction,  they  together 
see  these  two  points  as  one,  and  imagine  it  to  be 
situated  at  o.  But  the  right  eye,  though  looking 
in  the  direction  Rr,  also  receives  an  image  of  /  on 
another  part  of  the  retina,  and  the  left  eye  in  the 
same  way  an  image  of  r,  and  thus  three  images 
are  seen.  A  card,  however,  placed  in  the  position 
marked  by  the  dotted  line  will,  of  course,  cut  off 
the  two  side  pictures.  To  assist  the  eye  in  com- 
bining such  pairs  of  dissimilar  pictures,  both 
mirrors  and  lenses  have  been  made  use  of,  and  the 
instruments  in  which  either  of  these  are  adapted 
to  this  end  are  called  stereoscopes. 

623.  The  reflecting:  stereoscope. — In  the  reflecting  stereoscope  plane 
mirrors  are  used  to  change  the  apparent  position  of  the  pictures,  so  that  they 
are  both  seen  in  the  same  direction,  and  their  combination  by  the  eye  is  thus 
rendered  easy  and  almost  inevitable.  If  ab,  ab  (fig.  525)  are  two  plane 


Fig-  524- 


C6 

L  R 

Fig.  525- 

mirrors  inclined  to  one  another  at  an  angle  of  90°,  the  two  arrows,  .r,  _y,  would 
both  be  seen  by  the  eyes  situated  at  R  and  L  in  the  position  marked  by  the 
dotted  arrow.  If,  instead  of  the  arrows,  we  now  substitute  such  a  pair  of 
dissimilar  pictures  as  we  have  spoken  of  above,  of  the  same  solid  object,  it 
is  evident  that,  if  the  margins  of  the  pictures  coincide,  other  corresponding 
points  of  the  pictures  will  not.  The  eyes,  however,  almost  without  effort, 
soon  bring  such  points  into  coincidence,  and  in  so  doing  make  them  appear 
to  recede  or  advance,  as  they  are  farther  apart  or  nearer  together  than  any 
two  corresponding  points  (the  right-hand  corner,  for  instance)  of  the  margins, 
when  the  pictures  are  placed  side  by  side,  as  in  the  diagram  fig.  525.  It  will 
be  plain,  also,  on  considering  the  position  for  the  arrows  in  fig.  525,  that  to 


-624]  The  Refracting  Stereoscope.  545 

adapt  such  pictures  as  those  in  fig.  524  for  use  in  a  reflecting  stereoscope 
one  of  them  must  be  reversed,  or  drawn  as  it  would  be  seen  through  the 
paper  if  held  up  to  the  light. 

624.  The  refracting  stereoscope.— Since  the  rays  passing  through  a 
convex  lens  are  bent  always  towards  the  thicker  part  of  the  lens,  any  seg- 
ment of  such  a  lens  may  be  readily  adapted  to  change  the  apparent  position 
of  any  object  seen  through  it.  Thus,  if  (fig.  526)  two  segments  be  cut  from 
a  double  convex  lens,  and  placed  with  their  edges  together,  the  arrows,  x,  y, 
would  both  be  seen  in  the  position  of  the  dotted  arrow  by  the  eyes  at  R 
and  L. 

1  f  we  substitute  for  the  arrows  two  dissimilar  pictures  of  the  same  solid 
object,  or  the  same  landscape,  we  shall  then,  if  a  diaphragm,  ab,  be  placed 
between  the  lenses  to  prevent  the  pictures  being  seen  crosswise  by  the  eyes, 
see  but  one  picture,  and  that  apparently  in  the  centre,  and  magnified.  As 
before,  if  the  margins  are  brought  by  the  power  of  the  lenses  to  coincide, 
other  corresponding  points  will  not  be  coincident 
until  combined  by  an  almost  insensible  effort  of  the 
eyes.  Any  pair  of  corresponding  points  which  are 
farther  apart  than  any  other  pair  will  then  be  seen 
farther  back  in  the  picture,  just  as  any  point  in  the 
background  of  a  landscape  would  be  found  (if  we 
came  to  compare  two  pictures  of  the  landscape,  one 
drawn  by  the  right  eye,  and  the  other  by  the  left)  to 
be  represented  by  two  points  farther  apart  from  one 
another  than  two  others  which  represented  a  point  in 
the  foreground. 

To  any  one  curious  in  such  experiments,  it  will  be 
instructive  to  notice  that  there  is  also  a  second  point 
on  this  side  of  the  paper,  at  which,  if  a  person  look 
steadily,  the  diagrams  in  fig.  527  will  combine,  and  form  quite  a  different 
stereoscopic  picture.  Instead  of  a  solid  pyramid,  a  hollow  pyramidal  box 
will  then  be  seen.  The  point  may  easily  be  found  by  experiment.  Here 
again  two  external  images  will  also  be  seen.  If  we  wish  to  shut  these  out, 
and  see  only  their  central  stereoscopic  combination,  we  must  use  a  diaphragm 
of  paper  held  parallel  to  the  plane  of  the  picture  with  a  square  hole  in  it. 
This  paper  screen  must  be  so  adjusted  that  it  may  conceal  the  right-hand 
figure  from  the  left  eye,  and  the  left-hand  figure  from  the  right  eye,  while  the 
central  stereoscopic  picture  may  be  seen  through  the  hole.  It  will  be  plain 
from  the  diagram  that  o  is  the  point  to  which  the  eyes  must  be  directed, 
and  at  which  they  will  imagine  the  point  to  be  situated,  which  is  formed 
by  the  combination  of  the  two  points  r  and  /.  The  dotted  line  shows  the 
position  of  the  screen.  A  stereoscope  with  or  without  lenses  may  easily  be 
constructed,  which  will  thus  give  us,  with  the  ordinary  stereoscopic  slides,  a 
reversed  picture  ;  for  instance,  if  the  subject  be  a  landscape,  the  foreground 
will  retire  and  the  background  come  forward. 

When  the  two  retinas  view  simultaneously  two  different  colours,  the  im- 
pression produced  is  that  of  a  single  mixed  tint.  The  power,  however,  of 
combining  the  two  tints  into  a  single  one  varies  in  different  individuals,  and 
in  some  is  extremely  weak.  If  two  white  discs  at  the  base  of  the  stereoscope 


546  On  Light.  [624- 

be  illuminated  by  two  pencils  of  complementary  colours,  and  if  each  coloured 
disc  be  looked  at  with  one  eye,  a  single  white  one  is  seen,  showing  that  the 
sensation  of  white  light  may  arise  from  two  complementary  and  simultaneous 
chromatic  impressions  on  each  of  the  two  retinas. 

Dove  states  that  if  a  piece  of  printing  and  a  copy  are  placed  in  the  stereo- 
scope, a  difference  in  the  distance  of  the  words,  which  is  not  apparent  to 
the  naked  eye,  causes  them  to  stand  out  from  the  plane  of  the  paper. 

625.  Persistence   of  impressions    on  the  retina. — When    an    ignited 
piece  of  charcoal  is  rapidly  rotated,  we  cannot  distinguish  it ;  the  appearance 
of  a  circle  of  fire  is  produced  ;  similarly,  rain,  in  falling  drops,  appears  in 
the  air  like  a  series  of  liquid  threads.     In  a  rapidly  rotating  toothed  wheel 
the  individual  teeth  cannot  be  seen.     But  if,  during  darkness,  the  wheel  be 
suddenly  illuminated,  as  by  the  electric  spark,  the  individual  parts  may  be 
clearly  made  out.     These  various  appearances  are  due  to  the  fact  that  the 
impression  of  these  images  on  the  retina  remains  for  some  time  after  the 
object  which  has  produced  them  has  disappeared   or  become   displaced. 
The  duration  of  the  persistence  varies  with  the  sensitiveness  of  the  retina 
and  the  intensity  of  light.     The  following  experiment  is  a  further  illustration 
of  this  property  : — A  series  of  equal  sectors  are  traced  on  a  disc  of  glass, 
and  they  are  alternately  blackened  ;  in  the  centre  there  is  a  pivot,  on  which 
a  second  disc  is  fixed  of  the  same  dimensions  as  the  first,  but  completely 
blackened,  with  the  exception  of  a  single  sector  ;  then  placing  the  apparatus 
between  a  window  and  the  eye,  the  second  disc  is  made  to  rotate.     If  the 
movement  is  slow,  all  the  transparent  sectors  are  seen,  but  only  one  at  a 
time  ;  by  a  more  rapid  rotation  we  see  simultaneously  two,  three,  or  a  greater 
number. 

Plateau  investigated  the  duration  of  the  impression  by  numerous  similar 
methods,  and  has  found  that  it  is  on  the  average  half  a  second.  Among 
many  curious  instances  of  these  phenomena,  the  following  is  one  of  the  most 
remarkable.  If,  after  having  looked  at  a  brightly  illuminated  window,  the 
eyes  are  suddenly  closed,  the  image  remains  for  a  few  instants — that  is,  a 
sashwork  is  seen  consisting  of  luminous  panes  surrounded  by  dark  frames  ; 
after  a  few  seconds  the  colours  become  interchanged,  the  same  framework  is 
now  seen,  but  the  frames  are  now  bright,  and  the  glasses  are  perfectly  black ; 
this  new  appearance  may  again  revert  to  its  original  appearance. 

The  impression  of  colours  remains  as  well  as  that  of  the  form  of  objects ; 
for  if  circles  divided  into  sectors  are  painted  in  different  colours,  they  be- 
come confounded,  and  give  the  sensation  of  the  colour  which  would  result 
from  their  mixture.  Yellow  and  red  give  orange  ;  blue  and  red  violet  ;  the 
seven  colours  of  the  spectrum  give  white,  as  shown  in  Newton's  disc  (fig. 
471).  This  is  a  convenient  method  of  studying  the  tints  produced  by  mixed 
colours. 

A  great  number  of  pieces  of  apparatus  are  founded  on  the  persistence 
of  sensation  on  the  retina,  such  are  the  thaumatrope,  the  phenakistoscope, 
Faraday's  wheel,  the  kaleidophone. 

626.  Accidental  images. — A  coloured  object  being  placed  upon  a  black 
ground,  if  it  is  steadily  looked  at  for  some  time,  the  eye  is  soon  tired,  and 
the  intensity  of  the  colour  enfeebled  ;  if  now  the  eyes  are  directed  towards 
a  white  sheet,  or  to  the  ceiling,  an  image  will  be  seen  of  the  same  shape  as 


-627]  Irradiation.  547 

the  object,  but  of  the  complementary  colour  (570) ;  that  is,  such  a  one  as 
united  to  that  of  the  object  would  form  white.  For  a  green  object  the  image 
will  be  red  ;  if  the  object  is  yellow,  the  image  will  be  violet. 

Accidental  colours  are  of  longer  duration  in  proportion  as  the  object  has 
been  more  brilliantly  illuminated,  and  the  object  has  been  longer  looked  at. 
When  a  lighted  candle  has  been  looked  at  for  some  time,  and  the  eyes  are 
turned  towards  a  dark  part  of  the  room  the  appearance  of  the  flame  remains, 
but  it  gradually  changes  colour  ;  it  is  first  yellow,  then  it  passes  through 
orange  to  red,  from  red  through  violet  to  greenish  blue,  which  is  gradually 
feebler  until  it  disappears.  If  the  eye  which  has  been  looking  at  the  light  be 
turned  towards  a  white  wall,  the  colours  follow  almost  the  opposite  direction  : 
there  is  first  a  dark  picture  on  a  white  ground,  which  gradually  changes  into 
blue,  is  then  successively  green  and  yellow,  and  ultimately  cannot  be  distin- 
guished from  a  white  ground. 

The  reason  of  this  phenomenon  is,  doubtless,  to  be  sought  in  the  fact 
that  the  subsequent  action  of  light  on  the  retina  is  not  of  equal  duration  for 
all  colours,  and  that  the  decrease  in  the  intensity  of  the  subsequent  action 
does  not  follow  the  same  law  for  all  colours. 

627.  Irradiation. — This  is  a  phenomenon  in  virtue  of  which  white  objects, 
or  those  of  a  very  bright  colour,  when  seen  on  a  dark  ground,  appear  larger 
than  they  really  are.     Thus,  a  white  square  upon  a  black 
ground  seems  larger  than  an  exactly  equal  black  square 
upon  a  white  ground  (fig.   528).     Irradiation  arises  from 
the  fact  that  the  impression  produced  on  the  retina  extends 
beyond  the  outline  of  the  image.     It  bears  the  same  rela- 
tion to  the  space  occupied  by  the  image  that  the  duration 
of  the  impression  does  to  the  time  during  which  the  image 
is  seen. 

The  effect  of  irradiation  is  very  perceptible  in  the  appa- 
rent magnitude  of  stars,  which  may  thus  appear  much 
larger  than  they  really  are  ;  also  in  the  appearance  of  the 
moon  when  two  or  three  days  old,  the  brightly  illuminated  Fig.  528. 

crescent  seeming  to  extend  beyond  the  darker  portion  of 
the  disc,  and  hold  it  in  its  grasp. 

Plateau  found  that  irradiation  differs  very  much  in  different  people,  and 
even  in  the  same  person  it  differs  on  different  days.  He  also  found  that 
irradiation  increases  with  the  lustre  of  the  object,  and  the  length  of  time 
during  which  it  is  viewed.  It  manifests  itself  at  all  distances  ;  diverging 
lenses  increase  and  condensing  lenses  diminish  it. 

Accidental  haloes  are  the  colours  which,  instead  of  succeeding  the  im- 
pression of  an  object  like  accidental  colours,  appear  round  the  object  itself 
when  it  is  looked  at  fixedly.  The  impression  of  the  halo  is  the  opposite  to 
that  of  the  object :  if  the  object  is  bright  the  halo  is  dark,  and  vice  versa. 
These  appearances  are  best  produced  in  the  following  manner  : — A  white 
surface,  such  as  a  sheet  of  paper,  is  illuminated  by  coloured  light,  and  a 
narrow  opaque  body  held  so  as  to  cut  off  some  of  the  coloured  rays.  In 
this  manner  a  narrow  shadow  is  obtained  which  is  illuminated  by  the  sur- 
rounding white  daylight,  and  appears  complementary  to  the  coloured  ground. 


548  On  Light.  [627- 

If  red  glass  is  used,  the  shadow  appears  'green,  and  blue  when  a  yellow 
glass  is  used. 

The  contrast  of  colours  is  a  reciprocal  action  exerted  between  two  adja- 
cent colours,  and  in  virtue  of  which  to  each  one  is  added  the  complemen- 
tary colour  of  the  other.  Chevreul  found  that  when  red  and  yellow  colours 
are  adjacent,  red  acquires  a  violet  and  yellow  an  orange  tint.  If  the  experi- 
ment is  made  with  red  and  blue,  the  former  acquires  a  yellow,  and  the  latter 
a  green  tint :  with  yellow  and  blue,  yellow  passes  to  orange,  and  blue  towards 
indigo  :  and  so  on  for  a  vast  number  of  combinations.  The  importance  of 
this  phenomenon  in  its  application  to  the  manufacture  of  cloths,  carpets, 
curtains,  &c.,  may  be  readily  conceived. 

628.  The  eye  is  not  achromatic. — It  had  long  been  supposed  that  the 
human  eye  was  perfectly  achromatic  ;  but  this  is  clearly  impossible,  as  all  the 
refractions  are  made  the  same  way,  viz.  towards  the  axis  ;  moreover,  the  ex- 
periments of  Wollaston,  of  Young,  of  Fraunhofer,  and  of  Miiller,  have  shown 
that  it  was  not  true  in  any  absolute  sense. 

Fraunhofer  showed  that  in  a  telescope  with  two  lenses,  a  very  fine  wire 
placed  inside  the  instrument  in  the  focus  of  the  object-glass  is  seen  distinctly 
through  the  eyepiece,  when  the  telescope  is  illuminated  with  red  light  ;  but 
it  is  invisible  by  violet  light  even  when  the  eyepiece  is  in  the  same  position. 
In  order  to  see  the  wire  again,  the  distance  of  the  lenses  must  be  diminished 
to  a  far  greater  extent  than  would  correspond  to  the  degree  of  refrangibility 
of  violet  light  in  glass.  In  this  case,  therefore,  the  effect  must  be  due  to  a 
chromatic  aberration  in  the  eye. 

Miiller,  on  looking  at  a  white  disc  on  a  dark  ground,  found  that  the  image 
is  sharp  when  the  eye  is  accommodated  to  the  distance  of  the  disc — that  i.s, 
when  the  image  forms  on  the  retina  ;  but  he  found  that,  if  the  image  is  formed 
in  front  of  or  behind  the  retina,  the  disc  appears  surrounded  by  a  very  nar- 
row blue  edge.  If  a  finger  be  held  up  in  front  of  one  eye  (the  other  being 
closed)  in  such  a  manner  as  to  allow  the  light  to  enter  only  one-half  of  the 
pupil,  and,  of  course,  obliquely,  and  the  eye  be  then  directed  to  any  well- 
defined  line  of  light,  such  as  a  slit  in  the  shutter  of  a  darkened  room,  or 
a  strip  of  white  paper  on  a  black  ground,  this  line  of  light  will  appear  as  a 
complete  spectrum. 

Miiller  concluded  from  these  experiments  that  the  eye  is  sensibly  achro- 
matic as  long  as  the  image  is  received  at  the  focal  distance,  or  when  it  is 
accommodated  to  the  distance  of  the  object.  The  cause  of  this  apparent 
achromatism  cannot  be  exactly  stated.  It  has  generally  been  attributed  to 
the  tenuity  of  the  luminous  beams  which  pass  through  the  pupillary  aperture, 
and  that  these  unequally  refrangible  rays,  meeting  the  surfaces  of  the  media 
of  the  eye  almost  at  the  normal  incidence,  are  very  little  refracted,  from 
which  it  follows  that  the  chromatic  aberration  is  imperceptible  (584). 

Spherical  aberration,  as  we  have  already  seen,  is  corrected  by  the  iris 
(612).  The  iris  is,  in  point  of  fact,  a  diaphragm,  which  stops  the  marginal 
rays,  and  only  allows  those  to  pass  which  are  near  the  axis. 

629.  Short  sight  and  long  sight;  myopy  and  presbytism. — The  most 
usual  affections  of  the  eye  are  myopy  and  presbytism,  or  short  sight  and  long 
sight.     Short  sight  is  the  habitual  accommodation  of  the  eyes  for  a  distance 
less  than  that  of  ordinary  vision,  so  that  persons  affected  in  this  way  only 


-630]  Eye-glasses.     Spectacles.  549 

see  very  near  objects  distinctly.  The  usual  cause  of  short  sight  is  a  too 
great  convexity  of  the  cornea  or  of  the  crystalline  ;  the  eye  being  then  too 
convergent,  'the  focus,  in  place  of  forming  on  the  retina,  is  formed  in  front, 
so  that  the  image  is  indistinct.  It  may  be  remedied  by  means  of  diverging 
glasses,  which  in  making  the  rays  deviate  from  their  common  axis  throw 
the  focus  farther  back,  and  cause  the  image  to  be  formed  on  the  retina. 

The  habitual  contemplation  of  small  objects—  as  when  children  are  too 
much  accustomed,  in  reading  and  writing,  to  place  the  paper  close  to  their 
eyes,  or  working  with  a  microscope  —  may  produce  short  sight.  It  is  common 
in  the  case  of  young  people,  but  diminishes  with  age. 

Long  sight  is  the  contrary  of  short  sight  :  the  eye  can  see  distant  objects 
very  well,  but  cannot  distinguish  those  which  are  very  near.  The  cause  of 
long  sight  is  that  the  eye  is  not  sufficiently  convergent,  and  hence  the  image 
of  objects  is  formed  beyond  the  retina  :  but  if  the  objects  are  removed 
farther  off,  the  image  approaches  the  retina,  and  when  they  are  at  a  suitable 
distance  is  exactly  formed  upon  it,  so  that  the  object  is  clearly  seen.  Long 
sight  is  corrected  by  means  of  converging  lenses.  These  glasses  bring  the 
rays  together  before  their  entrance  into  the  eye,  and,  therefore,  if  the  converg- 
ing power  is  properly  chosen,  the  image  will  be  formed  exactly  on  the  retina. 

It  is  not  many  years  since  double  convex  lenses  were  alone  used  for 
long-sighted  persons,  and  double  concave  for  short-sighted  persons.  Wol- 
laston  first  proposed  to  replace  these  glasses  by  concavo-convex  lenses,  C 
and  F  (fig.  447),  so  placed  that  their  curvature  is  in  the  same  direction  as 
that  of  the  eye.  By  means  of  these  glasses  a  much  wider  range  is  attained, 
and  hence  they  have  been  called  periscopic  glasses.  They  have  the  disad- 
vantage of  reflecting  too  much. 

630.  Eye-glasses.  Spectacles.  —  The  glasses  commonly  used  by  short  - 
or  long-sighted  persons  are  known  under  the  general  name  of  eye-glasses  or 
spectacles.  Generally  speaking,  numbers  are  engraved  on  these  glasses 
which  express  their  focal  length  in  inches.  The  spectacles  must  be  so  chosen 
that  they  are  close  to  the  eye,  and  that  they  make  the  distance  of  distinct 
vision  10  or  12  inches. 

The  number  which  a  short-  or  long-sighted  person  ought  to  use  may  be 
calculated,  knowing  the  distance  of  distinct  vision.  The  formula 


serves  for  long-sighted  persons,  where/being  the  'number  'of  the  spectacles 
which  ought  to  be  taken  —  that  is,  the  number  expressing  the  focal  length—/  is 
the  distance  of  distinct  vision  in  ordinary  cases  (about  12  inches),  and  d  the 
distance  of  distinct  vision  for  the  person  affected  by  long  sight. 

The  above  formula  is  obtained  from  the  equation  —  —  L  =  L   by  substitu- 

p    p     f 

ting  d  for  p'.  In  this  case  the  formula  (6)  of  article  559  is  used,  and  not 
formula  (5),  because  the  image  seen  by  spectacles  being  on  the  same  side  of 
the  object  in  reference  to  the  lens,  the  sign  p'  ought  to  be  the  opposite 
of  that  of/,  as  in  the  case  of  virtual  images  from  the  paragraph  already  cited. 

For  short-sighted  persons,  /  is   calculated   by  the  formula  1  -  1  =  -  I 

P    P        f 


550  On  Light.  [630- 

(559))  which  refers  to  concave  lenses,  and  which,  replacing^'  by  d,  gives 


To  calculate,  for  instance,  the  number  of  a  glass  which  a  person  ought 
to  use  in  whom  the  distance  of  distinct  vision  is  36,  knowing  that  the  dis- 
tance of  ordinary  distinct  vision  is  12  inches  ;  making  p-12  and  d=-  36  in 

the  above  formula  (i),  we  get  /=  ^  —  l—  =  18. 

631.  Diplopy.  —  Diplopy  is  an  affection  of  the  eye  which  causes  objects 
to  be  seen  double  ;  that  is,  that  two  images  are  seen  instead  of  one.     Usually 
the  two  images  are  almost  entirely  superposed,  and  one  of  them  is  much 
more  distinct  than  the  other.     Diplopy  may  be  caused  by  the  co-operation 
of  two  unequal  eyes,  but  it  may  also  affect  a  single  eye.     The  latter  case  is, 
doubtless,  due  to  some  affect  of  conformation  in  the  crystalline  or  other 
parts  of  the  eye  which  produces  a  bifurcation  of  the  luminous  ray,  and  thus 
two  images  are  formed  on  the  retina  instead  of  one.     A  single  eye  may  also 
be  affected  with  triplopy,  but  in  this  case  the  third  image  is  exceedingly 
weak. 

632.  Achromatopsy.     Daltonism.  —  Achromatopsy,  or  colour  disease,  is 
a  curious  affection  which  renders  us  incapable  of  distinguishing  colours,  or  at 
any  rate  certain  colours.     Persons  affected  in  this  manner  can  distinguish  the 
outlines  of  bodies  without  difficulty,  and  they  can  also  discriminate  between 
light  and  shade,  but  they  are  unable  to  distinguish  the  different  colours. 

The  commonest  case  is  that  of  red-blindness  ;  Dalton  had  it  in  a  pre- 
eminent degree,  and  from  the  fact  that  he  has  very  carefully  described  it, 
the  disease  is  often  known  as  Daltonism.  To  a  person  so  affected  red  appears 
like  black,  and  the  brighter  shades  bluish-green  ;  bluish-green  and  white 
seem  the  same,  or  at  all  events  only  different  in  shade.  Yellow  appears 
like  green,  but  he  distinguishes  between  them,  for  the  yellow  appears 
brighter. 

He  who  is  blind  for  green,  sees  that  colour  as  black,  and  its  lighter  shades 
red.  He  only  sees  red  and  blue  with  their  intermediate  stages  ;  yellow 
appears  bright  red  ;  white  and  pink  are  alike,  the  spectrum  is  only  red  and 
blue  ;  in  the  green  there  is  a  grey  band.  Violet-blindness  is  very  infrequent 
and  not  well  known  ;  it  can  be  artificially  produced  by  taking  Santonine. 
Colour  disease  is  usually  congenital  ;  it  has,  however,  been  produced  by 
straining  the  eyes  in  dim  light. 

Owing  to  the  difference  in  even  healthy  individuals  as  regards  their  per- 
ception of  different  shades  of  colour,  the  only  certain  means  of  discerning 
any  particular  tint  is  to  define  its  position  by  means  of  the  nearest  Fraun- 
hofer's  line  (574). 

633.  Ophthalmoscope.  —  This  instrument,  as  its  name  indicates,  is  de- 
signed for  the  examination  of  the  eye,  and  was  invented  in   1851  by  Prof. 
Helmholtz.     It  consists  :  —  I.  Of  a  concave  spherical  reflector  of  glass  or 
metal,  M  (figs.  529,  530),  in  the  middle  of  which  is  a  small  hole  about  a 
sixth  of  an  inch  in  diameter.     The  focal  length  of  the  reflector  is  from  8  to 
10  inches.     2.  Of  a  converging  achromatic  lens,  o,  which  is  held  in  front  of 
the  eye  of  the  patient.     3.  Of  several  lenses,  some  convergent,  others  diver- 


-633]  Ophthalmoscope.  551 

gent,  any  one  of  which  can  be  fixed  in  a  frame  behind  the  mirror  so  as  to 
correct  any  given  imperfection  in  the  observer's  sight.  If  the  mirror  is  of 
silvered  glass,  it  is  not  necessary  that  it  be  pierced  at  the  centre  ;  it  is  suf- 
ficient that  the  silvering  at  the  centre  be  removed. 

To  make  use  of  the  ophthalmoscope,  the  patient  is  placed  in  a  darkened 
room,  and  a  lamp  furnished  with  a  screen  put  beside  him,  E.     The  screen 


Fig.  529- 

serves  to  shade  the  light  from  his  head,  and  keep  it  in  darkness.  The  ob- 
server, A,  holding  in  one  hand  the  reflector,  employs  it  to  concentrate  the 
light  of  the  lamp  near  the  eye,  B,  of  the  patient,  and  with  his  other  hand 
holds  the  achromatic  lens,  0,  in  front  of  the  eye.  By  this  arrangement  the 
back  of  the  eye  is  lighted  up,  and  its  structure  can  be  clearly  discerned. 

Fig.  530  shows  how  the  image  of  the  back  of  the  eye  is  produced,  which 
the  observer,  A,  sees  on  looking  through  the  hole  in  the  reflector.     Let  ab 


530. 


be  the  part  of  the  retina  on  which  the  light  is  concentrated,  pencils  of  rays 
proceeding  from  ab  would  form  an  inverted  and  aerial  image  of  ab  at  ab'  . 
These  pencils,  however,  on  leaving  the  eye,  pass  through  the  lens  0,  and 
thus  the  image  a"b"  is  in  fact  formed,  inverted,  but  distinct,  and  in  a  position 
fit  for  vision.  The  great  quantity  of  light  concentrated  by  the  ophthalmoscope 
is  apt  to  irritate  painfully  the  eye  of  the  patient.  There  are,  therefore,  inter- 
posed between  the  -lamp  and  the  reflector  coloured  glasses,  to  cut  off  the 
irritating  rays,  viz.  the  red,  yellow,  and  violet  rays.  The  glasses  generally 
employed  are  stained  green  or  cobalt  blue. 

By  means  of  the  ophthalmoscope  Helmholtz  has  found  that  in  an  optical 
point  of  view  no  eye  is  free  from  defects. 


552  On  Light.  [634- 


CHAPTER  VII. 

SOURCES   OF  LIGHT.      PHOSPHORESCENCE. 

634.  Various  sources  of  light. — The  various  sources  of  light  are  the 
sun,  the  stars,  heat,  chemical  combination,  phosphorescence,  electricity,  and 
meteoric  phenomena.     The  last  two  sources  will  be  treated  under  the  articles 
Electricity  and  Meteorology. 

The  origin  of  the  light  emitted  by  the  sun  and  by  the  stars  is  unknown  ; 
it  is  assumed  that  the  ignited  envelope  by  which  the  sun  is  surrounded  is 
gaseous,  because  the  light  of  the  sun,  like  that  emitted  from  all  gaseous 
bodies,  gives  no  trace  of  polarisation  in  the  polarising  telescope  (Chapter 
VIII.). 

As  regards  the  light  developed  by  heat,  Pouillet  has  observed  that  bodies 
begin  to  be  luminous  in  the  dark  at  a  temperature  of  500°  to  600°  ;  above 
that  the  light  is  brighter  in  proportion  as  the  temperature  is  higher. 

The  luminous  effects  witnessed  in  many  chemical  combinations  are  due 
to  the  high  temperatures  produced.  This  is  the  case  with  the  artificial  lights 
used  for  illuminations,  for  ordinary  luminous  flames  are  nothing  more  than 
gaseous  matters  containing  solids  heated  to  incandescence. 

635.  Phosphorescence :    its  sources. — Phosphorescence  is  the  property 
which  a  large  number  of  substances  possess  of  emitting  light  when  placed 
under  certain  conditions. 

The  various  phenomena  may  be  referred  to  five  causes  : — 

i.  Spontaneous  phosphorescence  in  certain  vegetables  and  animals  ;  for 
instance,  it  is  very  intense  in  the  glow-worm  and  in  the  lampyre,  and  the 
brightness  of  their  light  appears  to  depend  on  their  will.  In  tropical  climates 
the  sea  is  often  covered  with  a  bright  phosphorescent  light  due  to  some 
extremely  small  zoophytes.  These  animalculas  emit  a  luminous  matter  so 
subtile  that  Quoy  and  Gaimard,  during  a  voyage  under  the  equator,  having 
placed  two  in  a  tumbler  of  water,  the  liquid  immediately  became  luminous 
throughout  its  entire  mass. 

ii.  Phosphorescence  by  elevation  of  temperature.  This  is  best  seen  in 
certain  species  of  'diamonds,  and  particularly  in  chlorophane,  a  variety  of 
fluorspar,  which,  when  heated  to  300°  or  400°,  suddenly  becomes  luminous, 
emitting  a  greenish-blue  light. 

iii.  Phosphorescence  by  mechanical  effects,  such  as  friction,  percussion, 
cleavage,  &c.  ;  for  example,  when  two  crystals  of  quartz  are  rubbed  against 
each  other  in  darkness,  or  when  a  lump  of  sugar  is  broken. 

iv.  Phosphorescence  by  electricity,  like  that  which  results  from  the  friction 
of  mercury  against  the  glass  in  a  barometric  tube,  and  especially  from  the 
electric  sparks  proceeding  either  from  an  ordinary  electrical  machine,  or 
from  a  Ruhmkorff's  coil. 


-636]  Phosphorescence  by  Insolation.  553 

v.  Phosphorescence  by  insolation  or  exposure  to  the  sun.  A  large  number 
of  substances,  after  having  been  exposed  to  the  action  of  sunlight,  or  of 
the  diffused  light  of  the  atmosphere,  emit  in  darkness  a  phosphorescence, 
the  colour  and  intensity  of  which  depend  on  the  nature  and  physical  condi- 
tion of  these  substances. 

636.  Phosphorescence  toy  insolation. — This  was  first  observed  in  1604 
in  Bolognese  phosphorus  (sulphide  of  barium),  but  Becquerel  also  disco- 
vered it  in  a  great  number  of  substances.  The  sulphides  of  calcium  and 
strontium  are  those  which  present  it  in  the  highest  degree.  When  well  pre- 
pared, after  being  exposed  to  the  light,  they  are  luminous  for  several  hours  in 
darkness.  But  as  this  phosphorescence  takes  place  in  a  vacuum  as  well  as 
in  a  gaseous  medium,  it  cannot  be  attributed  to  a  chemical  action,  but  rather 
to  a  temporary  modification  which  the  body  undergoes  from  the  action  of  light. 
After  the  substances  above  named,  the  best  phosphorescents  are  the 
following,  in  the  order  in  which  they  are  placed  :  a  large  number  of  diamonds 
(especially  yellow  ones),  and  most  specimens  of  fluorspar  ;  then  arragonite, 
calcareous  concretions,  chalk,  apatite,  heavy  spar,  dried  nitrate  of  calcium 
and  dried  chloride  of  calcium,  cyanide  of  calcium,  a  large  number  of 
strontium  or  barium  compounds,  magnesium  and  its  carbonate,  &c.  Besides 
these  a  large  number  of  organic  substances  also  become  phosphorescent  by 
insolation  ;  for  instance,  dry  paper,  silk,  cane-sugar,  milk-sugar,  amber,  the 
teeth,  &c. 

The  different  spectral  rays  are  not  equally  well  fitted  to  render  substances 
phosphorescent.  The  maximum  effect  takes  place  in  the  violet  rays,  or  even 
a  little  beyond  ;  while  the  light  emitted  by  phosphorescent  bodies  generally 
corresponds  to  rays  of  a  smaller  refrangibility  than  those  of  the  light  received 
by  them  and  giving  rise  to  the  action. 

The  tint  which  phosphorescent  bodies  assumes  is  very  variable,  and  even 
in  the  same  body  it  changes  with  the  manner  in  which  it  is  prepared.  In 
strontium  compounds  green  and  blue  tints  predominate  ;  and  orange,  yellow, 
and  green  tints  in  the  sulphides  of  barium. 

The  duration  of  phosphorescence  varies  also  in  different  bodies.  In  the 
sulphides  of  calcium  and  strontium,  phosphorescence  lasts  as  long  as  thirty 
hours  ;  with  other  substances  it  does  not  exceed  a  few  seconds,  or  even  a 
fraction  of  a  second. 

The  colour  emitted  by  an  artificial  phosphorescent  alters  with  the 
temperature  during  insolation.  Thus  with  sulphide  of  strontium  the  light  is 
dark  violet  at  —20°  C,  bright  blue  at  +40°,  bluish  green  at  70°,  greenish 
yellow  at  100°,  and  reddish  yellow  of  feeble"  luminosity  at  200°  C. 

Phosphoroscope.  In  experimenting  with  bodies  whose  phosphorescence 
lasts  a  few  minutes  or  even  a  few  seconds,  it  is  simply  necessary  to  expose 
them  to  solar  or  diffused  light  for  a  short  time,  and  then  place  them  in  dark- 
ness :  their  luminosity  is  very  apparent,  especially  if,  care  has  been  taken  to 
close  the  eyes  previously  for  a  few  moments.  But  in  the  case  of  bodies  whose 
phosphorescence  lasts  only  a  very  short  time,  this  method  is  inadequate. 
Becquerel  invented  a  very  ingenious  apparatus,  \hzphosphoroscope,  by  which 
bodies  can  be  viewed  immediately  after  being  exposed  to  light  :  the  interval 
which  separates  the  insolation  and  observation  can  be  made  as  small  as  pos- 
sible, and  measured  with  great  precision. 

B  B 


554 


On  Light. 


[636- 


This  apparatus,  which  is  constructed  by  Duboscq,  consists  of  a  closed 
cylindrical  box,  AB  (fig.  532),  of  blackened  metal ;  on  the  ends  are  two 
apertures  opposite  each  other  which  have  the  form  of  a  circular  sector.  One 
only  of  these,  o,  is  seen  in  the  figure.  The  box  is  fixed,  but  it  is  traversed  in 
the  centre  by  a  movable  axis,  to  which  are  fixed  two  circular  screens,  MM 
and  PP,  of  blackened  metal  (fig.  531).  Each  of  these  screens  is  perforated 
by  four  apertures  of  the  same  shape  as  those  in  the  box  ;  but  while  the  latter 


Fig.  532- 

correspond  to  each  other,  the  apertures  of  the  screens  alternate,  so  that  the 
open  parts  of  the  one  correspond  to  the  closed  parts  of  the  other.  The  two 
screens,  as  already  mentioned,  are  placed  in  the  box,  and  fixed  to  the  axis, 
which  by  means  of  a  train  of  wheels,  worked  by  a  handle,  can  be  made  to 
turn  with  any  velocity. 

In  order  to  investigate  the  phosphorescence  of  any  body  by  means  of 
this  instrument,  the  body  is  placed  on  a  stirrup  interposed  between  the  two 
rotating  screens.  The  light  cannot  pass  at  the  same  time  through  the 
opposite  apertures  of  the  sides  A  and  B,  because  one  of  the  closed  parts  of 
the  screen  MM,  or  of  the  screen  PP,  is  always  between  them.  So  that  when 


-636]  Phosphoroscope.  555 

a  body,  «,  is  illuminated  by  light  from  the  other  side  of  the  apparatus,  it 
could  not  be  seen  by  an  observer  looking  at  the  aperture  o,  for  then  it  would 
be  masked  by  the  screen  PP.  Accordingly,  when  an  observer  saw  the  body 
«,  it  would  not  be  illuminated,  as  the  light  would  be  intercepted  by  the  closed 
parts  of  the  screen  MM.  The  body  a  would  alternately  appear  and  dis- 
appear ;  it  would  disappear  during  the  time  of  its  being  illuminated,  and 
appear  when  it  was  no  longer  so.  The  time  which  elapses  between  the 
appearance  and  disappearance  depends  on  the  velocity  of  rotation  of  the 
screens.  Suppose,  for  instance,  that  they  made  1 50  turns  in  a  second  ;  as 
one  revolution  of  the  screens  is  effected  in  ~o  °f  a  second,  there  would  be 
four  appearances  and  four  disappearances  during  that  time.  Hence  the 
length  of  time  elapsing  between  the  time  of  illumination  and  of  observation 
would  be  J  of  T|5  of  a  second  or  0-0008  of  a  second. 

Observations  with  the  phosphoroscope  are  made  in  a  dark  chamber,  the 
observer  being  on  that  side  on  which  is  the  wheelwork.  A  ray  of  solar  or 
electric  light  is  allowed  to  fall  upon  the  substance  #,  and,  the  screens 
being  made  to  rotate  more  or  less  rapidly,  the  body  a  appears  luminous  by 
transparence  in  a  continuous  manner,  when  the  interval  between  insolation 
and  observation  is  less  than  the  duration  of  the  phosphorescence  of  the  body. 
By  experiments  of  this  kind,  Becquerel  has  found  that  substances  which 
usually  are  not  phosphorescent  become  so  in  the  phosphoroscope  ;  such,  for 
instance,  is  Iceland  spar.  Uranium  compounds  present  the  most  brilliant 
appearance  in  this  apparatus  ;  they  emit  a  very  bright  luminosity  when  the 
observer  can  see  them  0-03  or  0-04  of  a  second  after  insolation.  But  a  large 
number  of  bodies  present  no  effect  in  the  phosphoroscope  ;  for  instance, 
quartz,  sulphur,  phosphorus,  metals,  and  liquids. 


B  H  2 


556  On  Light.  [637- 


CHAPTER   VIII. 

DOUBLE  REFRACTION.      INTERFERENCE.      POLARISATION. 

637.  The  undulatory  theory  of  light. — It  has  been  already  stated  (499) 
that  the  phenomenon  of  light  is  ascribed  to  undulations  propagated  through 
an  exceedingly  rare  medium  called  the  luminiferous  ether,  which  is  supposed 
to  pervade  all  space,  and  to  exist  between  the  molecules  of  the  ordinary 
forms  of  matter.  In  short,  it  is  held  that  light  is  due  to  the  undulations  of 
the  ether,  just  as  sound  is  due  to  undulations  propagated  through  the  air. 
In  the  latter  case  the  undulations  cause  the  drum  of  the  ear  to  vibrate 
and  produce  the  sensation  of  sound.  In  the  former  case,  the  undulations 
cause  points  of  the  retina  to  vibrate  and  produce  the  sensation  of  light. 
The  two  cases  differ  in  this,  that  in  the  case  of  sound  there  is  independent 
evidence  of  the  existence  and  vibration  of  the  medium  (air)  which  propagates 
the  undulation  ;  whereas  in  the  case  of  light  the  existence  of  the  medium 
and  its  vibrations  is  assumed,  because  that  supposition  connects  and  explains 
in  the  most  complete  manner  a  long  series  of  very  various  phenomena. 
There  is,  however,  no  independent  evidence  of  the  existence  of  the  luminife- 
rous ether. 

The  analogy  between  the  phenomena  of  sound  and  light  is  very  close  ; 
thus,  the  intensity  of  a  sound  is  greater  as  the  amplitude  of  the  vibration  of 
each  particle  of  the  air  is  greater,  and  the  intensity  of  light  is  greater  as  the 
amplitude  of  the  vibration  of  each  particle  of  the  ether  is  greater.  Again,  a 
sound  is  more  acute  as  the  length  of  each  undulation  producing  the  sound  is 
less,  or,  what  comes  to  the  same  thing,  according  as  the  number  of  vibrations 
per  second  is  greater.  In  like  manner,  the  colour  of  light  is  different  ac- 
cording to  the  length  of  the  undulation  producing  the  light  :  a  red  light  is 
due  to  a  comparatively  long  undulation,  and  corresponds  to  a  deep  sound, 
while  a  violet  light  is  due  to  a  short  undulation,  and  corresponds  to  an  acute 
sound. 

Although  the  length  of  the  undulations  cannot  be  observed  directly,  yet 
they  can  be  inferred  from  certain  phenomena  with  great  exactness.  The 
following  table  gives  the  lengths,  in  decimals  of  an  inch,  of  the  undulations 
corresponding  to  the  light  at  the  principal  dark  lines  of  the  spectrum  : — 

Length  of  Length  of 

Dark  Undulation  Undulation 

L»ne  in  inches  in  millimetres 

B.    .    .    .    .    .    .    .    .  0-0000271  0-0006874 

C 0-0000258  0-0006562 

D!             ..*....  0-0000232  0-0005897 

E 0-0000207  0-0005271 

F 0-0000191  0-0004862 

G 0-0000169  0-0004311 

Hj 0-0000159  0-0003969 


-638]          Physical  Explanation  of  Single  Refraction.  557 

It  will  he  remarked  that  the  limits  are  very  narrow  within  which  the 
lengths  of  the  undulations  of  the  ether  must  be  comprised,  if  they  are  to  be 
capable  of  producing  the  sensation  of  light.  In  this  respect  light  is  in 
marked  contrast  to  sound.  For  the  limits  are  very  wide  within  which  the 
lengths  of  the  undulations  of  the  air  may  be  comprised  when  they  produce 
the  sensation  of  sound  (244). 

The  undulatory  theory  readily  explains  the  colours  of  different  bodies. 
According  to  that  theory,  certain  bodies  have  the  property  of  exciting  undula- 
tions of  different  lengths,  and  thus  producing  light  of  given  colours.  White 
light  or  daylight  results  from  the  coexistence  of  undulations  of  all  possible 
lengths. 

The  colour  of  a  body  is  due  to  the  power  it  has  of  extinguishing  certain 
vibrations,  and  of  reflecting  others  ;  and  the  body  appears  of  the  colour  pro- 
duced by  the  coexistence  of  the  reflected  vibrations.  A  body  appears  white 
when  it  reflects  all  different  vibrations  in  the  proportion  in  which  they  are 
present  in  the  spectrum  :  it  appears  black  when  it  reflects  light  in  such 
small  quantities  as  not  to  affect  the  eye.  A  red  body  is  one  which  has  the 
property  of  reflecting  in  predominant  strength  those  vibrations  which  pro- 
duce the  sensation  of  red.  This  is  seen  in  the  fact  that,  when  a  piece  of  red 
paper  is  held  against  the  daylight,  and  the  reflected  light  is  caught  on  a 
white  wall,  this  also  appears  red.  A  piece  of  red  paper  in  the  red  part  of 
the  spectrum  appears  of  a  brighter  red,  and  a  piece  of  blue  paper  held  in 
the  blue  part  appears  a  brighter  blue  ;  while  a  red  paper  placed  in  the  violet 
or  blue  part  appears  almost  black,  In  the  last  case  the  red  paper  can  only 
reflect  red  rays,  while  it  extinguishes  the  blue  rays,  and  as  the  blue  of  the 
spectrum  is  almost  free  from  red,  so  little  is  reflected  that  the  paper  appears 
black. 

The  undulatory  theory  likewise  explains  the  colours  of  transparent  bodies. 
Thus,  a  vibrating  motion  on  reaching  a  body  sets  it  in  vibration.  So  also  the 
vibrations  of  the  luminiferous  ether  are  communicated  to  the  ether  in  a  body, 
and.  setting  it  in  motion,  produce  light  of  different  colours.  When  this  motion 
is  transmitted  through  any  body,  it  is  said  to  be  transparent  or  translucent, 
according  to  the  different  degrees  of  strength  with  which  this  transmission  is 
effected.  In  the  opposite  case  it  is  said  to  be  opaque. 

When  light  falls  upon  a  transparent  body,  the  body  appears  colourless  if 
all  the  vibrations  are  transmitted  in  the  proportion  in  which  they  exist  in  the 
spectrum.  But  if  some  of  the  vibrations  are  checked  or  extinguished,  the 
emergent  light  will  be  of  the  colour  produced  by  the  coexistence  of  the  un- 
checked vibrations.  Thus,  when  a  piece  of  blue  glass  is  held  before  the  eye, 
the  vibrations  producing  red  and  yellow  are  extinguished,  and  the  colour  is 
due  to  the  emergent  vibrations  which  produce  blue  light. 

The  undulatory  theory  also  accounts  for  the  reflection  and  refraction  of 
light,  as  well  as  other  phenomena  which  are  yet  to  be  described.  The  ex- 
planation of  the  refraction  of  light  is  of  so  much  importance  that  we  shall 
devote  to  it  the  following  article. 

638.  Physical  explanation  of  single  refraction. — The  explanation  of 
this  phenomenon  by  means  of  the  undulatory  theory  of  light  presupposes 
that  of  the  mode  of  propagation  of  a  plane  wave.  Now,  if  a  disturbance 
originated  at  any  point  of  the  ether,  it  would  be  propagated  as  a  spherical 


558 


On  Light. 


[638- 


wave  in  all  directions  round  that  point  with  a  uniform  velocity.  If,  instead 
of  a  single  point,  we  consider  the  front  of  a  plane  wave,  it  is  evident  that 
disturbances  originate  simultaneously  at  all  points  of  the  front,  and  that 
spherical  waves  proceed  from  each/tof/f/  with  the  same  uniform  velocity. 
Consequently  all  these  spheres  will  at  any  subsequent  instant  be  touched  by 
a  plane  parallel  to  the  original  plane.  The  disturbances  propagated  from  the 
points  in  the  first  position  of  the  wave  will  mutually  destroy  each  other,  ex- 
cept in  the  tangent  plane  ;  consequently  the  wave  advances  as  a  plane  wave, 
its  successive  positions  being  the  successive  positions  of  the  tangent  plane. 
If  the  wave  moves  in  any  medium  with  a  velocity  v,  it  will  describe  a  space 
vt  in  a  time  /,  in  a  direction  at  right  angles  to  the  wave  front. 

In  any  given  moment  let  mn  (fig.  533)  be  the  position  of  the  wave  front  of 
a  ray  of  light,  which,  moving  through  any  medium,  meets  the  plane  surface 

AB  of  any  denser  refracting 
medium.  In  the  same  mo- 
ment in  which  the  wave 
front  reaches  «,  m  becomes 
the  centre  of  a  spherical 
wave  system  which  moves  in 
jf  the  second  medium  ;  and  as 
the  elasticity  of  the  second 
medium  is  different  from 
that  of  the  first,  the  velocity 

533>  of  propagation  of  the  wave  in 

two  media  will  be  different. 
While  the  plane  wave  moves  from  n  to  K,  the  corresponding  wave  starting 
from  m  reaches  the  surface  of  a  sphere  the  radius  of  which  is  less  than  «K, 
if  the  second  medium  is  more  strongly  refracting  than  the  first.  The  incident 
wave  in  like  manner  reaches  mf  and  nf  simultaneously,  and  while  n  moves  to 
K,  m'  moves  to  0',  the  surface  of  a  sphere  the  radius  of  which,  m'o',  is  to  mo 
as  n'  is  to  nK.  All  the  elementary  waves  proceeding  from  points  interme- 
diate to  n  and  K  which  arise  from  the  same  incident  wave,  all  touch  one 
and  the  same  plane  Ko'o,  and  the  refracted  ray  proceeds  in  the  new  medium 
perpendicular  to  this  tangent  plane. 

Now  nK  and  mo  represent  the  velocities  of  light  in  the  unit  of  time  in  the 
two  media  respectively  ;  let  mK  be  taken  as  unit  of  length,  then 

72 K  =  sin  nmK  and  mo  =  sin  mK0. 

Now  mnK  is  the  angle  of  incidence  of  the  ray,  and  mKo  is  the  angle  of1 
refraction;  and  nK  and  mo  are  the  velocities  of  light  in  the  two  media 
respectively  ;  hence  we  see  that  these  velocities  are  to  each  other  in  the 
same  ratio  as  the  sines  of  the  angles  of  incidence  and  refraction  ;  a  conclu- 
sion which  agrees  with  the  results  of  direct  observation  (506)  and  forms  a 
beautiful  confirmation  of  the  truth  of  the  undulatory  theory. 


DOUBLE   REFRACTION. 


639.  Double  refraction. — It  has  been  already  stated  (536),  that  a  large 
number  of  crystals  possess  the  property  of  double  refraction,  in  virtue  of 
which  a  single  incident  ray  in  passing  through  any  one  of  them  is  divided 


-640]  Uniaxial  Crystals.  559 

into  two,  or  undergoes  bifurcation,  whence  it  follows  that,  when  an  object 
is  seen  through  one  of  these  crystals,  it  appears  double.  The  fact  of 
the  existence  of  double  refraction  in  Iceland  spar  was  first  stated  by 
Bartholin  in  1669,  but  the  law  of  double  refraction  was  first  enunciated 
exactly  by  Huyghens  in  his  treatise  on  light  written  in  1678  and  published 
in  1690. 

Crystals  which  possess  this  peculiarity  are  said  to  be  double  refracting. 
It  is  found  to  a  greater  or  less  extent  in  all  crystals  which  do  not  belong  to 
the  cubical  system.  Bodies  which  crystallise  in  this  system,  and  those 
which,  like  glass,  are  destitute  of  crystallisation,  have  no  double  refraction. 
The  property  can,  however,  be  imparted  to  them  when  they  are  unequally 
compressed,  or  when  they  are  cooled  quickly  after  having  been  heated,  in 
which  state  glass  is  said  to  be  unannealed.  Of  all  substances,  that  which 
possesses  it  most  remarkably  is  Iceland  spar  or  carbonate  of  calcium.  In 
many  substances,  the  power  of  double  refraction  can  hardly  be  proved  to 
exist  directly  by  the  bifurcation  of  an  incident  ray  ;  but  its  existence  is  shown 
indirectly  by  their  being  able  to  depolarise  light  (665). 

Fresnel  has  explained  double  refraction  by  assuming  that  the  ether  in 
double  refracting  bodies  is  not  equally  elastic  in  all  directions  ;  from  which 
it  follows  that  the  vibrations,  in  certain  directions  at  right  angles  to  each 
other,  are  transmitted  with  unequal  velocities  ;  these  directions  being  depen- 
dent on  the  constitution  of  the  crystal.  This  hypothesis  is  confirmed  by  the 
property  which  glass  acquires  of  becoming  double  refracting  by  being  un- 
annealed and  by  pressure. 

640.  Uniaxial  crystals. — In  all  double  refracting  crystals  there  is  one 
direction,  and  in  some  a  second  direction  possessing  the  following  property  : — 
When  a  point  is  looked  at  through  the  crystal  in  this  particular  direction,  it 
does  not  appear  double.  The  lines  fixing  these  directions  are  called  optic 
axes  ;  and  sometimes,  though  not  very  properly,  axes  of  double  refraction. 
A  crystal  is  called  uniaxial  when  it  has  one  optic  axis  ;  that  is  to  say,  when 
there  is  one  direction  within  the  crystal  along 
which  a  ray  of  light  can  proceed  without 
bifurcation.  When  a  crystal  has  two  such 
axes,  it  is  called  a  biaxial  crystal. 

The  uniaxial  crystals  most  frequently 
used  in  optical  instruments  are  Iceland  spar, 
quartz,  and  tourmaline.  Iceland  spar  crystal- 
lises in  rhombohedra,  whose  faces  form  with 
each  other  angles  of  105°  5'  or  74°  55'.  It 
has  eight  solid  angles  (see  fig.  534).  Of  Flg' 534* 

these,  two,  situated  at  the  extremities  of  one  of  the  diagonals,  are  severally 
contained  by  three  obtuse  angles.  A  line  drawn  within  one  of  these  two 
angles  in  such  a  manner  as  to  be  equally  inclined  to  the  three  edges  contain- 
ing the  angle  is  called  the  axis  of  the  crystal.  If  all  the  edges  of  the  crystal 
were  equal,  the  axis  of  the  crystal  would  coincide  with  the  diagonal,  ab. 

Brewster  showed  that  in  all  uniaxial  crystals  the  optic  axis  coincides  with 
the  axis  of  crystallisation. 

The  principal  plane  with  reference  to  a  point  of  any  face  of  a  crystal, 
whether  natural  or  artificial,  is  a  plane  drawn  through  that  point  at  right 


560  On  Light.  [640- 

angles  to  the  face  and  parallel  to  the  optic  axis.  If  in  fig.  534  we  suppose 
the  edges  of  the  rhombohedron  to  be  equal,  the  diagonal  plane  abed  contains 
the  optic  axis  (ab),  and  is  at  right  angles  to  the  faces  aedfand  chbg',  conse- 
quently, it  is  parallel  to  the  principal  plane  at  any  point  of  either  of  those 
two  faces.  For  this  reason  abed  is  often  called  the  principal  plane  with 
respect  to  those  faces. 

641.  Ordinary  and  extraordinary  ray. — Of  the  two  rays  into  which  an 
incident  ray  is  divided  on  entering   a  uniaxial  crystal,  one  is  called    the, 
ordinary  and  the  other  the  extraordinary  ray.     The  ordinary  ray  follows 
the  laws  of  single  refraction  ;  that  is,  with  respect  to  that  ray  the  sine  of  the 
angle  of  incidence  bears  a  constant  ratio  to  the  sine  of  the  angle  of  refraction, 
and  the  plane  of  incidence  coincides  with  the  plane  of  refraction.     Except 
in  particular  positions,  the  extraordinary  ray  follows  neither  of  these  laws. 
The  images  corresponding  to  the  ordinary  and  extraordinary  rays  are  called 
the  ordinary  and  extraordinary  images  respectively. 

If  a  transparent  specimen  of  Iceland  spar  be  placed  over  a  dot  of  ink, 
on  a  sheet  of  white  paper,  two  images  will  be  seen.  One  of  them,  the 
ordinary  image,  will  seem  slightly  nearer  to  the  eye  than  the  other,  the  extra- 
ordinary image.  Suppose  the  spectator  to  view  the  dot  in  a  direction  at 
right  angles  to  the  paper,  then,  if  the  crystal,  with  the  face  still  on  the  paper, 
be  turned  round,  the  ordinary  image  will  continue  fixed,  and  the  extraordinary 
image  will  describe  a  circle  round  it,  the  line  joining  them  being  always  in 
the  direction  of  the  shorter  diagonal  of  the  face  of  the  crystal,  supposing  its 
edges  to  be  of  equal  length.  In  this  case  it  is  found  that  the  angle  between, 
the  ordinary  and  extraordinary  ray  is  6°  12'. 

642.  The  laws   of  double   refraction   in  a  uniaxial  crystal. — These 
phenomena  are  found  to  obey  the  following  laws  : — 

i.  Whatever  be  the  plane  of  incidence,  the  ordinary  ray  always  obeys  the 
two  general  laws  of  single  refraction  (537).  The  refractive  index  for  the 
ordinary  ray  is  called  the  ordinary  refractive  index. 

ii.  In  every  section  perpendicular  to  the  optic  axis  the  extraordinary  ray 
also  follows  the  laws  of  single  refraction.  Consequently  in  this  plane  the 
extraordinary  ray  has  a  constant  refractive  index,  which  is  called  the  ordinary 
refractive  index. 

iii.  In  every  principal  section  the  extraordinary  ray  follows  the  second 
law  only  of  single  refraction  ;  that  is,  the  planes  of  incidence  and  refraction 
coincide,  but  the  ratio  of  the  sines  of  the  angles  of  incidence  and  refraction 
is. not  constant.  .., 

iv.  The  velocities  of  light  along  the  rays  are  unequal.  It  can  be  shown 
that  the  difference  between  the  squares  of  the  reciprocals  of  the  velocities 
along  the  ordinary  and  extraordinary  rays  is  proportional  to  the  square  of  the 
sine  of  the  angle  between  the  latter  ray  and  the  axis  of  the  crystal. 

There  is  an  important  difference  between  the  velocity  of  the  ray  and  the 
velocity  of  the  corresponding  plane  wave.  If  the  velocities  of  the  plane 
waves  corresponding  to  the  ordinary  and  extraordinary  rays  are  considered, 
the  difference  between  the  squares  of  these  velocities  is  proportional  to  the 
square  of  the  sine  of  the  angle  between  the  axis  of  the  crystal,  and  the  normal 
to  that  plane  wave  which  corresponds  to  the  extraordinary  ray.  The  normal 
and  the  ray  do  not  generally  coincide. 


-644]  Double  Refraction  in  Biaxial  Crystals.  561 

Huyghens  gave  a  very  remarkable  geometrical  construction,  by  means  of 
which  the  directions  of  the  refracted  rays  can  be  determined  when  the  direc- 
tions of  the  incident  ray  and  of  the  axis  are  known  relatively  to  the  face  of 
the  crystal.  This  construction  was  not  generally  accepted  by  physicists 
until  Wollaston  and  subsequently  Malus  showed  its  truth  by  numerous  exact 
measurements. 

643.  Positive  and  negative  uniaxial  crystal.— The  term  extraordinary 
refractive  index  has  been  defined  in  the  last  article.     For  the  same  crystal 
its  magnitude  always  differs  from  that  of  the  ordinary  refractive  index  ;  for 
example,  in   Iceland  spar  the  ordinary  refractive  index  is  1-654,  while  the 
extraordinary  refractive  index  is    1-483.     In  this  case  the   ordinary  index 
exceeds  the  extraordinary  index.     When  this  is  the  case,  the  crystal  is  said 
to  be  negative.     On  the  other  hand,  when  the  extraordinary  index  exceeds 
the  ordinary  index,  the  crystal  is  said  to  be  positive.     The  following  list  gives 
the  names  of  some- of  the  principal  uniaxial  crystals  : — 

Negative  Uniaxial  Crystals. 

Iceland  spar  Ruby  Pyromorphite 

Tourmaline  Emerald  Ferrocyanide  of  potassium 

Sapphire  Apatite  Nitrate  of  sodium 

Positive  Unia.vial  Crystals. 

Zircon  Apophyllite  Titanite 

Quartz  Ice  Boracite 

644.  Doable    refraction   in    biaxial    crystals. — A    large    number    of 
crystals,  including  all  those  belonging  to  the  trimetric,  the  monoclinic,  and 
the  triclinic  systems,  possess  two  optic  axes  ;  in  other  words,  in  each  of  these 
crystals  there  are  two  directions  along  which  a  ray  of  light  passes  without 
bifurcation.     A  line  bisecting  the  acute   angle  between    the  optic  axes  is 
called  the  medial  line  ;  one  that  bisects  the  obtuse  angle  is  called  the  sup- 
plementary line.     It  has  been  found  that  the  medial  and  supplementary 
lines  and  a  third  line  at  right  angles  to  both  are  closely  related  to  the  funda- 
mental form  of  the  crystal  to  which  the  optic  axes  belong.     The  acute  angle 
between  the   optic  axes  is   different  in  different   crystals.     The   following 
table  gives  the  magnitude  of  this  angle  in  the  case  of  certain  crystals  : — 

Nitre       .  .  .  5°  20'  Anhydrite        .  .  .28°    7' 

Strontianite  .  .  6    56  Heavy  spar     .  .  .     37   42 

Arragonite  .  .  .     18    18  Mica        .         .  .  .     45     o 

Sugar      .  .  .  .     50     o  Epidote  .         .  .  .     14    19 

Selenite  .  .  .  .     60     o  Sulphate  of  iron  .  .     90     o 

When  a  ray  of  light  enters  a  biaxial  crystal,  and  passes  in  any  direction 
not  coinciding  with  an  optic  axis,  it  bifurcates  ;  in  this  case,  however, 
neither  ray  conforms  to  .the  laws  of  single  refraction,  but  both  are  extra- 
ordinary rays.  To  this  general  statement  the  following  exception  must  be 
made  : — In  a  section  of  a  crystal  at  right  angles  to  the  medial  line  one  ray 
follows  the  law  of  ordinary  refraction,  and  in  a  section  at  right  angles  to 
the  supplementary  line  the  other  ray  follows  the  laws  of  ordinary  refraction. 

BB3 


562 


On  Light. 


[645- 


INTERFERENCE  AND   DIFFRACTION. 

645.  Interference  of  light. — The  name  interference  is  given  to  the 
mutual  action  which  two  luminous  rays  exert  upon  each  other  when  they  are 
emitted  from  two  neighbouring  sources,  and  meet  each  other  under  a  very 
small  angle.  This  action  may.  be  observed  by  means  of  the  following  ex- 
periment : — In  the  shutter  of  a  dark  room  two  very  small  apertures  of  the 
same  diameter  are  made  close  to  each  other.  The  apertures  are  closed 
by  pieces  of  coloured  glass — red,  for  example — by  which  two  pencils  of 
homogeneous  light  are  introduced.  These  two  pencils  form  two  divergent 
luminous  cones,  which  meet  at  a  certain  distance  ;  they  are  received  on  a 
white  screen  a  little  beyond  the  place  at  which  they  meet,  and  in  the  segment 
common  to  the  two  discs  which  form  upon  this  screen  some  very  well-defined 
alternations  of  red  and  black  bands  are  seen.  If  one  of  the  two  apertures 
be  closed,  the  fringes  disappear,  and  are  replaced  by  an  almost  uniform  red 
tint.  From  the  fact  that  the  dark  fringes  disappear  when  one  of  the  beams 
is  intercepted,  it  is  concluded  that  they  arise  from  the  interference  of  the  two 
pencils  which  cross  obliquely. 

This  experiment  was  first  made  by  Grimaldi,  but  was  modified  by 
Young.  Grimaldi  had  drawn  from  it  the  conclusion  that  light  added  to  light 


Fig-  535- 

produced  darkness.  The  full  importance  of  this  principle  remained  for 
a  long  time  unrecognised,  until  hese  inquiries  were  resumed  by  Young 
and  Fresnel,  of  whom  the  latter,  by  a  modification  of  Grimaldi's  experi- 
ment, rendered  it  an  experimentum  cruets  of  the  truth  of  the  undulatory 
hypothesis. 

In  Grimaldi's  experiment  diffraction  (646)  takes  place,  for  the  luminous 
rays  pass  by  the  edge  of  the  aperture.  In  Fresners  experiment  the  two 
pencils  interfere  without  the  possibility  of  diffraction. 

Two  plane  mirrors,  AB  and  BC  (fig.  535),  of  metal,  are  arranged  close  to 


-645]  Interference  of  Light.  563 

each  other,  so  as  to  form  a  very  obtuse  angle,  ABC,  which  must  be  very 
little  less  than  180°.  A  pencil  of  red  light,  which  passes  into  the  dark 
chamber,  is  brought  by  means  of  a  lens,  L,  to  a  focus  F.  On  diverging  from 
F  the  rays  fall  partly  on  AB,  and  partly  on  BC.  If  BA  is  produced  to  P  and 
FPF,-  is  drawn  at  right  angles  to  AP,  and  if  PFX  is  made  equal  to  PF,  then 
the  rays  which  fall  on  AB  will,  after  reflection,  proceed  as  if  they  diverged 
from  Fr  If  a  similar  construction  is  made  for  the  rays  falling  on  BC,  they 
will  proceed  after  reflection  as  if  they  diverged  from  F2.  A  little  considera- 
tion will  show  that  F,  and  F7  are  very  near  each  other.  Suppose  the  re- 
flected rays  to  fall  on  a  screen  SS!  placed  nearly  at  right  angles  to  their 
directions.  Every  point  of  the  screen  which  receives  light  from  both  pencils 
is  illuminated  by  both  rays,  viz.  one  from  F,,  the  other  from  F2  ;  thus  the 
point  H  is  illuminated  by  two  rays,  as  also  are  K  and  I.  Now  the  combined 
action  of  these  two  pencils  is  to  form  a  series  of  parallel  bands  alternately 
light  and  dark  on  the  screen  at  right  angles  to  the  plane  of  the  paper.  This 
is  the  fundamental  phenomenon  of  interference  ;  and  that  it  results  from  the 
joint  action  of  the  tiuo  pencils  is  plain,  for  if  the  light  which  falls  upon  either 
of  the  mirrors  is  cut  off,  the  dark  bands  disappear. 

This  remarkable  experiment  is  explained  in  the  most  satisfactory  manner 
by  the  undulatory  theory  of  light.  The  explanation  exactly  resembles  that 
already  given  of  the  formation  of  nodes  and  loops  by  the  combined  action  of 
two  aerial  waves  (262) ;  the  only  difference  being  that  in  that  case  the  vibrating 
particles  were  supposed  to  be  particles  of  air,  whereas,  in  the  present  case,  the 
vibrating  particles  are  supposed  to  be  those  of  the  luminiferous  ether.  Con- 
sider any  point  K  on  the  screen,  and  first  let  us  suppose  the  distance  of  K  from 
F,  and  F2  to  be  equal.  Then  the  undulations  which  reach  K  will  always  be 
in  the  same  phase,  and  the  particle  of  ether  at  K  will  vibrate  as  if  Ahe  light 
came  from  one  source  :  the  amplitude  of  the  vibration,  however,  will  be 
increased  in  exactly  the  same  manner  as  happens  at  a  loop  or  ventral  point ; 
consequently  at  K  the  intensity  of  the  light  will  be  increased.  And  the 
same  will  be  true  for  all  parts  on  the  screen,  such  that  the  difference  between 
their  distances  from  the  two  images  equals  the  length  of  one,  two,  three,  &c., 
undulations.  If,  on  the  other  hand,  the  distances  of  K  from  Fj  and  F2  differ 
by  the  length  of  half  an  undulation,  then  the  two  waves  would  reach  K  in 
exactly  opposite  phases.  Consequently,  whatever  velocity  would  be  com- 
municated at  any  instant  to  a  particle  of  ether  by  the  one  undulation,  an 
exactly  equal  and  opposite  velocity  would  be  communicated  by  the  other 
undulation,  and  the  particle  would  be  permanently  at  rest,  or  there  would  be 
darkness  at  that  point  ;  this  result  being  produced  in  a  manner  precisely 
resembling  the  formation  of  a  nodal  point  already  explained.  The  same 
will  be  true  for  all  positions  of  K,  such  that  the  differences  between  its 
distances  from  F,  and  F2  is  equal  to  three  halves,  or  five  halves,  or  seven 
halves,  &c.,  of  an  undulation.  Accordingly,  there  will  be  on  the  screen  a 
succession  of  alternations  of  light  and  dark  points,  or  rather  lines — for  what 
is  true  of  points  in  the  plane  of  the  paper  (fig.  534)  will  be  equally  true  of 
other  points  on  the  screen  which  is  supposed  to  be  at  right  angles  to  the 
plane  of  the  paper.  Between  the  light  and  dark  lines  the  intensity  of  the 
light  will  vary,  increasing  gradually  from  darkness  to  its  greatest  intensity, 
and  then  decreasing  to  the  second  dark  line,  and  so  on. 


564 


On  Light. 


[645- 


If  instead  of  red  light  any  other  coloured  light  were  used — for  example, 
violet  light — an  exactly  similar  phenomenon  would  be  produced,  but  the  dis- 
tance from  one  dark  line  to  another  would  be  different.  If  white  light  were 
used,  each  separate  colour  tends  to  produce  a  different  set  of  dark  lines. 
Now  these  sets  being  superimposed  on  each  other,  and  not  coinciding,  the 
dark  lines  due  to  one  colour  are  illuminated  by  other  colours,  and  instead  of 
dark  lines  a  succession  of  coloured  bands  is  produced.  The  number  of 
coloured  bands  produced  by  white  light  is  much  smaller  than  the  number  of 
dark  lines  produced  by  a  homogeneous  light  ;  since  at  a  small  distance  from 
the  middle  band  the  various  colours  are  completely  blended,  and  a  uniform 
white  light  produced. 

646.  Diffraction  and  fringes. — Diffraction  is  a  modification  which  light 
undergoes  when  it  passes  the  edge  of  a  body,  or  when  it  traverses  a  small 
aperture — a  modification  in  virtue  of  which  the  luminous  rays  appear  to 
become  bent,  and  to  penetrate  into  the  shadow. 

This  phenomenon  may  be  observed  in  the  following  manner  : — A  beam  of 
solar  light  is  allowed  to  pass  through  a  very  small  aperture  in  the  shutter  of 
a  dark  room,  where  it  is  received  on  a  condensing  lens,  L  (fig.  536),  with  a 


Fig.  536. 

short  fooal  length.  A  red  glass  is  placed  in  the  aperture  so  as  only  to  allow 
red  light  to  pass.  An  opaque  screen,  ^,  with  a  sharp  edge  a — a  razor,  for 
instance — is  placed  behind  the  lens  beyond  its  focus,  and  intercepts  one  por- 
tion of  the  luminous  cone,  while  the  other  is  projected  on  the  screen  £,  of 
which  B  represents  a  front  view.  The  following  phenomena  are  now  seen  : — 
Within  the  geometrical  shadow,  the  limit  of  which  is  represented  by  the  line 
ab,  a  faint  light  is  seen,  which  gradually  fades  in  proportion  as  it  is  farther 
from  the  limits  of  the  shadow.  In  this  part  of  the  screen — which,  being  above 
the  line  ab,  might  be  expected  to  be  uniformly  illuminated — a  series  of  alternate 
dark  and  light  bands  or  fringes  are  seen  parallel  to  the  line  of  shadow,  which 
gradually  become  more  indistinct  and  ultimately  disappear.  The  limits 
between  the  light  and  dark  fringes  are  not  quite  sharp  lines  ;  there  are  parts 
of  maximum  and  minimum  intensity  which  gradually  fade  oft  into  each 
other. 

All  the  colours  of  the  spectrum  give  rise  to  the  same  phenomenon,  but 
the  fringes  are  broader  in  proportion  as  the  light  is  less  refrangible.  Thus, 
with  red  light  they  are  broader  than  with  green,  and  with  green  than  with 
violet.  Hence,  with  white  light,  which  is  composed  of  different  colours,  the 
dark  spaces  of  one  tint  overlap  the  light  spaces  of  another,  and  thus  a  series 
of  prismatic  colours  will  be  produced. 

If,  instead  of  placing  the  edge  of  an  opaque  body  between  the  light  and 
the  screen,  a  very  narrow  body  be  interposed,  such  as  a  hair  or  a  fine  metallic 
wire,  the  phenomena  will  be  different  Outside  the  space  corresponding  to 


-647] 


Gratings. 


565 


fiiiiiifft 

iiiiiiiii 


the  geometrical  shadow,  there  is  a  series  of  fringes,  as  in  the  former  case. 
Hut  within  the  shadow  also  there  is  a  series  of  alternate  light  and  dark  bands. 
They  are  called  interior  fringes,  and  are  much  narrower  and  more  numerous 
than  the  external  fringes. 

When  a  small  opaque  circular  disc  is  interposed,  white  light  being  used, 
its  shadow  on  the  screen  shows  in  the  middle  a  bright  spot  surrounded  by  a 
series  of  coloured  concentric  rings  ;  the  bright  spot  is  of  various  colours 
according  to  the  relative  positions  of  the  disc  and  screen.  The  haloes 
sometimes  seen  round  the  sun  and  moon  belong  to  this  class  of  phenomena. 
They  are  due,  as  Fraunhofer  showed,  fo  the  diffraction  of  light  by  small 
globules  of  fog  in  the  atmosphere.  Fraunhofer  even  gave  a  method  of 
estimating  the  mean  diameter  of  these  globules  from  the  dimensions  of  the 
haloes.  A  beautiful  phenomenon  of  the  same  kind  is  produced  by  looking 
at  a  flame  through  lycopodium  powder  strewed  on  glass. 

647.  Gratings. — Phenomena  of  diffraction  of  another  class  are  produced 
by  allowing  the  pencil  of  light  from  the  luminous  point  to  traverse  an  aper- 
ture in  the  form  of  a  narrow  slit  in  an  opaque  screen.  The  diffracted  light 
may  be  received  on  a  sheet  of 
white  paper,  but  the  images 
are  much  better  seen  through 
a  small  telescope  placed  behind 
the  aperture.  If  the  aperture 
is  very  small,  the  telescope 
may  be  dispensed  with,  and 
the  figure  may  be  viewed  by 
placing  the  aperture  before  the  F-  .  • 

eye.     If   now    monochromatic 

light,  red  for  instance  (572),  be  allowed  to  fall  through  such  a  narrow  slit, 
a  bright  band  of  red  light  is  seen,  and  right  and  left  of  it  a  series  of 
similar  bands  gradually  diminishing  in  brightness  and  separated  by  dark 
bands. 

The  breadth  of  these  bands  differs  with  the  nature  of  the  light,  being 
narrower  and  nearer  together  in  violet  than  in  green,  and  these  again  nar- 
rower and  nearer  than  in  red,  as  shown  in  fig.  537.  If  ordinary  white  light 
be  used,  then  the  colours  are  not  exactly  superposed,  but  a  series  of  equi- 
distant spectra  are  formed  on  each  side  of  the  bright  line,  with  their  violet 
side  turned  inwards. 

In  order  to  explain  this,  let  us  refer  to  fig.  538,  which  represents  the 
formation  of  the  first  dark  band.  When  light  is  incident  on  the  slit,  AB,  the 
particles  of  ether  there,  which  we  will  represent  by  the  dotted  lines,  will  be 
set  in  vibration,  and  each  point  will  become  the  centre  of  a  new  series  of 
oscillations.  Consider  now  the  undulations  which  constitute  a  ray  pro- 
ceeding at  right  angles  to  the  plane  of  the  slit :  all  such  undulations  will 
form  a  band  of  light  on  the  screen  MN.  Those  which  are  not  parallel 
but  proceed  at  equal  inclinations,  and  meet  at  the  point  r,  will  be  in  the 
same  phase  and  will  reinforce  each  other,  and  the  line  of  maximum  bright- 
ness will  be  at  r.  Consider,  however,  a  pencil  of  rays  which  proceeds  from 
the  slit  in  an  oblique  direction  and  which  meets  the  screen,  or  the  retina,  in 
the  point  s,  and  let  us  suppose  that  the  difference  between  the  lengths  of  the 


566 


On  Light. 


[647- 


paths  of  the  undulations  proceeding  from  the  edges  b  and  a — that  is,  bs  and 
as — is  equal  to  the  length  of  an  undulation.  Make  sc  =  sb  and  join  be  ;  then 
ac  is  the  length  of  the  undulation. 

Let  us  suppose  that  the  whole  set  of  undulations  which  proceeds  from 
the  slit  ab  is  divided  at  d  into  two  equal  groups  of  undulations.  Then  a 
little  consideration  will  show  that  at  any  part  of  the  path  there  will  be  a 
difference  of  phase  of  half  an  undulation  between  the  ray  from  the  margin 

a,  and  that  from  the  centre  d ;  and  to  each 
undulation  constituting  the  group  on  the 
left  there  will  be  a  corresponding  one 
among  the  groups  on  the  right,  which  just 
differs  from  it  by  half  an  undulation  ;  the 
general  effect  will  be  that  the  group  on  the 
left  will  be  half  an  undulation  behind  the 
group  on  the  right,  and  both  arriving  at  the 
screen  in  opposite  phases  neutralise  each 
other  and  produce  darkness. 

When  the  difference  between  the  paths 
of  the  marginal  undulations  is  equal  to  half 
a  wave-length,  a  partial  destruction  of  light 
takes  place  ;  the  luminous  intensity  cor- 
responding to  this  obliquity  is  a  little  less 
than  half  that  of  the  undiffracted  light. 

M.  ^  *          K   If  the  marginal  distance  is  one  and  a  half 

Fig  53g  undulations,  we    can,    as  before,  conceive 

the  whole  pencil  divided  into  three  parts, 

of  whicji  two  will  neutralise  each  other,  and  the  third  only  will  be  effective. 
There  will  be  a  luminous  band,  but  one  of  less  intensity.  In  like  manner 
where  the  marginal  undulations  differ  by  two  whole  wave-lengths,  they  will 
again  extinguish  each  other,  and  a  dark  band  will  be  the  result.  Thus  there 
will  be  formed  a  series  of  alternate  dark  and  bright  bands  of  rapidly  diminish- 
ing intensity.  In  general,  when  the  difference  of  path  of  the  rays  proceeding 
from  the  margin  of  the  slit  amounts  to  n  wave-lengths,  n  being  any  whole 
number,  we  have  a  dark  band,  and  when  it  amounts  to  n  +  £  wave-lengths,  a 
bright  band. 

The  phenomena  of  diffraction  produced  when  other  than  straight  lines  are 
used  are  often  of  great  beauty.  They  have  been  more  particularly  examined 
by  Schwerdt,  and  the  whole  of  the  phenomena  are  in  exact  accordance  with 
the  undulatory  theory,  though  the  explanation  is  in  many  cases  somewhat 
intricate.  The  theory  renders  it  possible  to  predict  the  appearance  which 
any  particular  aperture  will  produce,  just  as  astronomy  enables  us  to  foretell 
the  motions  of  the  heavenly  bodies.  Some  of  the  simpler  forms — such  as 
straight  lines,  triangles,  squares — may  be  cut  out  of  tinfoil  pasted  on  glass, 
and  apertures  of  any  form  may  be  produced  with  great  accuracy  by  taking 
on  glass  a  collodion  picture  of  a  sheet  of  paper,  on  which  the  required  shapes 
are  drawn  in  black. 

Looking  through  any  of  these  apertures  at  a  luminous  point,  we  see  it  sur- 
rounded with  coloured  spectra  of  very  various  forms,  and  of  great  beauty. 
The  beautiful  colours  seen  on  looking  through  a  bird's  feather  at  a  distant 


-648]  Diffraction  Spectra.  567 

source  of  light,  and  the  colours  of  striated  surfaces,  such  as  mother-of-pearl, 
are  due  to  a  similar  cause. 

648.  Diffraction  Spectra.— The  most  important  of  these  figures  are  the 
gratings  proper,  which  may  be  produced  by  arranging  a  series  of  fine  wires 
parallel  to  each  other,  or  by  careful  ruling  on  a  piece  of  smoked  glass,  or  by 
photographic  reduction.  Nobert  has  made  such  gratings  by  ruling  lines  on 
glass  with  a  diamond,  in  which  there  are  no  less  than  12,000  lines  in  an  inch 
in  breadth.  Dr.  Stone  has  constructed  such  gratings  for  reflection,  by  ruling 
lines  on  plates  of  nickel ;  this  metal  has  the  advantage  of  hardness,  non- 
liability to  tarnish,  and  great  reflecting  power. 

If  a  grating  be  used  instead  of  a  single  slit,  as  above  described,  the 
phenomena  are  in  general  the  same,  though  of  greater  intensity.  With 
homogeneous  light  and  such  a  grating,  there  is  seen,  on  each  side  of  the 
central  bright  line,  a  series  of  sharply  defined  narrow  bands  and  lines  of 
light,  gradually  increasing  in  breadth  and  diminishing  in  intensity  as  their 
distance  from  the  central  line  increases.  If  white  light  be  used  there  is  seen 
then  in  the  centre,  the  white  band,  and  on  each  side  of  it  a  sharply  defined 
isolated  spectrum  with  the  violet  edges  inwards.  Next  to  this,  and  separated 
by  a  dark  interval,  is  on  each  side  a  somewhat  broader  but  similar  spectrum, 
and  then  follow  others  which  become  fainter  and  broader  and  overlap 
each  other.  The  brightness  and  sharpness  of  these  spectra  depend  on  the 
closeness  of  the  lines,  and  on  the  opacity  of  the  intermediate  space.  In 
those  which  are  ruled  by  diamond  on  glass,  the  parts  scratched  represent 
the  opaque  parts. 

The  spectra  produced  by  means  of  a  grating  are  known  as  interference  or 
diffraction  spectra.  Very  accurate  gratings  can  now  be  easily  and  cheaply 
prepared  by  means  of  photography,  and  their  use  for  scientific  purposes  is 
extending. 

For  objective  representation  the  image  of  a  slit  in  a  dark  shutter, 
through  which  the  sunlight  enters,  is  focussed  by  means  of  a  convex  lens 
on  a  screen  at  a  distance,  and  then  a  grating  is  placed  in  the  path  of  the 
rays. 

There  are  many  points  of  difference  between  these  spectra  and  those 
produced  by  the  prism,  and  for  scientific  work  the  former  are  preferable. 

A  diffraction  spectrum  is  the  purer  the  greater  the  number  of  lines  in  the 
grating,  provided  they  are  equidistant.  The  spectra  are,  however,  not  more 
than  i  as  bright  as  prismatic  spectra  ;  and  to  obtain  the  maximum  bright- 
ness the  opaque  intervals  should  be  as  opaque  and  the  transparent  ones  as 
transparent  as  possible. 

On  the  other  hand,  in  diffraction  spectra,  the  colours  are  uniformly  dis- 
tributed in  their  true  order  and  extent  according  to  the  difference  in  their 
wave-lengths,  and  according  therefore  to  a  property  which  is  inherent  in  the 
light  itself;  while  in  prismatic  spectra  the  red  rays  are  concentrated,  and 
the  violet  ones  dispersed.  In  diffraction  spectra  the  centre  is  the  brightest 
part. 

Diffraction  spectra  have,  moreover,  the  advantage  of  giving  a  far  larger 
number  of  dark  lines,  and  of  giving  them  in  their  exact  relative  positions. 
Thus,  in  a  particular  region  in  which  Angstrom  had  mapped  118  lines, 
Draper,  by  means  of  a  diffraction  spectrum,  was  able  to  photograph  at  least 


568  On  Light.  [648- 

293.  Diffraction  spectra  also  extend  farther  in  the  direction  of  the  ultra- 
violet, and  give  more  dark  lines  in  that  region. 

649.  Determination  of  wave-length. — The  relative  positions  of  these 
bright  and  dark  lines  furnish   a  means  of  calculating  the  wave-length  or 
length  of  undulation  of  any  particular  colour.     We  must  first  of  all  know 
the  distance  rs  of  the  first  dark  band  from  the  bright  one.     The  bands  are 
not  uniform  in  brightness  or  darkness,  but  there  is  in  each  case  a  position  of 
maximum  intensity,  and  it  is  from  these  that  the  distances  are  measured. 
If  the  bands  are  viewed  through  a  telescope  the  angle  is  observed  through 
which  the  axis  must  be  turned  from  the  position  in  which  the  cross  wire 
coincides  with  the  centre  of  the  bright  band  to  that  in  which  it  coincides 
with  the  centre  of  the  dark  band.     From  the  angle,  which  can  be  very  ac- 
curately measured,  the  distance  is  easily  calculated.     When  the  diffraction 
bands  are  received  on  a  screen  the  distance  may  be  directly  measured,  and 
most  accurately  by  taking  half  the  distance  between  the  centres  of  the  first 
pair  of  dark  bands. 

We  have  thus  the  similar  triangles  abc,  and  rds,  in  which  ac  \  bt  =  rs  :  rd 
(fig.  538).  Now  be  may  be  taken  equal  to  ab,  the  width  of  the  slit,  which  can 
be  measured  directly  with  great  accuracy  by  means  of  a  micrometric  screw 
(u),  and  rd'is  the  distance  of  the  screen.  Hence 

rs  x  ab 

ac  =  . 

rd 

Now  ac,  the  difference  between  as  and  sc,  is  equal  to  the  length  of  an  undu- 
lation of  this  particular  colour.  In  one  experiment  with  red  light  the  width 
of  the  slit  ab  was  0*015  m->  tne  distance  rs  0-15  in.,  and  the  distance  of  the 

screen  93  in.,  which  gave  ac= 5— t     —?  0*000024  m-  as  the  wave-length 

of  red  light.  Using  blue  light  the  distance  of  rs  was  found  to  be  OT,  which 
gives  0*000016. 

Knowing  the  length  of  the  undulations,  we  can  easily  calculate  their 

number  in  a  second,  //,  from  the  formula  n=  —  (232),  where  v  is  the  velocity 

of  light.  Taking  this  at  186,000  miles,  we  get  for  the  red  corresponding  to 
the  dark  line  B  434,420,000,000,000  as  the  number  of  oscillations  in  a.  second, 
and  for  the  H  in  the  violet  758,840,000,000,000  undulations. 

If,  instead  of  a  single  slit,  gratings  be  used,  we  have  the  possibility  of 
more  accurate  results,  for  the  contrast  is  greater,  and  thus  the  distance  is 
more  easily  determined.  The  breadth  of  the  slit  is  then  easily  calculated  if 
we  know  the  number  of  lines  in  a  given  space. 

650.  Colours  of  thin  plates.     Newton's  rings. — All  transparent  bodies, 
solids,  liquids,  or  gases,  when  in  sufficiently  fine  laminae,  appear  coloured 
with  very  bright  tints,  especially  by  reflection.     Crystals  which  cleave  easily, 
and  can  be  obtained  in  very  thin  plates,  such  as  mica  and  selenite,  show  this 
phenomenon,  which  is  also  well  seen  in  soap-bubbles  and  in  the  layers  of  air 
in  cracks  in  glass  and  in  crystals.     A  drop  of  oil  spread  rapidly  over  a  large 
sheet  of  water  exhibits  all  the  colours  of  the  spectra  in  a  constant  order.     A 
soap-bubble  appears  white  at  first,  but,  in  proportion  as  it  is  blown  out, 
brilliant  iridescent  colours  appear,  especially  at  the  top,  where  it  is  thinnest. 


-651]  Explanation  of  Newton* s  Rings.  569 

These  colours  are  arranged  in  horizontal  zones  around  the  summit,  which 
appears  black  when  there  is  not  thickness  enough  to  reflect  light,  and  the 
bubble  then  suddenly  bursts. 

Newton,  who  first  studied  the  phenomena  of  the  coloured  rings  in  soap- 
bubbles,  wishing  to  investigate  the  relation  between  the  thickness  of  the 
thin  plate,  the  colour  of  the 
rings,  and  their  extent,  pro- 
duced them  by  means  of  a  "^^v^^^^^MM'MM^^' 
layer  of  air  interposed  be-  r  "~"~~ .  """  ; 

tween  two  glasses,  one  plane 
and  the  other  convex,  and 
with  a  very  long  focus  (fig. 

539).  The  two  surfaces  being  cleaned  and  exposed  to  ordinary  light  in 
front  of  a  window,  so  as  to  reflect  light,  there  is  seen  at  the  point  of  contact 
a  black  spot  surrounded  by  six  or  seven  coloured  rings,  the  tints  of  which 
become  gradually  less  strong.  If  the  glasses  are  viewed  by  transmitted 
li.L,rht,  the  centre  of  the  rings  is  white,  and  each  of  the  colours  is  exactly 
complementary  of  that  of  the  rings  by  reflection. 

With  homogeneous  light,  red  for  example,  the  rings  are  successively 
black  and  red  ;  the  diameters  of  corresponding  rings  are  less  as  the  colour 
is  more  refrangible,  but  with  white  light  the  rings  are  of  the  different  colours, 
of  the  spectrum,  which  arises  from  the  fact  that,  as  the  rings  of  the  different 
simple  colours  have  different  diameters,  they  are  not  exactly  superposed,  but 
are  more  or  less  separated. 

If  the  focal  length  of  the  lens  is  from  three  to  four  yards,  the  rings  can  be 
seen  with  the  naked  eye ;  but  if  the  length  is  less,  the  rings  must  be  looked 
at  \vith  a  lens. 

651.  Explanation  of  Newton's  rings. — Newton's  rings,  and  all  pheno- 
mena of  thin  plates,  are  simple  cases  of  interference. 

In  fig.  540,  let  MNOP  represent  a  thin  plate  of  a  transparent  body,  on, 
which  a  pencil  of  parallel  rays  of  homogeneous  light,  ab,  impinges  :  this  will, 
be  partially  reflected  in  the  direction  be,  and  partially 
refracted  towards   d.     But  the  refracted  ray  will  un- 
dergo  a  second  reflection  at  the  surface,  OP  ;  the  re- 
fleeted  ray  will  emerge  at  e  in  the  same  direction  as 
the  pencil  of  light  reflected  at  the  first  surface  ;  and 
consequently  the  two  pencils  be  and  ej "will  destroy  or 
augment  each  others  effect  according  as  they  are  in 
the  same  or  different  phases.     We  shall  thus  have  an    '        // 
effect  produced  similar  to  that  of  the  fringes. 

It  is  usual  to  speak  of  the  successive  rings  as  the       *•'  y 
first,  second,  third,  &c.     By  theyfrj-/  ring  is  understood  Fit?.  540. 

that  of  least  diameter.     Knowing  the  radius   of  any 

particular  ring,  p,  and  the  radius  of  curvature,  R,  of  the  lens,  the  thickness,  d, 
of  the  corresponding  layer  of  air  is  given  approximately  by  the  formula 

'-  £ 

Newton  found  that  the  thicknesses  corresponding  to  the  successive  dark 
rings  are  proportional  to  the  numbers  o,  2,  4,  6, ,  while  for  the 


570  On  Light.  [651- 

bright  rings  the  thicknesses  were  proportional  to  I,  3,  5 He  found 

that  for  the  first  bright  ring  the  thickness  was  jy/ooo  of  an  incn-  when  the 
light  used  was  the  brightest  part  of  the  spectrum  ;  that  is,  the  part  on  the 
confines  of  the  orange  and  yellow  rays. 

POLARISATION   OF   LIGHT. 

652.  Polarisation  by  double  refraction. — It  has  been  already  seen  that, 
when  a  ray  of  light  passes  through  a  crystal  of  Iceland  spar  (641),  it  becomes 
divided  into  two  rays  of  equal  intensity  ;  viz.  the  ordinary  ray,  and  the  ex- 
traordinary ray.  These  rays  are  found  to  possess  other  peculiarities,  which 
are  expressed  by  saying  they  are  polarised ;  namely,  the  ordinary  ray  in  a 
principal  plane,  and  the  extraordinary  ray  in  a  plane  at  right  angles  to  a 
principal  plane.  The  phenomena  which  are  thus  designated  may  be  de- 
scribed as  follows  : — Suppose  a  ray  of  light  which  has  undergone  ordinary 
refraction  in  a  crystal  of  Iceland  spar  to  be  allowed  to  pass  through  a  second 
crystal,  it  will  generally  be  divided  into  two  rays  ;  namely,  one  ordinary,  and 
the  other  extraordinary,  but  of  unequal  intensities.  If  the  second  crystal 
be  turned  round  until  the  two  principal  planes  coincide — that  is,  until  the 
crystals  are  in  similar  or  in  opposite  positions— then  the  extraordinary  ray 
disappears,  and  the  ordinary  ray  is  at  its  greatest  intensity  ;  if  the  second 
crystal  is  turned  farther  round,  the  extraordinary  ray  reappears,  and  increases 
in  intensity  as  the  angle  increases,  while  the  ordinary  ray  diminishes  in  in- 
tensity until  the  principal  planes,  are  at  right  angles  to  each  other,  when  the 
extraordinary  ray  is  at  its  greatest  intensity,  and  the  ordinary  ray  vanishes. 
These  are  the  phenomena  produced  when  the  ray  which  experienced  ordi- 
nary refraction  in  the 'first  crystal  passes  through  the  second.  If  the  ray 
which  has  experienced  extraordinary  refraction  in  the  first  crystal  is  allowed 
to  pass  through  the  second  crystal,  the  phenomena  are  similar  to  those  above 
described  ;  but  when  the  principal  planes  coincide,  an  extraordinary  ray  alone 
emerges  from  the  second  crystal,  and  when  the  planes  are  at  right  angles,  an 
ordinary  ray  alone  emerges. 

These  phenomena  may  also  be  thus  described  : — Let  O  and  E  denote 
the  ordinary  and  extraordinary  rays  produced  by  the  first  crystal.  When 
O  enters  the  second  crystal,  it  generally  gives  rise  to  two  rays,  an  ordinary 
(O0),  and  an  extraordinary  (O),  of  unequal  intensities.  When  E  enters  the 
second  crystal,  it  likewise  gives  rise  to  two  rays,  viz.  an  ordinary  (E#)  and 
an  extraordinary  (E^),  of  unequal  intensities,  the  intensities  varying  vrith 
the  angle  between  the  principal  planes  of  the  crystals.  When  the  principal 
planes  coincide,  only  two  rays,  viz.  Oo  and  E^,  emerge  from  the  second 
crystal,  and  when  the  planes  are  at  right  angles,  only  two  rays,  viz.  Oe  and 
E0,  emerge  from  the  second  crystal.  Since  O  gives  rise  to  an  ordinary  ray 
when  the  principal  planes  are  parallel,  and  E  gives  rise  to  an  ordinary  ray 
when  they  are  at  right  angles,  it  is  manifest  that  O  is  related  to  the  principal 
plane  in  the  same  manner  that  E  is  related  to  a  plane  at  right  angles  to  a 
principal  plane. 

This  phenomenon,  which  is  produced  by  all  double  refracting  crystals, 
was  observed  by  Huyghens  in  Iceland  spar,  and  in  consequence  of  a  sug- 
gestion of  Newton's  was  afterwards  called  polarisation.  It  remained,  how- 
ever, an  isolated  fact  until  the  discovery  of  polarisation  by  reflection  recalled 


-654]  Angle  of  Polarisation.  571 

the  attention  of  physicists  to  the  subject.     The  latter  discovery  was  made 
by  Malus  in  1808. 

653.  Polarisation  by  reflection. — When  a  ray  of  light,  ab  (fig.  541),  falls 
on  a  polished  unsilvered  glass  surface,  fghi^  inclined  to  it  at  an  angle  of 
3  5°  25',  it  is  reflected,  and  the  reflected  ray  is 
polarised  in  the  plane  of  reflection.     If  it  were 
transmitted  through  a  crystal  of  Iceland  spar, 
it  would  be  transmitted  without  bifurcation, 
and  undergo  an  ordinary  refraction,  when  the 
principal  plane  coincides  with  the  plane  of  re- 
flection ;  it  would  also  be  transmitted  without 
bifurcation,  but  undergo  extraordinary  refrac- 
tion, when  the  principal  plane  is  at  right  angles 
to  the  plane  of  reflection  ;  in  other  positions 
of  the  crystal  it  would  give  rise  to  an  ordinary 
and  an  extraordinary  ray  of  different  intensi- 
ties, according  to  the  angle  between  the  plane 
of  reflection   and  the  principal  plane  of  the 
crystal.    The  peculiar  property  which  the  light 
has  acquired  by  reflection  at  the  surface  fghi 
can  also  be  exhibited   as  follows  : — Let   the 
polarised  ray  be  be  received  at  <:,  on  a  second  surface  of  unsilvered  glass,  at 
the  same  angle,  viz.  35°  25'.    If  the  surfaces  are  parallel,  the  ray  is  reflected  ;. 
but  if  the  second  plate  is  caused  to  turn  round  cb,  the  intensity  of  the  re- 
flected ray  continually  diminishes,  and  when  the  glass  surfaces  are  at  right 
angles  to  each  other,  no  light  is  reflected.     By  continuing  to  turn  the  upper 
mirror  the  intensity  of  the  reflected  ray  gradually  increases,  and  attains  a 
maximum  value  when  the  surfaces  are  again  parallel. 

The  above  statement  will  serve  to  describe  the  phenomenon  of  polarisa- 
tion by  reflection  so  far  as  the  principles  are  concerned  ;  the  apparatus  best 
adapted  for  exhibiting  the  phenomenon  will  be  described  farther  on. 

654.  Angle  of  polarisation. — The  polarising  angle  of  a  substance  is  the 
angle  which  the  incident  ray  must  make  with  the  normal  to  a  plane  polished 
surface  of  that  substance  in  order  that  the  polarisation  be  complete.  For 
glass  this  angle  is  54°  35',  and  if  in  the  preceding  experiment  the  lower 
mirror  were  inclined  at  any  other  angle  than  this,  the  light  would  not  be 
completely  polarised  in  any  position  ;  this  would  be  shown  by  its  being 
partially  reflected  from  the  upper  surface  in  all  positions.  Such  light  is  said, 
to  be  partially  polarised.  The  polarising  angle  for  water  is  52°  45' ;  for 
quartz,  57°  32' ;  for  diamond,  68°  ;  and  it  is  56°  30'  for  obsidian,  a  kind  of 
volcanic  glass  which  is  often  used  in  these  experiments. 

Light  which  is  reflected  from  the  surface  of  water,  from  a  slate  roof,  from 
a  polished  table,  is  all  more  or  less  polarised.  The  ordinary  light  of  the  at- 
mosphere is  frequently  polarised,  especially  in  the  earlier  and  later  periods  of 
the  day,  when  the  solar  rays  fall  obliquely  on  the  atmosphere.  Almost  all 
reflecting  surfaces  may  be  used  as  polarising  mirrors.  Metallic  surfaces 
form,  however,  an  important  exception. 

Brewster  has  discovered  the  following  remarkably  simple  law  in  reference 
to  the  polarising  angle  : — 


572  On  Light.  [654- 

The  polarising  angle  of  a  substance  is  that  angle  of  incidence  for  whicJi 
the  reflected  polarised  ray  is  at  right  angles  to  the  refracted  ray. 

Thus,  in  fig.  542,  if  si  is  the  incident,  ir 
the  refracted,  and  if  the  reflected  ray,  the 
polarisation  is  most  complete  when  fi  is  at 
right  angles  to  ir. 

The  plane  of  polarisation  is  the  plane  of 
reflection  in  which  the  light  becomes  polar- 
ised ;  it  coincides  with  the  plane  of  inci- 
dence, and  therefore  contains  the  polarising 
angle. 

655.  Polarisation  by  single  refraction. 
— When  an  unpolarised  luminous   ray  falls 
Fig.  542.  upon  a  glass  plate  placed  at  the  polarising 

angle,  one  part  is  reflected  ;  the  other  part 

in  passing  through  the  glass  becomes  refracted,  and  the  transmitted  light 
is  now  found  to  be  partially  polarised.  If  the  light  which  has  passed 
through  one  plate,  and  whose  polarisation  is  very  feeble,  be  transmitted 
through  a  second  plate  parallel  to  the  first,  the  effects  become  more  marked, 
and  by  ten  or  twelve  plates  are  tolerably  complete.  A  bundle  of  such  plates, 
for  which  the  best  material  is  the  glass  used  for  covering  microscopic 
objects,  fitted  in  a  tube  at  the  polarising  angle,  is  frequently  used  for  exam- 
ining or  producing  polarised  light. 

If  a  ray  of  light  fall  at  any  angle  on  a  transparent  medium,  the  same 
holds  good  with  a  slight  modification.  In  fact,  part  of  the  light  is  reflected 
and  part  refracted,  and  both  are  found  to  be  partially  polarised,  equal  quan- 
tities in  each  being  polarised,  and  their  planes  of  polarisation  being  at  right 
angles  to  each  other.  It  is,  of  course,  to  be  understood  that  the  polarised 
portion  of  the  reflected  light  is  polarised  in  the  plane  of  reflection,  which  is 
likewise  the  plane  of  refraction. 

656.  Polarising-  instruments. — Every  instrument  for  investigating  the 
properties  of  polarised  light  consists  essentially  of  two  parts — one  for  polaris- 
ing the  light,  the  other  for  ascertaining  or  exhibiting  the  fact  of  light  having 
undergone  polarisation.     The  former  part  is  called  the  polariser,  the  latter 
the  analyser.     Thus  in  art.  652  the  crystal  producing  the  first  refraction  is 
the  polariser,  that  producing  the  second  refraction  is  the  analyser.     In  art. 
653  the  mirror  at  which  the  first  reflection  takes  place  is  the  polariser,  that 
at  which  the  second  reflection  takes  place  is  the  analyser.     Some  of  the 
most  convenient  means  of  producing  polarised  light  will  now  be  described, 
and  it  will  be  remarked  that  any  instrument  that  can  be  used  as  a  polariser 
can  also  be  used  as  an  analyser.    The  experimenter  has  therefore  considerable 
liberty  of  selection. 

657.  Worremberg's  apparatus. — The  most  simple  but  complete  instru- 
ment for   polarising    light  is    that    invented    by  Norremberg.      It  may  be 
used  for  repeating  most  of  the  experiments  on  polarised  light. 

It  consists  of  two  brass  rods  b  and  d  (fig.  543),  which  support  an  unsil- 
vered  mirror,  n,  of  ordinary  glass,  movable  about  a  horizontal  axis.  A  small 
graduated  circle  indicates  the  angle  of  inclination  of  the  mirror.  Between 
the  feet  of  the  two  columns  there  is  a  silvered  glass,  p,  which  is  fixed  and 


-658]  Tourmaline.  5/3 

horizontal.  At  the  upper  end  of  the  columns  there  is  a  graduated  plate,  /, 
in  which  a  circular  disc,  o,  rotates.  This  disc,  in  which  there  is  a  square 
aperture,  supports  a  mirror  of  black  glass,  ///,  which  is  inclined  to  the  vertical 
at  the  polarising  angle.  An  annular  disc,  £,  can  be  fixed  at  different  heights 
on  the  columns  by  means  of  a  screw.  A  second  ring,  #,  may  be  moved 
around  the  axis.  It  supports  a 
black  screen,  in  the  centre  of 
which  there  is  a  circular  aper- 
ture. 

When  the  mirror  n  makes 
with  the  vertical  an  angle  of  35° 
25',  which  is  the  complement  of 
the  polarising  angle  for  glass, 
the  luminous  rays,  Sw,  which 
meet  the  mirror  at  this  angle, 
become  polarised,  and  are  re 
fleeted  in  the  direction  np  to- 
wards the  mirror/,  which  sends 
them  in  the  direction  ' nr.  After 
having  passed  through  the  glass, 
/;,  the  polarised  ray  falls  upon 
the  blackened  glass  /;/  under  an 
angle  of  35°  25',  because  the 
mirror  makes  exactly  the  same 
angle  with  the  vertical.  But  if 
the  disc,  0,  to  which  the  mirror, 
;//,  is  fixed,  be  turned  horizon- 
tally, the  intensity  of  the  light 
reflected  from  the  upper  mirror 
gradually  diminishes,  and  totally 
disappears  when  it  has  been 
moved  through  90°.  The  posi- 
tion is  that  represented  in  the 
diagram  :  the  plane  of  incidence 
on  the  upper  mirror  is  then  perpendicular  to  the  plane  of  incidence,  S;//,  on 
the  mirror  n.  When  the  upper  mirror  is  again  turned,  the  intensity  of  the 
light  increases  until  it  has  passed  through  180°,  when  it  again  reaches  a 
maximum.  The  mirrors  ///  and  n  are  then  parallel.  The  same  phenomena 
are  repeated  as  the  mirror  ///  continues  to  be  turned  in  the  same  direction, 
until  it  again  comes  into  its  original  position  ;  the  intensity  of  the  reflected 
light  being  greatest  when  the  mirrors  are  parallel,  and  being  reduced  to 
zero  when  they  are  at  right  angles.  If  the  mirror  m  is  at  a  greater  or  less 
angle  than  35°  25',  a  certain  quantity  of  light  is  reflected  in  all  positions  of 
the  plane  of  incidence. 

658.  Tourmaline. — The  primary  form  of  this  crystal  is  a  regular  hex- 
agonal prism.  Tourmaline,  as  already  stated,  is  a  negative  uniaxial  crystal, 
and  its  optic  axis  coincides  with  the  axis  of  the  prism.  For  optical  purposes 
a  plate  is  cut  from  it  parallel  to  the  axis.  When  a  ray  of  light  passes 
through  such  a  plate,  an  ordinary  ray  and  an  extraordinary  ray  are  produced 


Fig-  543- 


574  On  Light.  [658- 

polarised  in  planes  at  right  angles  to  each  other  ;  viz.  the  former  in  a  plane 
at  right  angles  to  the  plate  parallel  to  the  axis,  and  the  latter  in  a  plane  at 
right  angles  to  the  axis.  The  crystal  possesses,  however,  the  remarkable 
property  of  rapidly  absorbing  the  ordinary  ray  ;  consequently,  when  a  plate 
of  a  certain  thickness  is  used,  the  extraordinary  ray  alone  emerges — in 
other  words,  a  beam  of  common  light  emerges  from  the  plate  of  tourmaline 
polarised  in  a  plane  at  right  angles  to  the  axis  of  the  crystal.  If  the  light 
thus  transmitted  be  viewed  through  another  similar  plate  held  in  a  parallel 
position,  little  change  will  be  observed  excepting  that  the  intensity  of  the 
transmitted  light  will  be  about  equal  to  that  which  passes  through  a  plate  of 
double  the  thickness  ;  but  if  the  second  tourmaline  be  slowly  turned,  the 
light  will  become  feebler,  and  will  ultimately  disappear  when  the  axes  of  the 
two  plates  are  at  right  angles. 

The  objections  to  the  use  of  the  tourmaline  are  that  it  is  not  very  trans- 
parent, and  that  plates  of  considerable  thickness  must  be  used  if  the  polarisa- 
tion is  to  be  complete.  For  unless  the  ordinary  ray  is  completely  absorbed 
the  emergent  light  will  be  only  partially  polarised. 

Herapath  discovered  that  sulphate  of  iodoquinine  has  the  property  of 
polarising  light  in  a  remarkable  degree.  Unfortunately,  it  is  a  very  fragile 
salt,  and  difficult  to  obtain  in  large  crystals. 

659.  Double  refracting-  prisms  of  Iceland  spar. — When  a  ray  of  light 
passes  through  an  ordinary  rhombohedron  of  Iceland  spar,  the  ordinary  and 
extraordinary  rays  emerge  parallel  to  the  original  ray,  consequently  the 
separation  of  the  rays  is  proportional  to  the  thickness  of  the  prism.  But  if 
the  crystal  is  cut  so  that  its  faces  are  inclined  to  each  other,  the  deviations 
of  the  ordinary  and  extraordinary  rays  will  be  different,  they  will  not  emerge 
parallel,  and  their  separation  will  be  greater  as  their  distance  from  the  prism 
increases.  The  light,  however,  in  passing  through  the  prism  becomes  de- 
composed, and  the  rays  will  be  coloured.  It  is  therefore  necessary  to  achro- 
matise  the  prism,  which  is  done  by  combining  it  with  a  prism  of  glass  with 
its  refracting  angle  turned  in  the  contrary  direction  (fig.  545).  In  order  to 
obtain  the  greatest  amount  of  divergence,  the  refracting  edges  of  the  prism 
should  be  cut  parallel  to  the  optic  axis,  and  this  i^  always  done. 

Let  us  suppose  that  a  ray  of  polarised  light  passes  along 
the  axis  of  the  cylinder  (fig.  545),  and  let  us  suppose  that  the 
cylinder  is  caused  to  turn  slowly  round    its    axis  ;  then  the 
resulting  phenomena  are  exactly  like  those  already  described 
(643).     Generally  there  will  be  an  ordinary  and  extraordinary 
ray  produced,  whose  relative  intensities  will  vary  as  the  tube 
is   turned.      But   in  two  opposite  positions  the  ordinary  ray 
Fig  545         alone  will  emerge,  and  in  two  others  at  right  angles  to  the 
former  the  extraordinary  ray  will  alone  emerge.     When  the 
ordinary  ray  alone  emerges,  the  principal  plane  of  the  crystal — that  is,  a 
plane  at  right  angles  to  its  face,  and  parallel  to  its  refracting  edge — coincides 
with  the  original  plane  of  polarisation  of  the  ray.     Consequently,  by  means 
of  the  prism,  it  can  be  ascertained  both  that  the  ray  is  polarised,  and  like- 
wise the  plane  in  which  it  is  polarised. 

660.  Nicol's  prism.— The   Nicol's  prism  is  one  of  the  most  valuable 
means  of  polarising  light,  for  it  is  perfectly  colourless,  it  polarises  light  com- 


-661]  Physical  Theory  of  Polarised  Light.  575 

pletely,  and  it  transmits  only  one  beam  of  polarised  light,  the  other  being 
entirely  suppressed. 

It  is  constructed  out  of  a  rhombohedron  of  Iceland  spar,  about  an  inch 
in  height  and  \  of  an  inch  in  breadth.  This  is  bisected  in  the  plane  which 
passes  through  the  obtuse  angles  as  shown  in  fig.  547  ;  that  is,  along  the 
plane  abed  (fig.  534).  The  two  halves  are  then  again  joined  in  the  same 
order  by  means  of  Canada  balsam. 

The  principle  of  the  Nicol's  prism  is  this  :— The  refractive  index  of  Canada 
balsam,  i  -549,  is  less  than  the  ordinary  index  of  Iceland  spar  1*654,  but  greater 


Fig.  546.  Fig.  547. 

than  its  extraordinary  index  1*483.  Hence,  when  a  luminous  ray  SC  (fig. 
547)  enters  the  prism,  the  ordinary  ray  is  totally  reflected  on  the  surface,  ab, 
and  takes  the  direction  GfO,  by  which  it  is  refracted  out  of  the  crystal, 
while  the  extraordinary  ray,  C<?,  emerges  alone.  Since  the  Nicol's  prism 
allows  only  the  extraordinary-  ray  to  pass,  it  may  be  used,  like  a  tourmaline, 
as  an  analyser  or  as  a  polariser. 

Foucault  has  replaced  the  layer  of  Canada  balsam  by  one  of  air,  the  two 
prisms  being  kept  together  by  the  mounting.  The  advantage  of  this  is  that 
the  section  ab  (fig.  547)  need  not  be  so  acute,  so  that  the  prism  becomes 
shorter,  and  therefore  cheaper. 

Xicol's  prism  is  the  most  important  feature  of  most  polarising  apparatus. 
It  is  better  than  the  polarising  mirror  on  account  of  its  more  complete  polar- 
isation, and  has  the  advantage  over  tourmaline  of  giving  a  colourless  field 
of  view. 

66 1.  Physical  theory  of  polarised  light. — The  explanation  of  the  dark 
bands  produced  by  the  interference  of  light  is  stated  in  art.  650  to  resemble 
exactly  that  of  the  formation  of  nodes  and  loops  given  in  art.  276. 

It  might  hence  be  supposed  that  the  vibrations  producing  light  are  quite 
similar  to  those  producing  sound.  But  this  is  by  no  means  the  case.  In 
fact,  no  assumption  is  made  in  art.  652  as  to  the  direction  in  which  the 
vibrating  particles  move,  and  accordingly  the  explanation  is  equally  true 
whether  the  particles  vibrate  in  the  direction  AB,  BA,  or  at  right  angles  to 
AB.  As  a  matter  of  fact,  the  former  is  the  case  with  the  vibrations  produc- 
ing sound,  the  latter  with  the  vibrations  producing  light.  In  other  words, 
the  vibrations  producing  sound  take  place  in  the  direction  of  propagation, 
the  vibrations  producing  light  are  transversal  to  the  direction  of  propaga- 
tion. 

This  assumption  as  to  the  direction  of  the  vibration  of  the  particles  of 
ether  producing  light  is  rendered  necessary,  and  is  justified,  by  the  pheno- 
mena of  polarisation. 

When  a  ray  of  light  is  polarised,  all  the  particles  of  ether  in  that  ray 
vibrate  in  straight  lines  parallel  to  a  certain  direction  in  the  front  of  the 
wave  corresponding  to  the  ray. 


5;6  On  Light.  [661- 

When  a  ray  of  light  enters  a  double  refracting  medium,  such  as  Iceland 
spar,  it  becomes  divided  into  two,  as  we  have  already  seen.  Now  it  can  be 
shown  to  be  in  strict  accordance  with  mechanical  principles  that,  if  a  medium 
possesses  unequal  elasticity  in  different  directions,  a  plane  wave  produced 
by  transversal  vibrations  entering  that  medium  will  give  rise  to  two  plane 
waves  moving  with  different  velocities  within  the  medium,  and  the  vibrations 
of  the  particles  in  front  of  these  waves  will  be  in  directions  parallel  respect- 
ively to  two  lines  at  right  angles  to  each  other.  If,  as  is  assumed  in  the 
undulatory  theory  of  light,  the  ether  exists  in  a  double  refracting  crystal  in 
such  a  state  of  unequal  elasticity,  then  the  two  plane  waves  will  be  formed 
as  above  described,  and  these,  having  different  velocities,  will  give  rise  to 
two  rays  of  unequal  refrangibility  (compare  art.  638)  This  is  the  physical 
account  of  the  phenomenon  of  double  refraction.  It  will  be  remarked  that 
the  vibrations  corresponding  to  the  two  rays  are  transversal,  rectilinear,  and 
in  directions  perpendicular  to  each  other  in  the  rays  respectively.  Accord- 
ingly the  same  theory  accounts  for  the  fact  that  the  two  rays  are  both 
polarised,  and  in  planes  at  right  angles  to  each  other. 

It  is  a  point  still  unsettled  whether,  when  a  ray  of  light  is  polarised  with 
respect  to  a  given  plane,  the  vibrations  take  place  in  directions  within  or 
perpendicular  to  that  plane.  Fresnel  was  of  the  latter  opinion.  It  is,  how- 
ever, convenient  in  some  cases  to  regard  the  plane  of  polarisation  as  that 
plane  in  which  the  vibrations  take  place. 

COLOURS   PRODUCED    BY  THE   INTERFERENCE   OF   POLARISED    LIGHT. 

662.  Xiaws  of  the  Interference  of  polarised  rays. — After  the  discovery 
of  polarisation,  Fresnel  and  Arago  tried  whether  polarised  rays  presented 
the  same  phenomena  of  interference  as  ordinary  rays.  They  were  thus  led 
to  the  discovery  of  the  following  laws  in  reference  to  the  interference  of 
polarised  light,  and,  at  the  same  time,  of  the  brilliant  phenomena  of  colora- 
tion, which  will  be  presently  described  :  — 

I.  When  two  rays  polarised  in  the  same  plane  interfere  with  each  other, 
they  produce  by  their  interference  fringes  of  the  very  same  kind  as  if  they 
were  common  light. 

II.  When  two  rays  of  light  are  polarised  at  right  angles  to  each  other, 
they  produce  no  coloured  fringes  in  the  same  circumstances  under  which 
two  rays  of  common  light  would  produce  them.     When  the  rays  are  po- 
larised in  planes  inclined  to  each  other  at  any  other  angles,  they  produce 
fringes  of  intermediate  brightness  ;  and,  if  the  angle  is  made  to  change,  the 
fringes  gradually  decrease  in  brightness  from  o°  to  90°,  and  are  totally  ob- 
literated at  the  latter  angle. 

III.  Two  rays  originally  polarised  in  planes  at  right  angles  to  each  other 
may  be  subsequently  brought  into  the  same  plane  of  polarisation  without 
acquiring  the  power  of  forming  fringes  by  their  interference. 

IV.  Two  rays  polarised  at  right  angles  to  each  other,  and  afterwards 
brought  into  the  same  plane  of  polarisation,  produce  fringes  by  their  inter- 
ference like  rays  of  common  light,  provided  they  originated  in  a  pencil  the 
whole  of  which  was  originally  polarised  in  any  one  plane. 

V.  In  the  phenomena  of  interference  produced  by  rays  that  have  suf- 
fered double  refraction,  a  difference  of  half  an  undulation  must  be  allowed, 


-664]  Effect  produced  when  the  Plate  of  Crystal  is  very  thin.  577 

as  one  of  the  pencils  is  retarded  by  that  quantity,  from  some  unknown 
cause. 

663.  Effect  produced  by  causing:  a  pencil  of  polarised  rays  to  tra- 
verse a  double  refracting-  crystal. — The  following  important  experiment 
may  be  made  most  conveniently  by  Norremberg's  apparatus  (fig.  543).  At 
g  (fig.  544)  there  is  a  Nicol's  prism.  A  plate  of  a  double  refracting  crystal 
cut  parallel  to  its  axis  is  placed  on  the  disc  at  e.  In  the  first  place,  however, 
suppose  the  plate  of  the  crystal  to  be  removed.  Then,  since  the  Nicol's 
prism  allows  only  the  extraordinary  ray  to  pass  when  it  is  turned  so  that  its 
principal  plane  coincides  with  the  plane  of  reflection,  no  light  will  be  trans- 
mitted (660).  Place  the  plate  of  doubly  refracting  crystal,  which  is  supposed 
to  be  of  moderate  thickness,  in  the  path  of  the  reflected  ray  at  e.  Light  is 
now  transmitted  through  the  Nicol's  prism.  On  turning  the  plate,  the 
intensity  of  the  transmitted  light  varies  ;  it  reaches  its  maximum  when  the 
principal  plane  of  the  plate  is  inclined  at  an  angle  of  45°  to  the  plane  o* 
reflection,  and  disappears  when  these  planes  either  coincide  with  or  are  at 
right  angles  to  each  other.  The  light  in  this  case  is  white.  The  interposed 
plate  may  be  called  the  depolarising  plate.  The  same  or  equivalent  phe- 
nomena are  produced  when  any  other  analyser  is  used.  Thus,  assume  the 
double  refracting  prism  to  be  used.  Suppose  the  depolarising  plate  to  be 
removed.  Then,  generally,  two  rays  are  transmitted  ;  but  if  the  principal 
plane  of  the  analyser  is  turned  in  the  plane  of  primitive  polarisation,  the 
ordinary  ray  only  is  transmitted,  and  then,  when  turned  through  90°,  the 
extraordinary  ray  only  is  transmitted.  Let  the  analyser  be  turned  into 
the  former  position,  then,  when  the  depolarising  plate  is  interposed,  both 
ordinary  and  extraordinary  rays  are  seen,  and  when  the  depolarising  plate 
is  slowly  turned  round,  the  ordinary  and  extraordinary  rays  are  seen  to  vary 
in  intensity,  the  latter  vanishing  when  the  principal  plane  of  the  polarising 
plate  either  coincides  with  or  is  at  right  angles  to  the  plane  of  primitive 
polarisation. 

664.  Effect  produced  when  the  plate  of  crystal  is  very  thin. — In 
order  to  exhibit  this,  take  a  thin  film  of  selenite  or  mica  between  the  twentieth 
and  sixtieth  of  an  inch  thick,  and  interpose  it  as  in  the  last  article.  If  the 
thickness  of  the  film  is  uniform,  the  light  now  transmitted  through  the 
analyser  will  be  no  longer  white,  but  of  a  uniform  tint  ;  the  colour  of  the 
tint  being  different  for  different  thicknesses — for  instance,  red,  or  green,  or 
blue,  or  yellow,  according  to  the  thickness  ;  the  intensity  of  the  colour  de- 
pending on  the  inclination  of  the  principal  plane  of  the  film  to  the  plane  of 
reflection,  being  greatest  when  the  angle  of  inclination  is  45°.  Let  us  now 
suppose  the  crystalline  film  to  be  fixed  in  that  position  in  which  the  light  is 
brightest,  and  suppose  its  colour  to  be  red.  Let  the  analyser  (the  Nicol's 
prism)  be  turned  round,  the  colour  will  grow  fainter,  and  when  it  has  been 
turned  through  45°,  the  colour  disappears,  and  no  light  is  transmitted  ;  on 
turning  it  further,  the  complementary  colour,  green,  makes  its  appearance, 
and  increases  in  intensity  until  the  analyser  has  been  turned  through  90°  ; 
after  which  the  intensity  diminishes  until  an  angle  of  135°  is  attained,  when 
the  light  again  vanishes,  and,  on  increasing  the  angle,  it  changes  again  into 
red.  Whatever  be  the  colour  proper  to  the  plate,  the  same  series  of  pheno- 
mena will  be  observed,  the  colour  passing  into  its  complementary  when  the 

c  c 


5/8  On  Light.  [664- 

analyser  is  turned.  That  the  colours  are  really  complementary  is  proved 
by  using  a  double  refracting  prism  as  analyser.  In  this  case  two  rays  are 
transmitted,  each  of  which  goes  through  the  same  changes  of  colour  and  in- 
tensity as  the  single  ray  described  above  ;  but  whatever  be  the  colour  and 
intensity  of  the  one  ray  in  a  given  position,  the  other  ray  will  have  the  same 
when  the  analyser  has  been  turned  through  an  angle  of  90°.  Consequently, 
these  two  rays  give  simultaneously  the  appearances  which  are  successively 
presented  in  the  above  case  by  the  same  ray  at  an  interval  of  90°.  If  now 
the  two  rays  are  allowed  to  overlap,  they  produce  white  light  ;  thereby 
proving  their  colours  to  be  complementary. 

Instead  of  using  plates  of  different  thicknesses  to  produce  different  tints, 
the  same  plate  may  be  employed  inclined  at  different  angles  to  the  polarised 
ray.  This  causes  the  ray  to  traverse  the  film  obliquely,  and,  in  fact,  amounts 
to  an  alteration  in  its  thickness. 

With  the  same  substance,  but  with  plates  of  increasing  thickness,  the 
tints  follow  the  laws  of  the  colours  of  Newton's  rings  (650).  The  thickness 
of  the  depolarising  plate  must,  however,  be  different  from  that  of  the  layer  of 
air  in  the  case  of  Newton's  rings  to  produce  corresponding  colours.  Thus 
corresponding  colours  are  produced  by  a  plate  of  mica  and  a  layer  of  air 
when  the  thickness  of  the  former  is  about  400  times  that  of  the  latter.  In 
the  case  of  selenite  the  thickness  is  about  230  times,  and  in  the  case  of  Ice- 
land spar  about  13  times,  that  of  the  corresponding  layer  of  air. 

665.  Theory  of  the  phenomena  of  depolarisation. — The  phenomena 
described  in  the  last  articles  admit  of  complete  explanation  by  the  undulatory 
theory,  but  not  without  the  aid  of  abstruse  mathematical  calculations.    What 
follows  will,  show  the  nature  of  the  explanation.     Let  us  suppose,  for  con- 
venience, that  in  the  case  of  a  polarised  ray  the  particles  of  ether  vibrate 
in  the  plane  of  polarisation  (see  art.  66 1),  and  that  the  analyser  is  a  double 
refracting  prism,  with  its  principal  plane  in  the  plane  of  primitive  polarisa- 
tion ;  then  the  vibrations,  being  wholly  in  that  plane,  have  no  resolved  part  in 
a  plane  at  right  angles  to  it,  and,  consequently,  no  extraordinary  ray  passes 
through  the  analyser  ;  in  other  words,  only  an  ordinary  ray  passes.     Now 
take  the  depolarising  plate  cut  parallel  to  the  axis,  and  let  it  be  interposed  in 
such  a  manner  that  its  principal  plane  makes  any  angle  (6}  with  the  plane 
of  primitive  polarisation.     The  effect  of  this  will  be  to  cause  the  vibrations 
of  the  primitive  ray  to  be  resolved  in  the  principal  plane  and  at  right  angles 
to  the  principal  plane,  thereby  giving  rise  to  an  ordinary  ray  (O),  and  an  ex- 
traordinary ray  (E),  which,  however,  do  not  become  separated  on  account  of 
the  thinness  of  the  depolarising  plate.     They  will  not  form  a  single  plane 
polarised  ray  on  leaving  the  plate,  since  they  are  unequally  retarded  in  pass- 
ing through  it,  and  consequently  leave  it  in  different  phases.     Since  neither 
of  the  planes  of  polarisation  of  O  and  E  coincides  with  the  principal  plane 
of  the  analyser,  the  vibrations  composing  them  will  again  be  resolved — viz. 
O  gives  rise  to  Oo  and  O<?,  and  E  gives  rise  to  E0  and  ~Ee.     But  the  vibra- 
tions composing  Oo  and  E<?,  being  in  the  same  phase,  give  rise  to  a  single 
ordinary  ray,  !<?,  and  in  like  manner  Oe  and  ~Ee  give  rise  to  a  single  extraor- 
dinary ray,  le.     Thus  the  interposition  of  the  depolarising  plate  restores  the 
extraordinary  ray. 

Suppose  the  angle  6  to  be  either  o°  or  90°.     In  either  case  the  vibrations 


nr 


« 


-666]          Coloured  Rings  produced  by  Polarised  Light.  579 

are  transmitted  through  the  depolarising  plate  without  resolution,  conse- 
quently they  remain  wholly  in  the  plane  of  primitive  polarisation,  and  on 
entering  the  analyser  cannot  give  rise  to  an  extraordinary  ray. 

If  the  Nicol's  prism  is  used  as  an  analyser,  the  ordinary  ray  is  suppressed 
by  mechanical  means.  Consequently  only  \e  will  pass  through  the  prism, 
and  that  for  all  values  of  6  except  o°  and  90°. 

A  little  consideration  will  show  that  the  joint  intensities  of  all  the  rays 
existing  at  any  stage  of  the  above  transformations  must  continue  constant, 
but  that  the  intensities  of  the  individual  rays  will  depend  on  the  magnitude 
of  6 ;  and  when  this  circumstance  is  examined  in  detail,  it  explains  the  fact 
that  \e  increases  in  intensity  as  Q  increases  from  o°  to  45°,  and  then  decreases 
in  intensity  as  6  increases  from  45°  to  90°. 

In  regard  to  the  colour  of  the  rays,  it  is  to  be  observed  that  the  formulae 
for  the  intensities  of  \o  and  \e  contain  a  term  depending  on  the  length  of  the 
wave  and  the  thickness  of  the.  plate.  Consequently,  when  white  light  is  used, 
the  relative  intensities  of  its  component  colours  are  changed,  and,  therefore, 
\o  and  \e  will  each  have  a  prevailing  tint,  which  will  be  different  for  different 
thicknesses  of  the  plate.  The  tints  will,  however,  be  complementary,  since, 
the  joint  intensities  of  \o  and  \e  being  the  same  as  that  of  the  original  ray, 
they  will,  when  superimposed,  restore  all  the  components  of  that  ray  in  their 
original  intensities,  and  therefore  produce  white  light. 

666.  Coloured  rings  produced  by  polarised  light  in  traversing:  double 
refracting:  films. — In  the  experiments  with  Norremberg's  apparatus  which 
have  just  been  described  (663),  a  pencil  of  parallel  rays  traverses  the  film  of 


M 

Fig  548. 

crystal  perpendicularly  to  its  faces,  and  as  all  parts  of  the  film  act  in  the 
same  manner,  there  is  everywhere  the  same  tint.  But  when  the  incident 
rays  traverse  the  plate  under- different  obliquities,  which  comes  to  the  same 
thing  as  if  they  traversed  plates  differing  in  thickness,  coloured  rings  are 
formed  similar  to  Newton's  rings. 

The  best  method  of  observing  these  new  phenomena  is  by  means  of  the 
tourmaline  pincette  (fig.  548).  This  is  a  small  instrument  consisting  of  two 
tourmalines,  cut  parallel  to  the  axis,  each  of  them  being  fitted  in  a  copper 
disc.  These  two  discs,  which  are  perforated  in  the  centre,  and  blackened, 
are  mounted  in  two  rings  of  silvered  copper,  which  is  coiled,  as  shown  in 
the  figure,  so  as  to  form  a  spring,  and  press  together  the  tourmalines.  The 
tourmalines  turn  with  the  disc,  and  may  be  so  arranged  that  their  axes  are 
either  perpendicular  or  parallel. 

The  crystal  to  be  experimented  upon,  being  fixed  in  the  centre  of  a  cork 
disc,  is  placed  between  the  two  tourmalines,  and  the  pincette  is  held  before 
the  eye  so  as  to  view  diffused  light.  The  tourmaline  farthest  from  the  eye 
acts  as  polariser,  and  the  other  as  analyser.  If  the  crystal  thus  viewed  is 
uniaxial,  and  cut  perpendicularly  to  the  axis,  and  a  homogeneous  light — 
red,  for  instance — is 'looked  at,  a  series  of  alternately  dark  and  red  rings 

c  c  2 


582  On  Light.  [668- 

according  as  the  plates  of  glass  have  a  circular,  square,  rectangular,  or 
triangular  shape,  and  according  to  the  degree  of  tension  of  their  particles. 

When  the  polariser  is  a  mirror  of  black  glass,  on  which  the  light  of  the 
sky  is  incident,  and  the  analyser  is  a  Nicol's  prism,  through  which  the 
glass  plates  traversed  by  polarised  light  are  viewed,  figs.  549,  550,  552 
represent  the  appearances  presented  successively,  when  a  square  plate 
of  compressed  glass  is  turned  in  its  own  plane;  figs.  551  and  554  re- 
present the  appearances  produced  by  a  circular  plate  under  the  same 
circumstances;  and  fig.  553  that  produced  when  one  rectangular  plate  is 
superposed  on  another.  This  figure  also  varies  when  the  system  of  plates 
is  turned. 

ELLIPTICAL,   CIRCULAR,   AND   ROTATORY  POLARISATION. 

669.  Definition  of  elliptical  and  circular  polarisation. — In  the  cases 
hitherto  considered  the  particles  of  ether  composing  a  polarised  ray  vibrate 
in  parallel  straight  lines  ;  to  distinguish  this  case  from  those  we  are  now  to 
consider,  such  light  is  frequently  called  plane  polarised  light.     It  sometimes 
happens  that  the  particles  of  ether  describe  ellipses  round  their  positions  of 
rest,  the  planes  of  the  ellipses  being  perpendicular  to  the  direction  of  the 
ray.    If  the  axes  of  these  ellipses  are  equal  and  parallel,  the  ray  is  said  to  be 
elliptically  polarised.     In  this  case  the  particles  which,  when  at  rest,  occu- 
pied a  straight  line,  are,  when  in  motion,  arranged  in  a  helix  round  the  line 
of  their  original  position  as  an  axis,  the  helix  exchanging  from  instant  to 
instant.     If  the  axes  of  the  ellipses  are  equal,  they  become  circles,  and  the 
light  is  said  to  be  circularly  polarised.     If  the  minor  axes  become  zero,  the 
ellipses  coincide  with  their  major  axes,  and  the  light  becomes  plane  polarised. 
Consequently,  plane  polarised  light  and  circularly  polarised  light  are  parti- 
cular cases  of  elliptically  polarised  light. 

670.  Theory  of  the  origin  of  elliptical  and  circular  polarisation. — 
Let  us  in  the  first  place  consider  a  simple  pendulum  (55)  vibrating  in  any 
plane,  the  arc  of  vibration  being  small.     Suppose  that,  when  in  its  lowest 
position,  it  received  a  blow  in  a  direction  at  right  angles  to  the  direction  of 
its  motion,  such  as  would  make  it  vibrate  in  an  arc  at  right  angles  to  its 
arc  of  primitive  vibration,  it  follows  from   the  law  of  the  composition  of 
velocities  (52)  that  the  joint  effect  will  be  to  make  it  vibrate  in  an  arc  inclined 
at  a  certain  angle  to  the  arc  of  primitive  vibration,  the  magnitude  of  the 
angle  depending  on  the  magnitude  of  the  blow.     If  the  blow  communicated 
a  velocity  equal  to  that  with  which  the  body  is  already  moving,  the  angle 
would  be  45°.     Next  suppose  the  blow  to  communicate  an  equal  velocity, 
but  to  be  struck  when  the  body  is  at  its  highest  point,  this  will  cause  the 
particle  to  describe  a  circle,  and  to  move  as  a  conical  pendulum  (57).     If  the 
blow  is  struck  under  any  other  circumstances,  the  particle  will  describe  an 
ellipse.     Now  as  the  two  blows  would  produce  separately  two  simple  vibra- 
tions in  directions  at  right  angles  to  each  other,  we  may  state  the  result 
arrived   at  as  follows  : — If  two  rectilinear  vibrations  are  superinduced  on 
the  same  particle  in  directions  at  right  angles  to  each  other,  then  :  i.  If 
they  are  in  the  same  and  opposite  phases,  they  make  the  point  describe  a 
rectilinear  vibration  in  a  direction  inclined  at  a  certain  angle  to  either  of 
the  original  vibrations.     2.  But  if  their  phases  differ  by  90°  or  a  quarter 


-671]  Fresnei  *s  Rhomb.  583 

of  a  vibration,  the  particle  will  describe  a  circle,  provided  the  vibrations 
are  equal.    3.  Under  other  circumstances  the  particle  will  describe  an  ellipse. 

To  apply  this  to  the  case  of  polarised  light.  Suppose  two  rays  of  light 
polarised  in  perpendicular  planes  to  coincide,  each  would  separately  cause 
the  same  particles  to  vibrate  in  perpendicular  directions.  Consequently — i. 
If  the  vibrations  are  in  the  same  or  opposite  phases,  the  light  resulting  from 
the  two  rays  is  plane  polarised.  2.  If  the  rays  are  of  equal  intensity,  and 
their  phases  differ  by  90°,  the  resulting  light  is  circularly  polarised.  3.  Under 
other  circumstances  the  light  is  elliptically  polarised. 

As  an  example,  if  reference  is  made  to  arts.  656  and  657,  it  will  be  seen 
that  the  rays  denoted  by  O  and  E  are  superimposed  in  the  manner  above 
described.  Consequently,  the  light  which  leaves  the  depolarising  plate  is 
elliptically  polarised.  If,  however,  the  principal  plane  of  the  depolarising 
plate  is  turned  so  as  to  make  an  angle  of  45°  with  the  plane  of  primitive 
polarisation,  O  and  E  have  equal  intensities;  and  if,  further,  the  plate  is 
made  of  a  certain  thickness,  so  that  the  phases  of  O  and  E  may  differ  by 
90°,  or  by  a  quarter  of  a  vibration,  the  light  which  emerges  from  the  plate  is 
circularly  polarised.  This  method  may  be  employed  to  produce  circularly 
polarised  light. 

Circular  or  elliptical  polarisation  may  be  either  right-handed  or  left- 
handed,  or  what  is  sometimes  called  dextrogyrate  and  Icevogyrate.  If  the 
observer  looks  along  the  ray  in  the  direction  of  propagation,  from  polar- 
iser  to  analyser,  then,  if  the  particles  move  in  the  same  direction  as  the  hands 
of  a  watch  with  its  face  to  the  observer,  the  polarisation  is  right-handed. 

671.  Fresnel's  rhomb. — This  is  a  means  of  obtaining  circularly  polarised 
light.  We  have  just  seen  (670)  that,  to  obtain  a  ray  of  circularly  polarised 
light,  it  is  sufficient  to  decompose  a  ray  of  plane  polarised  light  in  such 
a  manner  as  to  produce  two  rays  of  light  of  equal  intensity  polarised 
in  planes  at  right  angles  to  each  other,  and  differing  in  their  paths  by  a 
quarter  of  an  undulation.  Fresnei  effected  this  by  means  of  a  rhomb,  which 
has  received  his  name.  It  is  made  of  glass  ;  its  acute  angle  is  54°,  and  its 
obtuse  126°.  If  a  ray  (#,  fig.  555)  of  plane  polarised  light  falls  perpendicu- 
larly on  the  face  AB,  it  will  undergo  two  total  internal  reflections  at  an  angle 
of  about  54°,  one  at  E,  and  the  other  at  F,  and  will  emerge  perpendicularly. 

If  the  plane  ABCD  be  inclined  at  an  angle  of 
45°  to  the  plane  of  polarisation,  the  polarised  ray 
will  be  divided  into  two  coincident  rays,  with  their 
planes  of  polarisation  at  right  angles  to  each  other, 
and  it  appears  that  one  of  them  loses  exactly  a 
quarter  of  an  undulation,  so  that  on  emerging  from 
the  rhomb  the  ray  is  circularly  polarised.  If  the  ray 
emerging  as  above  from  Fresnel's  rhomb  is  ex- 
amined, it  will  be  found  to  differ  from  plane  polarised 
light  in  this,  that,  when  it  passes  through  a  double 
refracting  prism,  the  ordinary  and  extraordinary 
rays  are  of  equal  intensity  in  all  positions  of  the 
prism.  Moreover,  it  differs  from  ordinary  light  in 
this,  that,  if  it  passed  through  a  second  rhomb  placed 
parallel  to  the  first,  a  second  quarter  of  an  undulation  will  be  lost,  so  that 


584  On  Light.  [671- 

the  parts  of  the  original  plane  polarised  ray  will  differ  by  half  an  undulation, 
and  the  emergent  ray  will  be  plane  polarised  ;  moreover  the  plane  of  polar- 
isation will  be  inclined  at  an  angle  of  45°  to  ABCD,  but  on  the  other  side 
from  the  plane  of  primitive  polarisation. 

672.  Elliptical  polarisation. — In  addition  to  the  method  already  men- 
tioned (671),  elliptically  polarised  light  is  generally  obtained  whenever  plane 
polarised    light  suffers   reflection.      Polarised    light  reflected   from    metals 
becomes  elliptically  polarised,  the  degree  of  ellipticity  depending  on  the  direc- 
tion of  the  incident  ray,  and  of  its  plane  of  polarisation,  as  well  as  on  the  nature 
of  the  reflecting  substance.     When  reflected  from  silver,  the  polarisation  is 
almost  circular,  and  from  galena  almost  plane.  If  elliptically  polarised  light  be 
analysed  by  the  Nicol's  prism,  it  never  vanishes,  though  at  alternate  positions 
it  becomes  fainter  :  it  is  thus  distinguished  from  plane  and  from  circular, 
polarised  light.     If  analysed  by  Iceland  spar  neither  image  disappears,  but 
they  undergo  changes  in  intensity. 

Light  can  also  be  polarised  elliptically  in  Fresnel's  rhomb.  If  the  angle 
between  the  planes  of  primitive  polarisation  and  of  incidence  be  any  other 
than  45°,  the  emergent  ray  is  elliptically  polarised. 

673.  Rotatory  polarisation. — Rock  crystal  or   quartz  possesses  a  re- 
markable property  which  was  long  regarded  as  peculiar  to  itself  among  all 
crystals,  though  it  has  been  since  found  to  be  shared  by  tartaric  acid  and  its 
salts,  together  with  some  other  crystalline  bodies.     This  property  is  called 
rotatory   polarisation,  and    may   be  described   as   follows  : — Let   a   ray  of 
homogeneous  light  be  polarised,  and  let  the  analyser,  say  a  Nicol's  prism,  be 
turned  till  the  light  does  not  pass  through  it.    Take  a  thin  section  of  a  quartz 
crystal  cut  at  right  angles  to  its  axis,  and  place  it  between  the  polariser  and 
the  analyser  with  its  plane  at  right  angles  to  the  rays.     The  light  will  now 
pass  through  the  analyser.     The  phenomenon  is  not  the  same  as  that  pre- 
viously described  (663),  for,  if  the  rock  crystal  is  turned  round  its  axis,  no 
effect  is  produced,  and  if  the  analyser  is  turned,  the  ray  is  found  to  be  plane 
polarised  in  a  plane  inclined  at  a  certain  angle  to  the  plane  of  primitive 
polarisation.     If  the  light  is  red,  and  the  plate  i  millimetre  thick,  this  angle 
is   about  17°.     In   some  specimens   of  quartz  the  plane   of  polarisation  is 
turned  to  the  right  hand,  in  others  to  the  left  hand.     Specimens  of  the 
former  kind  are  said  to  be  right-handed,  those  of  the  latter  kind  left-handed. 
This  difference  corresponds  to  a  difference  in   crystallographic    structure. 
The  property  possessed  by  rock  crystal  of  turning  the  plane  of  polarisation 
through  a  certain  angle  was  thoroughly  investigated  by  Biot,  who,  amongst 
other  results,  arrived  at  this  : — For  a  given  colour  the  angle  through  which 
the  plane  of  polarisation  is  turned  is  proportional  to  the  thickness  of  the 
quartz. 

674.  Physical  explanation  of  rotatory  polarisation. — The  explanation 
of  the  phenomenon  described  in  the  last  article  is  as  follows  : — When  a  ray 
of  polarised  light  passes  along  the  axis  of  the  quartz  crystal,  it  is  divided  into 
two  rays  of  circularly  polarised  light  of  equal  intensity,  which  pass  through 
the  crystal  with  different  velocities.     In  one  the  circular  polarisation  is  right- 
handed,  in  the  other  left-handed  (670).     The  existence  of  these  rays  was 
proved  by  Fresnel,  who  succeeded  in  separating  them.     On  emerging  from 
the  crystal,  they  are  compounded  into  a  plane  polarised  ray ;  but,  since  they 


-675]          Coloration  produced  by  Rotatory  Polarisation.  585 

move  with  unequal  velocities  within  the  crystal,  they  emerge  in  different 
phases,  and  consequently  the  plane  of  polarisation  will  not  coincide  with  the 
plane  of  primitive  polarisation.  This  can  be  readily  shown  by  reasoning 
similar  to  that  employed  in  art.  670.  The  same  reasoning  will  also  show 
that  the  plane  of  polarisation  will  be  turned  to  the  right  or  left,  according 
as  the  right-handed  or  left-handed  ray  moves  with  the  greater  velocity. 
Moreover,  the  amount  of  the  rotation  will  depend  on  the  amount  of  the 
retardation  of  the  ray  whose  velocity  is  least ;  that  is  to  say,  it  will  depend 
on  the  thickness  of  the  plate  of  quartz.  In  this  manner  the  phenomena  of 
rotatory  polarisation  can  be  completely  accounted  for. 

675.  Coloration  produced  by  rotatory  polarisation. — The  rotation  is 
different  with  different  colours  ;  its  magnitude  depends  on  the  refrangibility, 
and  is  greatest  with  the  most  refrangible  rays.  In  the  case  of  red  light  a 
plate  i  millimetre  in  thickness  will  rotate  the  plane  17°,  while  a  plate  of  the 
same  thickness  will  rotate  it  44°  in  the  case  of  violet  light.  Hence  with 
white  light  there  will,  in  each  position  of  the  analysing  Nicol's  prism,  be  a 
greater  or  less  quantity  of  each  colour  transmitted.  In  the  case  of  a  right- 
handed  crystal,  when  the  Nicol's  prism  is  turned  to  the  right,  the  colours  will 
successively  appear  from  the  less  refrangible  to  the  more  so — that  is,  in  the 
order  of  the  spectrum,  from  red  to  violet ;  with  a  left- 
handed  crystal  in  the  reverse  order.  Obviously  in 
turning  the  Nicol's  prism  to  the  left,  the  reverse  of 
these  results  will  take  place. 

When  a  quartz  plate  cut  perpendicularly  to  the 
axis  and  traversed  by  a  ray  of  polarised  light  is 
looked  at  through  a  doubly  refracting  prism,  two 

brilliantly  coloured  images  are  seen,  of  which  the  tints  are  complementary  : 
for  their  images  are  partially  superposed,  and  in  this  position  there  is 
white  light  (fig.  556).  When  the  prism  is  turned  from  left  to  right,  the  two 
images  change  colour  and  assume  successively  all  the  colours  of  the 
spectrum. 

This  will  be  understood  from  what  has  been  said  about  the  different 
rotation  for  different  colours.  Quartz  rotates  the  plane  of  polarisation  for 
red  17°  for  each  millimetre,  and  for  violet  44°  ;  hence  from  the  great  difference 
of  these  two  angles,  when  the  polarised  light  which  has  traversed  the  quartz 
plate  emerges,  the  various  simple  colours  which  it  contains  are  polarised  in 
different  planes.  Consequently,  when  the  rays  thus  transmitted  by  the 
quartz  pass  through  a  double  refracting  prism,  they  are  each  decomposed 
into  two  others  polarised  at  right  angles  to  each  other  :  the  various  simple 
colours  are  not  divided  in  the  same  proportion  between  the  ordinary  and 
extraordinary  rays  furnished  by  the  prism  ;  the  two  images  are,  therefore, 
coloured  ;  but,  since  those  which  are  wanting  in  one  occur  in  the  other,  the 
colours  of  the  images  are  perfectly  complementary. 

These  phenomena  of  coloration  may  be  well  seen  by  means  of  Norrem- 
berg's  apparatus  (fig.  544).  A  quartz  plate,  J,  cut  at  right  angles  to  the  axis 
and  fixed  in  a  cork  disc,  is  placed  on  a  screen,  e ;  the  mirror,  n  (fig.  543), 
being  then  so  inclined  that  a  ray  of  polarised  light  passes  through  the  quartz, 
the  latter  is  viewed  through  a  refracting  prism,  g ;  when  this  tube  is  turned 

cc3 


586  On  Light.  [675- 

the  complementary  images  furnished  by  the  passage  of  polarised  light 
through  the  quartz  are  seen. 

676.  Rotatory  power  of  liquids. — Biot  found  that  a  great  number  of 
liquids  and  solutions  possess  the  property  of  rotatory  polarisation.  He 
further  observed  that  the  deviation  of  the  plane  of  polarisation  can  reveal 
differences  in  the  composition  of  bodies  where  none  is  exhibited  by  chemical 
analysis.  For  instance,  the  two  sugars  obtained  by  the  action  of  dilute  acids 
on  cane-sugar  deflect  the  plane  of  polarisation,  the  one  to  the  right  and  the 
other  to  the  left,  although  the  chemical  composition  of  the  two  sugars  is  the 
same. 

The  rotatory  power  of  liquids  is  far  less  than  that  of  quartz.  In  con- 
centrated syrup  of  cane-sugar,  which  possesses  the  rotatory  power  in  the 
highest  degree,  the  power  is  ^  that  of  quartz,  so  that  it  is  necessary  to 
operate  upon  columns  of  liquids  of  considerable  length — 8  inches  for  example. 

Fig.  557  represents  the  apparatus  devised  by  Biot  for  measuring  the 
rotatory  power  of  liquids.  On  a  metal  groove,  g,  fixed  to  a  support,  r,  is  a 


brass  tube  20  centimetres  long,  in  which  is  contained  the  liquid  experimented 
upon.  This  tube,  which  is  tinned  inside,  is  closed  at  each  end  by  glass 
plates  fastened  by  screw  collars.  At  m  is  a  mirror  of  black  glass,  inclined 
at  the  polarising  angle  to  the  axis  of  the  tubes  bd  and  a,  so  that  the  ray  re- 
flected by  the  mirror  m,  in  the  direction  bda,  is  polarised.  In  the  centre  of 
the  graduated  circle  h,  inside  the  tube  a,  and  at  right  angles  to  the  axis,  bda> 
is  a  double  refracting  achromatic  prism,  which  can  be  turned  about  the  axis 
of  the  apparatus  by  means  of  a  button  ;/.  The  latter  is  fixed  to  a  limb  <;,  on 


-677]  Rotatory  power  of  Liquids.  587 

which  is  a  vernier,  to  indicate  the  number  of  degrees  turned  through.  Lastly, 
from  the  position  of  the  mirror  ;//,  the  plane  of  polarisation,  S0</,  of  the  re- 
flected ray  is  vertical,  and  the  zero  of  the  graduation  of  the  circle,  h,  is  on 
this  plane. 

Before  placing  the  tube  d  in  the  groove  g,  the  extraordinary  image  fur- 
nished by  the  double  refracting  prism  disappears  whenever  the  limb  c  corre- 
sponds to  the  zero  of  the  graduation,  because  then  the  double  refracting  prism 
is  so  turned  that  its  principal  section  coincides  with  the  plane  of  polarisation 
(661).  This  is  the  case  also  when  the  tube  d  is  full  of  water  or  any  other 
inactive  liquid,  like  alcohol,  ether,  &c.,  which  shows  that  the  plane  of  polari- 
sation has  not  been  turned.  But  if  the  tube  be  filled  with  a  solution  of  cane- 
sugar  or  any  other  active  liquid,  the  extraordinary  image  reappears,  and  to 
extinguish  it  the  limb  must  be  turned  to  a  certain  extent  either  to  the  right 
or  to  the  left  of  zero,  according  as  the  liquid  is  right-handed  or  left-handed, 
showing  that  the  polarising  plane  has  been  turned  by  the  same  angle.  With 
solution  of  cane-sugar  the  rotation  takes  place  to  the  right  ;  and  if  with  the 
same  solution  tubes  of  different  lengths  are  taken,  the  rotation  is  found  to 
increase  proportionally  to  the  length,  in  conformity  with  art.  673  ;  further, 
with  the  same  tube,  but  with  solutions  of  various  strengths,  the  rotation 
increases  with  the  quantity  of  sugar  dissolved,  so  that  the  quantitative 
analysis  of  a  solution  may  be  made  by  means  of  its  angle  of  deviation. 

In  this  experiment  homogeneous  light  must  be  used  ;  for,  as  the  various 
tints  of  the  spectra  have  different  rotatory  powers,  white  light  is  decomposed 
in  traversing  an  active  liquid,  and  the  extraordinary  image  does  not  disappear 
completely  in  any  position  of  the  double  refracting  prism — it  simply  changes 
the  tint.  The  transition  tint  (677)  may,  however,  be  observed.  To  avoid 
this  inconvenience,  a  piece  of  red  glass  is  placed  in  the  tube  between  the  eye 
and  the  double  refracting  prism,  which  only  allows  red  light  to  pass.  The 
extraordinary  image  disappears  in  that  case,  whenever  the  principal  section 
of  the  prism  coincides  with  the  plane  of  polarisation  of  the  red  ray. 

677.  Soleil's  saccharimeter. — Soleil  constructed  an.  apparatus,  based 
upon  the  rotatory  power  of  liquids,  for  analysing  saccharine  substances,  to 
which  the  name  saccharimeter  is  applied.  Figure  558  represents  the  sac- 
charimeter fixed  horizontally  on  its  foot,  and  fig.  559  gives  a  longitudinal 
section. 

The  principle  of  this  instrument  is  not  the  amplitude  of  the  rotation  of 
the  plane  of  polarisation,  as  in  Biot's  apparatus,  but  that  of  compensation  ; 
that  is  to  say,  a  second  active  substance  is  used  acting  in  the  opposite  direc- 
tion to  that  analysed,  and  whose  thickness  can  be  altered  until  the  contrary 
actions  of  the  two  substances  completely  neutralise  each  other.  Instead 
of  measuring  the  deviation  of  the  plane  of  polarisation,  the  thickness  is 
measured  which  the  plate  of  quartz  must  have  in  order  to  obtain  perfect 
compensation. 

The  apparatus  consists  of  two  parts — a  tube  containing  the  liquid  to  be 
analysed,  a  polariser,  and  an  analyser. 

The  tube  ;«,  containing  the  liquid,  is  made  of  copper,  tinned  on  the 
ins'de,  and  closed  at  both  ends  by  two  glass  plates.  It  rests  on  a  support, 
k,  terminated  at  both  ends  by  tubes,  r  and  #,  in  which  are  the  crystals  used 
as  analysers  and  polarisers,  and  which  are  represented  in  section  (fig.  559). 


588 


On  Light. 


[677- 


In  front  of  the  aperture,  S  (fig.  559),  is  placed  an  ordinary  moderator 
lamp.  The  light  emitted  by  this  lamp  in  the  direction  of  the  axis  first  meets 
a  double  refracting  prism,  r^  which  serves  as  polariser  (659).  The  ordinary 
image  alone  meets  the  eye,  the  extraordinary  image  being  projected  out  of 
the  field  of  vision  in  consequence  of  the  amplitude  of  the  angle  which  the 
ordinary  makes  with  the  extraordinary  ray.  The  double  refracting  prism  is 


Fig.  558. 

in  such  a  position  that  the  plane  of  polarisation  is  vertical,  and  passes  through 
the  axis  of  the  apparatus. 

Emerging  from  the  double  refracting  prism,  the  polarised  ray  meets  a 
plate  of  quartz  with  double  rotation  ;  that  is,  this  plate  rotates  the  plane 
both  to  the  right  and  to  the  left.  This  is  effected  by  constructing  the  plate 
of  two  quartz  plates  of  opposite  rotation  placed  one  on  the  other,  as  shown 
in  fig.  560,  so  that  the  line  of  separation  is  vertical  and  in  the  same  plane  as 
the  axis  of  the  apparatus.  These  plates,  cut  perpendicularly  to  the  axis, 
have  a  thickness  of  375  millimetres,  corresponding  to  a  rotation  of  90°,  and 
give  a  rose-violet  tint,  called  the  tint  of  passage  or  transition  tint.  As  the 
quartz,  whether  right-handed  or  left-handed,  turns  always  to  the  same  extent 
for  the  same  thickness,  it  follows  that  the  two  quartz  plates,  a  and  $,  turn 
the  plane  of  polarisation  equally,  one  to  the  right  and  the  other  to  the  left. 
Hence,  looked  at  through  a  double  refracting  prism,  they  present  exactly  the 
same  tint. 

Having  traversed  the  quartz,  q,  the  polarised  ray  passes  into  the  liquid 
in  the  tube  m,  and  then  meets  a  single  plate  of  quartz,  z,  of  any  thickness, 
the  use  of  which  will  be  seen  presently.  The  compensator,  «,  which  destroys 
the  rotation  of  the  column  of  liquid  m,  consists  of  two  quartz  plates,  with  the 


-677] 


Soleil  's  Saccharimeter. 


589 


same  rotation  either  to  the  right  or  the  left,  but  opposite  to  that  of  the  plate 
/'.  These  two  quartz  plates,  a  section  of  which  is  represented  in  fig.  560,  are 
obtained  by  cutting  obliquely  a  quartz  plate  with  parallel  sides,  so  as  to  form 
two  prisms  of  the  same  angle,  N,  N' ;  superposing,  then,  these  two  prisms, 
as  shown  in  the  figure,  a  single  plate  is  obtained  with  parallel  faces,  which 
can  be  varied  at  will.  This  is  effected  by  fixing  each  prism  to  a  slide,  so  as 
to  move  it  in  either  direction  without  disturbing  the  parallelism.  This  motion 
is  effected  by  means  of  a  double  rackwork  and  pinion  motion  turned  by  a 
milled  head,  b  (figs.  558,  559). 

When  these  plates  move  in  the  direction  indicated  by  the  arrows  (fig.  560), 
it  is  clear  that  the  sum  of  their  thicknesses  increases,  and  that  it  diminishes 

Fig-  559« 


Fig.  560. 


Fig.  562. 


when  the  plates  are  moved  in  the  contrary  direction.  A  scale  and  a  vernier 
follow  the  plates  in  their  motion,  and  measure  the  thickness  of  the  compen- 
sator. This  scale,  represented  with  its  vernier  in  fig.  561,  has  two  divisions 
with  a  common  zero,  one  from  left  to  right  for  right-handed  liquids,  and 
another  from  right  to  left  for  left-handed. 

When  the  vernier  is  at  zero  of  the  scale,  the  sum  of  the  thicknesses  of 
the  plates  NN'  is  exactly  equal  to  that  of  the  plate  z,  and  as  the  rotation  of 
the  latter  is  opposed  to  that 'of  the  compensator,  the  effect  is  zero.  But  by 
moving  the  plates  of  the  compensator  in  one  or  the  other  direction  either 
the  compensator  or  the  quartz,  z,  preponderates,  and  there  is  a  rotation  from 
left  to  right. 

Behind  the  compensator  is  a  double  refracting  prism,  c  (fig.  559),  serving 
as-  analyser  to  observe  the  polarised  ray  which  has  traversed  the  liquid  and 
the  various  quartz  plates.  In  order  to  understand  more  easily  the  object  of 
the  prism,  c,  we  will  neglect  for  a  moment  the  crystals  and  the  lenses  on  the 
left  of  the  drawing.  If  at  first  the  zero  of  the  vernier,  o,  coincides  with  that 
of  the  scale,  and  if  the  liquid  in  the  tube  is  inactive,  the  actions  of  the  com- 
pensator, and  of  the  plate  /,  neutralise  each  other  ;  and,  the  liquid  having  no 
action,  the  two  halves  of  the  plate  q,  seen  through  the  prism  <:,  give  exactly 
the  same  tint  as  has  been  observed  above.  But  if  the  tube  filled  with  inac- 
tive liquid  be  replaced  by  one  full  of  solution  of  sugar,  the  rotatory  power  of 
this  solution  is  added  to  that  of  one  of  the  halves  (a  or  b}  of  the  plate  q  (viz. 
that  half  which  tends  to  turn  the  plane  of  polarisation  in  the  same  direction 


5QO  On  Light  [677- 

as  the.  solution),  and  subtracted  from  that  of  the  other.  Hence  the  two 
halves  of  the  plate  q  no  longer  show  the  same  tint ;  the  half  a,  for  instance, 
is  red,  while  the  half  b  is  blue.  The  prisms  of  the  compensator  are  then 
moved  by  turning  the  milled  head  b,  either  to  the  right  or  to  the  left,  until 
the  difference  of  action  of  the  compensator  and  of  the  plate  i  compensates 
the  rotatory  power  of  the  solution,  which  takes  place  when  the  two  halves 
of  the  plate  Q,  with  double  rotation,  revert  to  their  original  tint. 

The  direction  of  the  deviation  and  the  thickness  of  the  compensator  are 
measured  by  the  relative  displacement  of  the  scale  *,  and  of  the  vernier  r. 
Ten  of  the  divisions  on  the  scale  correspond  to  a  difference  of  I  millimetre 
in  the  thickness  of  the  compensator  ;  and  as  the  vernier  gives  itself  tenths 
of  these  divisions,  it  therefore  measures  differences  of  T~  in  the  thickness  of 
the  compensator. 

When  once  the  tints  of  the  two  halves  of  the  plate  are  exactly  the  same, 
and  therefore  the  same  as  before  interposing  the  solution  of  sugar,  the 
division  on  the  scale  corresponding  to  the  vernier  is  read  off,  and  the  cor- 
responding number  gives  the  strength  of  the  solution.  This  depends  on  the 
experimental  fact  that  16-471  grains  of  pure  and  well-dried  sugar-candy  being 
dissolved  in  water,  and  the  solution  diluted  to  the  volume  of  100  cubic  cen- 
timetres, and  observed  in  a  tube  of  20  centimetres  in  length,  the  deviation 
produced  is  the  same  as  that  effected  by  a  quartz  plate  a  millimetre  thick. 
In  making  the  analysis  of  raw  sugar,  a  weight  of  16-4/1  .grains  of  sugar  is 
taken,  dissolved  in  water,  and  the  solution  made  up  to  100  cubic  centimetres 
with  which  a  tube  20  centimetres  in  length  is  filled,  and  the  number  indicated 
by  the  vernier  read  off,  when  the  primitive  tint  has  been  obtained.  This 
number  being  42,  for  example,  it  is  concluded  that  the  amount  of  crystallisable 
sugar  in  the  solution  is  42  per  cent,  of  that  which  the  solution  of  sugar-candy 
contained,  and,  therefore,  16-471  grains  x  T4|5  or  6-918  grains.  This  result 
is  only  valid  when  the  sugar  is  not  mixed  with  uncrystallisable  sugar  or 
some  other  left-handed  substance.  In  that  case  the  crystallisable  sugar, 
which  is  right-handed,  must  be,  by  means  of  hydrochloric  acid,  converted 
into  uncrystallisable  sugar,  which  is  left-handed  ;  and  a  new  determination 
is  made,  which,  together  with  the  first,  gives  the  quantity  of  crystallisable 
sugar. 

The  arrangement  of  crystals  and  lenses,  o,  g,f,  and  #,  placed  behind  the 
prism  c  forms  what  Soleil  calls  the  producer  of  sensible  tints.  For  the 
most  delicate  tint — that  by  which  a  very  feeble  difference  in  the  coloration 
of  the  two  halves  of  the  rotation  plate  can  be  distinguished — is  not  the  same 
for  all  eyes  ;  for  most  people  it  is  of  a  violet-blue  tint,  like  flax-blossom,  and 
it  is  important  either  to  produce  this  tint  or  some  other  equally  sensible  to 
the  eye  of  the  observer.  This  is  effected  by  placing  in  front  of  the  prism,  <:, 
at  first  a  quartz  plate,  0,  cut  perpendicular  to  the  axis,  then  a  small  Galilean 
telescope  consisting  of  a  double  convex  glass,  g,  and  a  double  concave  glass, 
f,  which  can  be  approximated  or  removed  from* each  other  according  to  the 
distance  of  distinct  vision  of  each  observer.  Lastly,  there  is  a  double  re- 
fracting prism,  c,  acting  as  polariser  in  reference  to  the  quartz,  and  the  prism 
a  as  analyser ;  and  hence,  when  the  latter  is  turned  either  right  or  left,  the 
light  which  has  traversed  the  prism  c,  and  the  plate  0,  changes  its  tint,  and 
finally  gives  that  which  is  the  most  delicate  for  the  experimenter. 


-679]  Polarisation  of  Heat.  591 

678.  Analysis  of  diabetic  urine. — In    the   disease  diabetes,  the  urine 
contains  a  large  quantity  of  fermentescible  sugar,  called  diabetic  sugar, 
which  in  the  natural  condition  of  the  urine  turns  the  plane  of  polarisation  to 
the  right.     To  estimate  the  quantity  of  this  sugar,  the  urine  is  first  clarified 
by  heating  it  with  ajcetate  of  lead  and  filtering  ;  the  tube  is  filled  with  the 
clear  liquid  thus  obtained  ;  and  the  milled  head,  b,  turned,  until  by  means  of 
the  double  rotating  plate  the  same  tint  is  obtained  as  before  the  interposition 
of  the  urine.     Experiment  has  shown  that  100  parts  of  the  saccharimetric 
scale  represent  the  displacement  which  the  quartz  compensators  must  have 
when  there  are  225-6  grains  of  sugar  in  a  litre  ;  hence  each  division  of  the 
scale  represents  2*256  of  sugar.     Accordingly,  to  obtain  the  quantity  of  sugar 
in  a  given  urine,  the  number  indicated  by  the  vernier,  at  the  moment  at 
which  the  primitive  tint  reappears,  must  be  multiplied  by  2*256. 

679.  Polarisation  of  beat. — The  rays  of  heat,  like  those  of  light,  may 
become  polarised  by  reflection  and  by  refraction.     The  experiments  on  this 
subject  are  difficult   of  execution  ;    they  were   first   made   by  Malus  and 
Berard,  in  1810  ;  after  the  death  of  Malus  they  were  continued  by  the  latter 
philosopher. 

In  his  experiments,  the  calorific  rays  reflected  from  one  mirror  were  re- 
ceived upon  a  second,  just  as  in  Norremberg's  apparatus  ;  from  the  second 
they  fell  upon  a  small  metallic  reflector,  which  concentrated  them  upon  the 
bulb  of  a  differential  thermometer.  Berard  observed  that  heat  was  not 
reflected  when  the  plane  of  reflection  of  the  second  mirror  was  at  right  angles 
to  that  of  the  first.  As  this  phenomenon  is  the  same  as  that  presented  by 
light  under  the  same  circumstances,  Berard  concluded  that  heat  became 
polarised  in  being  reflected. 

The  double  refraction  of  heat  may  be  shown  by  concentrating  the  sun's 
rays  by  means  of  a  heliostat  on  a  prism  of  Iceland  spar,  and  investigating 
the  resultant  pencil  by  means  of  a  thermopile,  which  must  have  a  sharp 
narrow  edge.  In  this  case  also  there  is  an  ordinary  and  an  extraordinary 
ray,  which  follow  the  same  laws  as  those  of  light.  In  the  optic  axis  of  the 
calcspar,  heat  is  not  doubly  refractive.  A  Nicol's  prism  can  be  used  for  the 
polarisation  of  heat  as  well  as  for  that  of  light ;  a  polarised  ray  does  not 
traverse  the  second  Nicolif  the  plane  of  its  principal  section  is  perpendicular 
to  the  vibrations  of  the  ray.  The  phenomena  of  the  polarisation  of  heat 
may  also  be  studied  by  means  of  plates  of  tourmaline  and  of  mica.  The 
angle  of  polarisation  is  virtually  the  same  for  heat  as  for  light.  In  all  these 
experiments  the  prisms  must  be  very  near  each  other. 

'The  diffraction,  and  therefore  the  interference,  of  rays  of  heat  has  recently 
been  established  by  the  experiments  of  Knoblauch  and  others.  And  Forbes, 
who  has  repeated  Fresnel's  experiment  with  a  rhombohedron  of  rock  salt, 
has  found  that  by  two  total  internal  reflections,  heat  is  circularly  polarised, 
just  as  is  the  case  with  light. 


592  On  Magnetism.  [680- 


BOOK   VIII. 

ON    MAGNETISM. 

CHAPTER    I. 
PROPERTIES   OF  MAGNETS. 

680.  Natural  and  artificial  magnets.— Magnets  are  substances  which 
have  the  property  of  attracting  iron,  and  the  term  magnetism  is  applied  to 
the  cause  of  this  attraction,  and  to  the  resulting  phenomena. 

This  property  was  known  to  the  ancients  ;  it  exists  in  the  highest  degree 
in  an  ore  of  iron  which  is  known  in  chemistry  as  the  magnetic  oxide  of  iron. 
Its  composition  is  represented  by  the  formula  Fe3O4. 

This  magnetic  oxide  of  iron,  or  lodestone,  as  it  is  called,  was  first  found 
at  Magnesia,  in  Asia  Minor,  the  name  magnet  being  derived  from  this  cir- 
cumstance. The  name  lodestone,  which  is  applied  to  this  natural  magnet, 
was  given  on  account  of  its  being  used  when  suspended  as  a  guiding  or  lead- 
ing stone,  from  the  Saxon  Icedan,  to  lead ;  so  also  the  word  lodestar.  Lode- 
stone  is  very  abundant  in  nature  :  it  is  met  with  in  the  older  geological  forma- 
tions, especially  in  Sweden  and  Norway,  where  it  is  worked  as  an  iron  ore, 
and  furnishes  the  best  quality  of  iron. 

When  a  bar  or  needle  of  steel  is  rubbed  with  a  magnet,  it  acquires 
magnetic  properties.  Such  bars  are  called  artificial  magnets  ;  they  are 
more  powerful  than  natural  magnets,  and,  as  they  are  also  more  convenient 
they  will  be  exclusively  referred  to  in  describing  the  phenomena  of  magnet- 
ism ;  the  best  modes  of  preparing  them  will  be  explained  in  a  subsequent 
article. 

681.  Poles  and  neutral  line. — When  a  small  particle  of  soft  iron  is  sus- 
pended by  a  thread  and  a  magnet  is  approached  to  it,  the  iron  is  attracted 
towards  the  magnet,  and  some  force  is  required  for  its  removal.     The  force 
of  the  attraction  varies   in  different  parts  of  the  magnet ;  it  is   strongest  at 
the  two  ends,  and  is  totally  wanting  in  the  middle. 

This  variation  may  also  be  seen  very  clearly  when  a  magnetic  bar  is 
placed  in  iron  filings  ;  these  become  arranged  round  the  ends  of  the  bar 
in  feathery  tufts,  which  decrease  towards  the  middle  of  the  bar,  where 
there  are  none.  That  part  of  the  surface  of  the  bar  where  there  is  no 
visible  magnetic  force  is  called  the  neutral  line ;  and  the  points  near  the 
ends  of  the  bar  where  the  attraction  is  greatest  are  called  the  poles.  Every 


-682] 


Reciprocal  Action  of  Two  Poles. 


593 

magnet,  whether  natural  or  artificial,  has  two  poles  and  a  neutral  line  : 
sometimes,  however,  in  magnetising  bars  and  needles,  poles  are  produced 
lying  between  the  extreme  points.  Such  magnets  are  abnormal,  and  these 
points  are  called  intcrviediate  or  consequent  poles.  The  shortest  line  joining 
the  two  poles  is  termed  the  axis  of  the  magnet ;  in  a  horseshoe  magnet  the 
axis  is  in  the  direction  of  the  keeper.  The  plane  at  right  angles  to  the  axis 
of  a  bar  magnet  and  passing  through  the  neutral  line  is  sometimes  called  the 
equator  of  the  magnet. 

\Ve  shall  presently  see  that  a  freely  suspended  magnet  always  sets  with 
one  pole  pointing  towards  the  north,  and  the  other  towards  the  south.     The 


Fig.  563. 

end  pointing  towards  the  north  is  called  in  this  country  the  north  pole,  and 
the  other  end  is  the  south  pole.  The  end  of  the  magnetic  needle  pointing  to 
the  north  is  also  sometimes  called  the  marked  end  of  the  needle.  Some- 
times also  the  end  pointing  to  the  north  is  called  the  red  pole,  and  that  to 
the  south,  the  blue  pole  ;  the  corresponding  terms  red  and  blue  magnetisms 
are  also  used. 

682.  Reciprocal  action  of  two  poles. — The  two  poles  of  a  magnet  appear 
identical  when  they  are  brought  in  contact 
with  iron  filings  (fig.  563),  but  this  identity 
is  only  apparent,  for  when  a  small  magnetic 
needle,  ab  (fig.  564),  is  suspended  by  -a 
fine  thread,  and  the  north  pole,  A,  of 
another  needle  is  brought  near  its  north 
pole,  a,  a  repulsion  takes  place.  If,  on 
the  contrary',  A  is  brought  near  the  south 
pole,  b,  of  the  movable  needle,  the  latter 
is  strongly  attracted.  Hence  these  two 
poles,  a  and  b,  are  not  identical,  for  one 
is  repelled  and  the  other  attracted  by  the 
same  pole  of  the  magnet,  A.  It  may  be 
shown  in  the  same  manner  that  the  two 
poles  of  the  latter  are  also  different,  by 
successively  presenting  them  to  the  same 
pole,  a,  of  the  movable  needle.  In  one 
case  there  is  repulsion,  in  the  other  attraction, 
may  be  enunciated  : — 

Poles  of  the  same  name  repel,  and  poles  of  contrary  name  attract,  one 
another. 

The  opposite  actions  of  the  north  and  south  poles  may  be  shown  by  the 
following  experiment  : — A  piece  of  iron,  a  key  for  example,  is  supported  by 
a  magnetised  bar.  A  second  magnetised  bar  of  the  same  dimensions  is  then 


Fig.  564- 

Hence  the  following  law 


594  On  Magnetism.  [682- 

moved  along  the  first,  so  that  their  poles  are  contrary  (fig.  565).  The  key 
remains  suspended  so  long  as  the  two  poles  are  at  some  distance,  but  when 
they  are  sufficiently  near,  the  key  drops,  just  as  if  the  bar  which  supported 
it  had  lost  its  magnetism.  This,  however,  is  not  the  case,  for  the  key  would 


Fig.  565- 

be  again  supported  if  the  first  magnet  were  presented  to  it  after  the  removal 
of  the  second  bar. 

The  attraction  which  a  magnet  exerts  upon  iron  is  reciprocal,  which  is 
indeed  a  general  principle  of  all  attractions.  It  is  easily  verified  by  present- 
ing a  mass  of  iron  to  a  movable  magnet,  when  the  latter  is  attracted. 

683.  Hypothesis  of  two  magnetic  fluids. — In  order  to  explain  the  phe- 
nomena of  magnetism,  the  existence  of  two  hypothetical  magnetic  fluids  has 
been  assumed,  each  of  which  acts  repulsively  on  itself,  but  attracts  the  other 
fluid.     The  fluid  predominating  at  the  north  pole  of  the  magnet  is  called 
the  north  fluid  or  red  magnetism,  and  that  at  the  south  pole  the  south  fluid 
or  blue  magnetism.     The  term   '  fluid '  is  apt  to  puzzle  beginners,  from  its 
ambiguity.     Ordinarily  the  idea  of  a  liquid  is  associated  with  the  term  '  a 
fluid  ; '  hence  the  use  of  this  term  to  explain  the  phenomena  of  magnetism 
and  electricity  has  produced  a  widely  prevailing  impression  of  the  material 
nature  of  these  two  forces.  The  word  'fluid,'  it  must  be  remembered,  embraces 
gases  as  well  as  liquids,  and  here  it  must  be  pictured  to  the  mind  as  repre- 
senting an  invisible,  elastic,  gaseous  atmosphere   or  shell  surrounding  the 
particles  of  all  magnetic  substances. 

It  is  assumed  that,  before  magnetisation,  these  fluids  are  combined  round 
each  molecule,  and  mutually  neutralise  each  other  ;  they  can  be  separated 
by  the  influence  of  a  force  greater  than  that  of  their  mutual  attraction,  and 
can  arrange  themselves  round  the  molecules  to  which  they  are  attached,  but 
cannot  be  removed  from  them. 

The  hypothesis  of  the  two  fluids  is  convenient  in  explaining  magnetic 
phenomena,  and  will  be  adhered  to  in  what  follows.  But  it  must  not  be 
regarded  as  anything  more  than  an  hypothesis,  and  it  will  afterwards  be 
shown  (878)  that  magnetic  phenomena  appear  to  result  from  electrical  cur- 
rents, circulating  in  magnetic  bodies  ;  a  mode  of  view  which  connects  the 
theory  of  magnetism  with  that  of  electricity. 

684.  Precise  definition  of  poles. — By  aid  of  the  preceding  hypothesis 
we  are  enabled  to  obtain  a  clearer  idea  of  the  distribution  of  the  magnetism 
in  a  magnetised  bar,  and  to  account  for  the  circumstance  that  there  is  no 
free  magnetism  in  the  middle  of  the  bar,  and  that  it  is  strongest  at  the  poles. 
If  AB  (fig.   566)  represents  a  magnet,  then  the  alternate  black  and  white 
spaces  may  be  taken  to  represent  the  position  of  the  magnetic  fluids  in  a 


-684]  Precise  Definition  of  Poles.  595 

series  of  particles  after  magnetisation  ;  in  accordance  with  what  has  been 
said,  the  white  spaces,  representing  the  south  fluid,  all  point  in  one  direction, 
and  the  north  fluid  in  the  opposite  direction.  The  last  half  of  the  terminal 
molecule  at  one  end  would  have  north  polarity,  and  at  the  other  south 
polarity.  Let  N  represent  the  north  pole  of  a  magnetic  needle  placed  near 
the  magnet  AB  ;  then  the  south  fluid,  s,  in  the  terminal  molecule  would  tend 

n"  s"  n  s  n  s 


Fig.  566. 

to  attract  N,  and  the  north  fluid  n  would  tend  to  repel  it  ;  but  as  the  mole- 
cule of  south  fluid  s  is  nearer  N  than  the  molecule  of  the  north  fluid  «,  the 
attraction  between  s  and  N  would  be  greater  than  the  repulsion  between  n 
and  N.  Similarly  the  attraction  between  s'  and  N  would  be  greater  than 
the  repulsion  between  n'  and  N,  and  so  on  with  the  following  s"  and  «",  £c. 
And  all  these  forces  would  give  a  resultant  tending  to  attract  N,  whose 
point  of  application  would  have  a  certain  fixed  position,  which  would  be  the 
south  pole  of  AB.  In  like  manner  it  might  be  shown  that  the  resultant  of 
the  forces  acting  at  the  other  end  of  the  bar  would  form  a  north  pole,  and 
would  hence  repel  the  north  pole  of  the  needle,  but  would  attract  its  south 
pole. 

That  such  a  series  of  polarised  particles  really  acts  like  an  ordinary 
magnet  may  be  shown  by  partly  filling  a  glass  tube  with  steel  filings,  and 
passing  the  pole  of  a  strong  magnet  several  times  along  the  outside  in  one 
constant  direction,  taking  care  not  to  shake  the  tube.  The  individual  filings 
will  thus  be  magnetised,  and  the  whole  column  of  them  presented  to  a  mag- 
netic needle  will  attract  and  repel  its  poles  just  like  an  ordinary  bar  magnet 
exhibiting  a  north  pole  at  one  end,  a  south  pole  at  the  other,  and  no  polarity 
in  the  middle  ;  fcut  on  shaking  the  tube,  or  turning  out  the  filings,  and  put- 
ting them  in  again  so  as  to  destroy  the  regularity,  every  trace  of  polarity  will 
disappear.  It  appears  hence  that  the  polarity  at  each  end  of  a  magnet  is 
caused  by  the  fact  that  the  resultant  action  on  a  magnetic  body  is  strongest 
near  the  ends,  and  does  not  arise  from  any  accumulation  of  magnetic  fluids 
at  the  ends. 

The  same  point  may  be  illustrated  by  the  following  experiment,  which  is 
due  to  Sir  W.  Grove  : — In  a  glass  tube  with  flat  glass  ends  is  placed  water  in 
which  is  diffused  magnetic  oxide  of  iron.  Round  the  outside  of  the  tube  is 
coiled  some  insulated  wire.  On  looking  at  a  light  through  the  tube  the 
liquid  appears  dark  and  muddy,  but  on  passing  a  current  of  electricity  through 
the  wire  it  becomes  clearer  (880).  This  is  due  to  the  fact  that  by  the  mag- 
netising action  of  the  current,  the  particles,  becoming  magnetised,  set  with 
their  longest  dimension  parallel  to  the.  axis  of  the  tube,  in  which  position 
they  obstruct  the  passage  of  light  to  a  less  extent. 


596  On  Magnetism.  [685- 

685.  Experiments    with    broken    magnets. — That    the    two   magnetic 
fluids  are  present  in  all  parts  of  the  bar,  and  are  not  simply  accumulated  at 
the  ends,  is  also  evident  from  the  following  experiment  : — A  steel  knitting- 
needle  is  magnetised  by  friction  with  one  of  the  poles  of  a  magnet,  and  then, 
the  existence  of  the  two  poles  and  of  the  neutral  line  having  been  ascertained 
by  means  of  iron  filings,  it  is  broken  in  the  middle.     But  now,  on  presenting 
successively  the  two  halves  to  a  magnet,  each  will  be  found  to  possess  two 
opposite  poles  and  a  neutral  line,  and  in  fact  is  a  perfect  magnet.     If  these 
new  magnets  are  broken  in  turn  in  two  halves,  each  will  be  a  complete 
magnet  with  its  two  poles  and  neutral  line,  and  so  on,  as  far  as  the  division 
can  be  continued.     It  is,  therefore,  concluded  by  analogy  that  the  smallest 
parts  of  a  magnet,  the  ultimate  molecules,  contain  the  two  magnetisms. 

686.  Magnetic  induction. — When  a  magnetic  substance  is  placed  in 
contact  with  a  magnet,  the  two  fluids  of  the  former  become  separated  ;  and 
so  long  as  the  contact  remains,  it  is  a  complete  magnet,  having  its  two  poles 
and  its  neutral  line.     For  instance,  if  a  small  cylinder  of  soft  iron,  ab  (fig. 
567),  be  placed  in  contact  with  one  of  the  poles  of  a  magnet,  the  cylinder  can 


Fig.  567- 


in  turn  support  a  second  cylinder  ;  this  in  turn  a  third  and  so  on,  to  as  many 
as  seven  or  eight,  according  to  the  power  of  the  magnet.  Each  of  these 
little  cylinders  is  a  magnet  ;  if  it  be  the  north  pole  of  the  magnet  to  which 
the  cylinders  are  attached,  the  part  a  will  have  south,  and  b  north  magnetism  ; 
b  will  in  like  manner  develop  in  the  nearest  end  of  the  next  cylinder  south 
magnetism,  and  so  on.  But  these  cylinders  are  only  magnets  so  long  as  the 
influence  of  a  magnetised  bar  continues.  For,  if  the  first  cylinder  be  re- 
moved from  the  magnet,  the  other  cylinders  immediately  drop,  and  retain  no 
trace  of  magnetism.  The  separation  of  the  two  magnetisms  is  only  momen- 
tary, which  proves  that  the  magnet  yields  nothing  to  the  iron.  Hence  we 
may  have  temporary  magnets  as  well  as  permanent  magnets  :  the  former  of 
iron  and  nickel,  the  latter  of  steel  and  cobalt  (688). 

This  action,  in  virtue  of  which  a  magnet  can  develop  magnetism  in 
iron,  is  called  magnetic  induction  or  influence,  and  it  can  take  place  without 
actual  contact  between  the  magnet  and  the  iron,  as  is  seen  in  the  following 
experiment  : — A  bar  of  soft  iron  is  held  with  one  end  near  a  magnetic  needle. 
If  now  the  north  pole  of  a  magnet  be  approached  to  the  iron  without  touch- 
ing it,  the  needle  will  be  attracted  or  repelled,  according  as  its  south  or 
north  pole  is.  near  the  bar.  For  the  north  pole  of  the  magnet  will  develop 
south  magnetism  in  the  end  of  the  bar  nearest  it,  and  therefore  north  mag- 
netism at  the  other  end,  which  would  thus  attract  the  south,  but  repel  the 
north,  end  of  the  needle.  Obviously,  if  the  other  end  of  the  magnet  were 
brought  near  the  iron,  the  opposite  effects  would  be  produced  on  the  needle ; 


-688]  Magnetic  Induction.  597 

or  if  the  opposite  pole  of  a  second  magnet  of  equal  strength  simultaneously 
be  brought  near  the  iron,  the  needle  would  be  unaffected,  as  one  magnet 
would  undo  the  work  of  the  other. 

Among  other  things,  magnetic  induction  explains  the  formation  of  the 
tufts  of  iron  filings  which  become  attached  to  the  poles  of  magnets.  The 
parts  in  contact  with  the  magnet  are  converted  into  magnets  ;  these  act 
inductively  on  the  adjacent  parts,  these  again  on  the  following  ones,  and 
so  on,  producing  a  filamentary  arrangement  of  the  filings.  The  bush-like 
appearance  of  these  filaments  is  due  to  the  repulsive  action  which  the 
free  poles  exert  upon  each  other.  Any  piece  of  soft  iron  while  being 
attracted  by  a  magnet  is  for  the  time  being  converted  into  a  magnet ; 
hence  is  explained  the  paradoxical  statement  that  'magnets  only  attract 
magnets.' 

687.  Coercive  force. — We  have  seen  from  the  above  experiments  that  soft 
iron  becomes  instantaneously  magnetised  under  the  influence  of  a  magnet  ; 
but  that  this  magnetism  is  not  permanent,  and  ceases  when  the  magnet  is 
removed.     Steel  likewise  becomes  magnetised  by  contact  with  a  'magnet ; 
but  the  operation  is  effected  with  difficulty,  and  the  more  so  as.  the  steel  is 
more  highly  tempered.     Placed  in  contact  with  a  magnet,  a  steel  bar  acquires 
magnetic  properties  very  slowly  ;  and,  to  make  the  magnetism  complete,  the 
steel  must  be  rubbed  with  one  of  the  poles.     But  this  magnetism,  once 
evoked  in  steel,  is  permanent,  and  does  not  disappear  when  the  inducing 
force  is  removed. 

These  different  effects  in  soft  iron  and  steel  are  ascribed  to  a  coercive 
force,  which,  in  a  magnetic  substance,  offers  a  resistance  to  the  separation  of 
the  two  magnetisms,  but  which  also  prevents  their  recombination  when  once 
separated.  In  steel  this  coercive  force  is  very  great ;  in  soft  iron  it  is  very 
small  or  almost  absent.  By  oxidation,  pressure,  or  torsion,  a  certain  amount 
of  coercive  force  may  be  imparted  to  soft  iron  :  and  by  heat,  hammering,  &c., 
the  coercive  force  may  be  lessened,  as  will  be  afterwards  seen. 

688.  Difference  between  magnets  and  magnetic  substances. — Mag- 
netic substances  are  substances  which,  like  iron,  steel,  and,  nickel  are  attracted 
by  the  magnet.     They  contain  the  two  fluids,  but  in  a  state  of  neutralisation. 
Compounds  containing  iron  are  usually  magnetic,  and  the  more  so  in  pro- 
portion as  they  contain  a  larger  quantity  of  iron.     Some,  however,  like  iron 
pyrites,  are  not  attracted  by  the  magnet. 

A  magnetic  substance  is  readily  distinguished  from  a  magnet.  The 
former  has  no  poles  ;  if  successively  presented  to  the  two  ends  of  a  magnetic 
needle,  ab  (fig.  564),  it  will  attract  both  ends  equally,  while  with  one  and  the 
same  end  a  magnet  would  attract  the  one  end  of  the  needle,  but  repel  the 
other.  Magnetic  substances  also  have  no  action  on  each  other  ;  while  mag- 
nets attract  or  repel  each  other,  according  as  unlike  or  like  poles  are  pre- 
sented. Attraction  is  no  proof  that  a  body  is  a  magnet  ;  repulsion  is. 

Iron  is  not  the  only  substance  which  possesses  magnetic  properties  ; 
nickel  has  considerable  magnetic  power,  but  far  less  than  that  of  iron  ;  cobalt 
is  less  magnetic  than  nickel ;  while  to  even  a  slighter  extent  chromium  and 
manganese  are  magnetic.  Further,  we  shall  see  that  powerful  magnets  exert 
a  peculiar  influence  on  all  substances. 


598  On  Magnetism.  [689- 


CHAPTER   II. 

TERRESTRIAL  MAGNETISM.      COMPASSES. 

689.  Directive  action  of  the  earth  on  magnets. — When  a  magnetised 
needle  is  suspended  by  a  thread,  as  represented  in  fig.  564,  or  when  placed 
on  a  pivot  on  which  it  can  move  freely  (fig.  568),  it  ultimately  sets  in  a 

position   which   is   more   or  less    north   and 
$-   south.       If    removed    from    this    position    it 
always  returns  to  it  after  a  certain  number  of 
oscillations. 

Analogous  observations  have  been  made 
in  different  parts  of  the  globe,  from  which  the 
earth  has  been  compared  to  an  immense  mag- 
net, whose  poles  are  very  near  the  terrestrial 
poles,  and  whose  neutral  line  virtually  coin- 
cides with  the  equator. 

The  polarity  in  the  northern  hemisphere 
is   called  the  northern  or  boreal  polarity,  and 
Fig.  568.  tnat  m  tne  southern  hemisphere  the  southern 

or  austral  polarity.     In  French  works  the  end 

of  the  needle  pointing  north  is  called  the  austral  or  southern  pole,  and  that 
pointing  to  the  south  the  boreal  or  northern  pole  ;  a  designation  based  on 
this  hypothesis  of  a  terrestrial  magnet,  and  on  the  law  that  unlike  magnet- 
isms attract  each  other.  In  practice  it  will  be  found  more  convenient  to 
use  the  English  names,  and  call  that  end  of  the  magnet  which  points  to  the 
north  the  north  pole,  and  that  which  points  to  the  south  the  south  pole  ;  the 
north  pole  of  a  magnet  is  a  north  seeking  pole,  and  a  south  pole  a  south  seek- 
ing pole.  To  avoid  ambiguity  that  end  of  the  needle  pointing  north  is  in 
England  sometimes  spoken  of  as  the  marked  end  of  the  needle  (688). 

690.  Terrestrial  magnetic  couple. — From  what  has  been  stated,  it  is 
clear  that  the  magnetic  action  of  the  earth  on  a  magnetised  needle  may  be 
compared  to  a  couple  ;  that  is,  to  a  system  of  two  equal  forces,  parallel,  but 
acting  in  contrary  directions. 

For  let  ab  (fig.  569)  be  a  movable  magnetic  needle  making  an  angle  with 
the  magnetic  meridian  M'M  (691).  The  earth's  north  pole  acts  attractively 
on  the  marked  pole,  «,  and  repulsively  on  the  other  pole,  <£,  and  two  contrary 
forces  are  produced  an  and  bnf,  which  are  equal  and  parallel  :  for  the 
terrestrial  pole  is  so  distant,  and  the  needle  so  small,  as  to  justify  the  assump- 
tion that  the  two  directions,  an  and  bri ,  are  parallel,  and  that  the  two  poles 
are  equidistant  from  the  earth's  north  pole.  But  the  earth's  south  pole  acts 
similarly  on  the  poles  of  the  needle,  and  produces  two  other  forces,  as  and  fo, 


-691]  Magnetic  Elements.     Decimation.  599 

which  are  also  equal  and  parallel,  but  the  two  forces  an  and  as  may  be  re- 
duced to  a  single  resultant  aN  (33),  and  the  forces  bn'  and  bs  to  a  resultant 
£S  ;  the  two  forces  #N  and  £S  are  equal,  parallel,  and  act  in  opposite  direc- 
tions, and  they  constitute  the  terrestrial  magnetic  couple ;  it  is  this  couple 


Fig.  569- 

which  makes  the  needle  set  ultimately  in  the  magnetic  meridian — a  position 
in  which  the  two  forces  N  and  S  are  in  equilibrium. 

The  force  which  determines  the  direction  of  the  needle  thus  is  neither 
attractive  nor  repulsive,  but  simply  directive.  If  a  small  magnet  be  placed 
on  a  cork  floating  in  water,  it  will  at  first  oscillate,  and  then  gradually  set  in 
a  line  which  is  virtually  north  and  south.  But  if  the  surface  of  the  water  be 
quite  smooth,  the  needle  will  not  move  either  towards  the  north  or  towards 
the  south. 

If,  however,  a  magnet  be  approached  to  a  floating  needle,  attraction  or 
repulsion  ensues,  according  as  one  or  the  other  vi  the  poles  is  presented. 
The  reason  of  the  different  actions  exerted  by  the  earth  and  by  a  magnet  on 
a  floating  needle  is  as  follows  : — When  the  north  pole,  for  instance,  of  the* 
magnet  is  presented  to  the  south  pole  of  the  needle,  the  latter  is  attracted  ; 
it  is,  however,  repelled  by  the  south  pole  of  the  magnet.  Now  the  force  of 
magnetic  attraction  or  repulsion  decreases  with  the  distance  ;  and,  as  the  dis- 
tance between  the  south  pole  of  the  needle  and  the  north  pole  of  the  magnet 
is  less  than  the  distance  between  the  south  pole  of  the  needle  and  the  south 
pole  of  the  magnet,  the  attraction  predominates  over  the  repulsion,  and  the 
needle  moves  towards  the  magnet.  But  the  earth's  magnetic  north  pole  is  so 
distant  from  the  floating  needle  that  its  length  may  be  considered  infinitely 
small  in  comparison,  and  one  pole  of  the  needle  is  just  as  strongly  repelled 
as  the  other  is  attracted. 

691.  Magnetic  elements.  Declination. — In  order  to  obtain  a  full  know- 
ledge of  the  earth's  magnetism  at  any  place  three  essentials  are  requisite ; 
these  are  :  i.  Declination  ;  ii.  Inclination  ;  iii.  Intensity.  These  three  are 
termed  the  magnetic  elements  of  the  place.  We  shall  explain  them  in  the 
order  in  which  they  stand. 

The  geographical  meridian  of  a  place  is  the  imaginary  plane  passing 
through  this  place  and  through  the  two  terrestrial  poles,  and  the  meridian 
is  the  outline  of  this  plane  upon  the  surface  of  the  globe.  Similarly  the 
magnetic  meridian  of  a  place  is  the  vertical  plane  passing  at  this  place 
through  the  two  poles  of  a  movable  magnetic  needle  in  equilibrium  about  its 
vertical  axis. 

In  general  the  magnetic  meridian  does  not  coincide  with  the  geographical 
meridian,  and  the  angle  which  the  magnetic  makes  with  the  geographical 
meridian — that  is  to  say,  the  angle  which  the  direction  of  the  needle  makes 


600  On  Magnetism.  [691- 

with  the  meridian — is  called  the  declination  or  variation  of  the  magnetic 
needle.  The  declination  is  said  to  be  east  or  west,  according  as  the  north 
pole  of  the  needle  is  to  the  east  or  west  of  the  geographical  meridian. 

692.  Variations  in  declination. — The  declination  of  the  magnetic 
needle,  which  varies  in  different  places,  is  at  present  west  in  Europe  and  in 
Africa,  but  east  in  Asia  and  in  the  greater  part  of  North  and  South  America. 
It  shows  further  considerable  variations  even  in  the  same  place  ;  these 
variations  are  of  two  kinds  ;  some  are  regular,  and  are  either  secular,  annual, 
or  diurnal  ;  others,  which  are  irregular,  are  called  magnetic  storms  (694). 

Secular  variations. — In  the  same  place,  the  declination  varies  in  the  course 
of  time,  and  the  needle  appears  to  make  oscillations  to  the  east  and  west  of 
the  meridian,  the  duration  of  which  extends  over  centuries.  The  declination 
has  been  known  at  Paris  since  1580,  and  the  following  table  represents  the 
variations  which  it  has  undergone  : — 

Year  Declination  Year  Declination 

1580      .  .  .       II°30'E.  1830      .  .  .      22°I2/W. 

1663      ...         0°  1835       .  .  .22°     4'W. 

1700  .  .  .       8°  10'  W.  1850  .  .  .  20°  30' W. 

1780  .  .  .     i9°55/W.  1855  .  .  .  i9°57'W. 

1785  .  .  .22°        W.  1860  .  .  .  i9°32'W.      ' 

1805  .  .  .22°    5'W.  1865  .  .  .  i8°44/W. 

1814  .  .  .     22°34/W.  1875  •  •  •  i7°2i'W. 

1825      .  .  .      22°22'W.  1878      .  .  .17°  W. 

This  table  shows  that  since  1580  the  declination  has  varied  at  Paris  as 
much  as  34°,  and  that  the  greatest  westerly  declination  was  attained  in  1814, 
since  which  time  the  needle  has  gradually  tended  towards  the  east. 

At  London,  the  needle  showed  in  1580  an  easterly  declination  of  11°  36'; 
in  1663  it  was  at  zero  ;  from  that  time  it  gradually  tended  towards  the  west, 
and  reached  its  maximum  declination  of  24°  41'  in  1818  ;  since  then  it  has 
steadily  diminished  ;  it  was  22°  30'  in  1850,  19°  32'  in  1873,  19°  24'  in  1874, 
19°  16'  in  1875,  I9°  i°'  m  I^76,  19°  3'  in  1877,  18°  52'  in  1878,  and  is  now 
(1881)  i8°4o'  W. 

At  Yarmouth  and  Dover  the  variation  is  about  40'  less  than  at  London  ; 
at  Hull  and  Southampton  about  2c/  greater  ;  at  Newcastle  and  Swansea 
about  i°  45',  and  at  Liverpool  2°  o',  at  Edinburgh  3°  o',  and  at  Glasgow  and 
Dublin  about  3°  50'  greater  than  at  London. 

The  following  are  the  observations  of  the  magnetic  elements  at  Kew  for 
the  last  sixteen  years  : — 

Year  Declination  Inclination       Horizontal  Intensity 

1865  .        .        .        .       20°  59'  68°    7'  3-829 

1866  ....      20°  51'  68°    6'  3-837 

1867  .        .        .        .       20°  4c/  68°    3'  3-844 

1868  ....       2o°33/  68°    2'  3-848 

1869  .        .        .        .20°  25'  68°    i'  3-852 
.    1870  ....       20°  19'  67°  58'  3-857 

1871  .        .        .        .20°  10'  67°  57'  3-863 

1872  .        .        .        .      20°    o'  67°  54'  3-869 

1873  ....       19°  57'  67°  52' 


lllilF^        k  ^xv 

!-^/     \      -^ 


f  . 


-693]  Annual  Variations  60 1 

Year  Declination  Inclination  Horizontal  Intensity 

1874  ....         19°  52'  67°  50'                   3'88l 

1875  ....         19°  41'  67°  48'                   3*885 

1876  ....         19°  31'  67°  46'                   3-885 

1877  ....  19°  22'  67°  45'  3-891 

1878  ....  19°  14'  67°  44'  3-895 

1879  •        •        •        .  19°    6'  67°  42'  3-900 

1880  .        .        .        .  1 8°  59'  67°  42'  3-899 

In  certain  parts  of  the  earth  the  magnet  coincides  with  the  geographical 
meridian.  These  points  are  connected  by  an  irregularly  curved  imaginary 
line,  called  a  line  of  no  variation,  or  agonic  line.  Such  a  line  cuts  the  east 
of  South  America,  and,  passing  east  of  the  West  Indies,  enters  North  America 
near  Philadelphia,  and  traverses  Hudson's  Bay ;  thence  it  passes  through 
the  North  Pole,  entering  the  Old  World  east  of  the  White  Sea,  traverses 
the  Caspian,  cuts  the  east  of  Arabia,  turns  then  towards  Australia,  and 
passes  through  the  South  Pole,  to  join  itself  again. 

Isogonic  lines  are  lines  connecting  those  places  on  the  earth's  surface  in 
which  the  declination  is  the  same.  The  first  of  the  kind  was  constructed  in 
1700  by  Halley  ;  as  the  elements  of  the  earth's  magnetism  are  continually 
changing,  the  course  of  such  a  line  can  only  be  determined  for  a  certain 
time.  A  set  of  isogonic  lines  was  constructed  by  Captain  Evans  for  the 
year  1857,  and  is  given  in  the  British  Association  Report  for  1861. 

Maps  on  which  such  isogonic  lines  are  depicted  are  called  declination 
maps ;  and  a  comparison  of  these  in  various  years  is  well  fitted  to  show  the 
variation  which  this  magnetic  element  undergoes.  Plate  III.  represents  a 
map  in  Mercator's  projection  giving  these  lines  for  the  year  1860.  It  extends 
from  80°  N.  to  60°  S.  latitude,  and  from  the  nature  of  the  case  cannot  include 
both  poles,  for  which  a  map  in  polar  projection  is  needed.  The  figures 
attached  to  the  red  lines  represent  the  observed  angles  of  declination  ;  the 
dotted  red  lines  are  the  result  of  calculation. 

693.  Annual  variations. — Cassini  first  discovered  in  1780  that  the 
declination  is  subject  to  small  annual  variations.  At  Paris  and  London  it  is 
greatest  about  the  vernal  equinox,  diminishes  from  that  time  to  the  summer 
solstice,  and  increases  again  during  the  nine  following  months.  It  does  not 
exceed  from  15'  to  18',  and  it  varies  somewhat  at  different  epochs. 

The  diurnal  variations  were  first  discovered  by  Graham  in  1722;  they 
can  only  be  observed  by  means  of  long  needles  or  delicate  indicators  such 
as  the  reflection  of  a  ray  of  light  (522)  and  very  sensitive  instruments  (702). 
In  this  country  the  north  pole  moves  every  day  from  east  to  west  from  sun- 
rise until  one  or  two  o'clock ;  it  then  tends  towards  the  east,  and  at  about 
ten  o'clock  regains  its  original  position.  During  the  night  the  needle  is 
almost  stationary.  Thus  the  westerly  declination  is  greatest  during  the 
warmest  part  of  the  day. 

At  Paris  the  mean  amplitude  of  the  diurnal  variation  from  April  to 
September  is  from  13'  to  15',  and  for  the  other  months  from  8'  to  10'.  On 
some  days  it  amounts  to  25',  and  on  others  does  not  exceed  5'.  The  greatest 
variation  is  not  always  at  the  same  time.  The  amplitude  of  the  daily  varia- 

D  D 


602 


On  Magnetism. 


[693- 


tions  decreases  from  the  poles  towards  the  equator,  where  it  is  very  feeble. 
Thus  in  the  island  of  Rewak  it  never  exceeds  3'  to  4'. 

694.  Accidental  variations  and   perturbations — The    declination  is 
accidentally  disturbed  in  its  daily  variations  by  many  causes,  such  as  earth- 
quakes,  the   aurora  borealis,  and   volcanic  eruptions.     The  effect  of  the 
aurora  is  felt  at  great  distances.     Auroras,  which  are  only  visible  in  the  most 
northerly  parts  of  Europe,  act  on  the  needle  even  in  these  latitudes,  where 
accidental  variations  of  i°  or  2°  have  been  observed.     In  polar  regions  the 
needle  frequently  oscillates  several  degrees  ;    its    irregularity  on  the  day 
before  the  aurora  borealis  is  a  presage  of  the  occurrence  of  this  phenomenon. 

Another  remarkable  phenomenon  is  the  simultaneous  occurrence  of  mag- 
netic perturbations  in  very  distant  countries.  Thus  Sabine  mentions  a  mag- 
netic disturbance  which  was  felt  simultaneously  at  Toronto,  the  Cape,  Prague, 
and  Van  Diemen's  Land.  Such  simultaneous  perturbations  have  'received 
the  name  of  magnetic  storms. 

695.  Declination  compass. — The  declination  compass  is  an  instrument 
by  which  the  magnetic  declination  of  any  place  may  be  determined  when  its 

astronomical  meridian  is 
known.  It  consists  of  a  brass 
box,  AB  (fig.  570),  in  the 
bottom  of  which  is  a  gradu- 
ated circle,  M.  In  the  centre 
is  a  pivot  on  which  oscillates 
a  very  light  lozenge-shaped 
magnetic  needle,  ab.  To  the 
box  are  attached  two  up- 
rights supporting  a  horizontal 
axis,  X,  on  which  is  fixed  an 
astronomical  telescope,  L, 
movable  in  a  vertical  plane. 
The  box  rests  on  a  foot,  P, 
about  which  it  can  turn  in  a 
horizontal  plane,  taking  with 
it  the  telescope.  A  fixed 
circle,  QR,  which  is  called 
the  azinmthal  circle,  mea- 
sures the  number  of  degrees 
through  which  the  telescope 
has  been  turned,  by  means 
of  a  vernier,  V,  fixed  to  the 
box.  The  inclination  of  the 
telescope,  in  reference  to  the 
horizon,  may  be  measured 
by  another  vernier,  K,  which 

moves  with  the  axis  of  the  telescope,  and  is  read  off  on  a  fixed  graduated 

arc,  x. 

The  first  thing  in  determining  the  declination  is  to  adjust  the  compass 

horizontally  by  means  of  the  screws,  SS,  and  the  level,  n.     The  astronomical 

meridian  is  then  found,  either  by  an  observation  of  the  sun  at  noon  exactly, 


Fig.  570. 


-697] 


Manners  Compass. 


6o3 


or  by  any  of  the  ready  methods  known  to  astronomers.  The  box,  AB,  is 
then  turned  until  the  telescope  is  in  the  plane  of  the  astronomical  meridian. 
The  angle  made  by  the  magnetic  needle  with  the  diameter,  N,  which  corre- 
sponds with  the  zero  of  the  scale,  and  is  exactly  in  the  plane  of  the  telescope, 
is  then  read  off  on  the  graduated  limb,  and  this  is  east  or  west,  according  as 
the  pole,  <z,  of  the  needle  stops  at  the  east  or  west  of  the  diameter,  N. 

696.  Correction  of  errors. — These  indications  of  the  compass  are  only 
correct  when  the  magnetic  axis  of  the  needle— that  is,  the  right  line  passing 
through  the  two  poles — coincides  with  its  axis  of  figure,  or  the  line  connecting 
its  two  ends.     This  is 

not  usually   the    case, 

and  a  correction  must 

therefore      be     made, 

which  is  done  by  the 

method    of   reversion. 

For  this   purpose   the 

needle  is  not  fixed  in 

the    cap,    but    merely 

rests  on  it,  so  that  it 

can   be  removed    and 

its  positions  reversed  ; 

thus  what  was  before 

the   lower  is   now  the 

upper  face.     The  mean  between  the  observations  made  in  the  two  cases 

gives  the  true  declination. 

For,  let  NS  be  the  astronomical  meridian,  ao  the  axis  of  figure  of  the 
needle,  and  mn  its  magnetic  axis  (fig.  571).  The  true  declination  is  not  the 
arc  Xa  but  the  arc  Xw,  which  is  greater.  If  now  the  needle  be  turned,  the 
line  mn  makes  the  same  angle  with  the  meridian  XS  ;  but  the  north  end  of 
the  needle  which  was  on  the  right  of  mn  is  now  on  the  left  (fig.  572),  so  that 
the  declination  which  was  previously  too  small  by  a  certain  amount,  is  now 
too  large  by  the  same  amount.  Hence  the  true  declination  is  given  by  the 
mean  of  these  two  observations. 

697.  Mariner's  compass. — The  magnetic  action  of  the  earth  has  received 
its  most  important  application  in  the  mariner's  compass.     This  is  a  declina- 
tion compass  used  in  guiding  the  course  of  a  ship.     Fig.  573  represents  a 
view  of  the  whole,  and  fig.  574  a  vertical  section.     It  consists  of  a  cylindrical 
case,  BB',  which,  to  keep  the  compass  in  a  horizontal  position  in  spite  of 
the  rolling  of  the  vessel,  is  supported  on  gimbals.     These  are  two  concentric 
rings,  one  of  which,  attached  to  the  case  itself,  moves  about  the  axis  xd  which 
plays  in  the  outer  ring  AB,  and  this  moves  in  the  supports  PQ,  about  the 
axis  mn  at  right  angles  to  the  first. 

In  the  bottom  of  the  box  is  a  pivot,  on  which  is  placed,  by  means  of  an 
agate  cap,  a  magnetic  bar  ab,  which  is  the  needle  of  the  compass.  On  this 
is  fixed  a  disc  of  mica,  a  little  larger  than  the  length  of  the  needle,  on  which 
is  traced  a  star  or  rose  with  thirty-two  branches,  making  the  eight  points  or 
rhumbs  of  the  wind,  the  demi-rhumbs  and  the  quarters.  The  branch  ending 
in  a  small  star  and  called  X,  corresponds  to  the  bar  afi,  which  is  underneath 
the  disc. 

D  D  2 


604  On  Magnetism.  [697- 

The  compass  is  placed  near  the  stern  of  the  vessel  in  the  binnacle. 
Knowing  the  direction  of  the  compass  in  which  the  ship  is  to  be  steered,  the 
pilot  has  the  rudder  turned  till  the  direction  coincides  with  the  sight  vane 


573- 


passing  through  a  line  d  marked  on  the  inside  of  the  box,  and  parallel  with 
the  keel  of  the  vessel. 

Neither  the  inventor  of  the  compass,  nor  the  exact  time  of  its  invention, 
is  known.  Guyot  de  Provins,  a  French  poet  of  the  twelfth  century,  first 
mentions  the  use  of  the  magnet  in  navigation,  though  it  is  probable  that  long 


Fig.  574- 

before  this  the  Chinese  had  used  it.  The  ancient  navigators,  who  were  un- 
acquainted with  the  compass,  had  only  the  sun  or  pole  star  as  a  guide,  and 
were  accordingly  compelled  to  keep  constantly  in  sight  of  land  for  fear  of 
steering  in  a  wrong  direction  when  the  sky  was  clouded. 

698.  Inclination.  Magnetic  equator.— It  might  be  supposed  from  the 
northerly  direction  which  the  magnetic  needle  takes,  that  the  force  acting 
upon  it  is  situated  in  a  point  of  the  horizon.  This  is  not  the  case,  for  if  the 
needle  be  so  arranged  that  it  can  move  freely  in  a  vertical  plane  about  a 
horizontal  axis,  it  will  be  seen  that,  although  the  centre  of  gravity  of  the 
needle  coincides  with  the  centre  of  suspension,  the  north  pole  in  our  hemi- 
sphere dips  downwards.  In  the  other  hemisphere  the  south  pole  is  inclined 
downwards. 

The  angle  which  the  magnetic  needle  makes  with  the  horizon,  when  the 
vertical  plane,  in  which  it  moves,  coincides  with  the  magnetic  meridian,  is 
called  the  inclination  or  dip  of  the  needle.  In  any  other  plane  than  the 


-698]  Inclination.     Magnetic  Equator.  605 

magnetic  meridian,  the  inclination  increases,  and  is  90°  in  a  plane  at  right 
angles  to  the  magnetic  meridian.  For  the  magnetic  inclination  represents 
the  direction  of  the  total  magnetic  force,  and  may  be  decomposed  into  two 
forces,  one  acting  in  a  horizontal  and  the  other  in  a  vertical  plane.  When 
the  needle  is  moved  so  that  it  is  at  right  angles  to  the  magnetic  meridian, 
the  horizontal  component  can  only  act  in  the  direction  of  the  axis  of  suspen- 
sion, and,  therefore,  cannot  affect  the  needle,  which  is  then  solely  influenced 
by  the  vertical  component,  and  stands  vertically.  The  following  considera- 
tions will  make  this  clearer  : — 

Let  NS  (fig.  575)  represent  a  magnetic  needle  capable  of  moving  in  a 
vertical  plane.  Let  NT  represent  in  direction  and  intensity  the  entire 
force  of  the  earth's  magnetism  acting 
on  the  pole  N.  Then  NT  can  be  re- 
solved into  the  forces  N^:  and  NV  ; 
TX//  being  the  angle  of  inclination  or 
dip. 

NT  is  termed  the  Mai  force,  and 
its  components  are  N//,  or  the  hori-  Fig.  575. 

zontal  force,  and  NV,  or  the  vertical  force. 

Now,  it  is  clear  that  the  greater  the  angle  of  dip,  TX//,  the  less  becomes 
N^,  or  the  horizontal  force,  and  the  greater  NV,  or  the  vertical  force. 
Hence,  in  high  latitudes  the  directive  force  of  a  compass,  which  depends  on 
the  horizontal  force,  is  less  than  in  low  latitudes.  At  the  magnetic  poles  the 
horizontal  force  will  be  nil,  and  the  vertical  force  a  maximum  :  here,  there- 
fore, the  needle  will  be  vertical.  At  the  magnetic  equator  the  reverse  is  the 
case,  and  the  needle  will  be  horizontal.  Hence,  the  oscillations  of  a  compass 
needle,  by  which,  as  will  presently  be  explained,  the  strength  of  the  earth's 
magnetism  is  measured,  become  fewer  and  fewer  in  a  given  time  as  the 
magnetic  poles  are  approached,  although  there  is  really  an  increase  in  the 
total  force  of  the  earth. 

Again,  the  reason  why  a  dipping-needle  stands  vertical  when  placed  E. 
and  W.  is  clearly  because  in  those  positions  the  horizontal  force  now  acting 
at  right  angles  to  the  plane  of  motion  of  the  needle  is  ineffectual  to  move  it, 
and  therefore  merely  produces  a  pressure  on  the  pivot  which  supports  the 
needle.  But  the  vertical  component  of  the  total  force  remains  unaffected  by 
the  new  position  of  the  needle.  Acting,  therefore,  entirely  alone  when  the 
dipping-needle  is  exactly  E.  and  W.,  this  vertical  component  drags  the 
needle  into  a  line  with  itself;  that  is,  90°  from  the  horizontal  plane. 

The  value  of  the  dip,  like  that  of  the  declination,  differs  in  different 
localities.  It  is  greatest  in  the  polar  regions,  and  decreases  with  the  latitude 
to  the  equator,  where  it  is  approximately  zero.  In  London  at  the  present 
time,  1 88 1,  the  dip  is  67°  35',  reckoning  from  the  horizontal  line.  In 
the  southern  hemisphere  the  inclination  is  again  seen,  but  in  a  contrary 
direction  ;  that  is,  the  south  pole  of  the  needle  dips  below  the  horizontal 
line. 

The  magnetic  poles  are  those  places  in  which  the  dipping-needle  stands 
vertical ;  that  is,  where  the  inclination  is  90°.  In  1830  the  first  of  these,  the 
terrestrial  north  pole,  was  found  by  Sir  James  Ross  in  96°  43'  west  longitude 
and  70°  north  latitude.  The  same  observer  found  in  the  South  Sea,  in  76" 


606  On  Magnetism.  [698- 

south  latitude  and  168°  east  longitude,  that  the  inclination  was  88°  37'. 
From  this  and  other  observations,  it  has  been  calculated  that  the  position  of 
the  magnetic  south  pole  was  at  that  time  in  about  1 54°  east  longitude  and 
75|°  south  latitude.  The  line  of  no  declination  passes  through  these  poles, 
and  the  lines  of  equal  declination  converge  towards  them. 

The  magnetic  equator  or  aclinic  line  is  the  line  which  joins  all  those 
places  on  the  earth  where  there  is  no  dip  ;  that  is,  all  those  in  which  the 
dipping-needle  is  quite  horizontal.  It  is  a  somewhat  sinuous  line,  not  differ- 
ing much  from  a  great  circle  inclined  to  the  equator  at  an  angle  of  12°,  and 
cutting  it  on  two  points  almost  exactly  opposite  each  other — one  in  the 
Atlantic,  and  one  in  the  Pacific.  These  points  appear  to  be  gradually  moving 
their  position,  and  travelling  from  east  to  west. 

Lines  connecting  places  in  which  the  dipping-needle  makes  equal  angles 
are  called  isoclinic  lines.  Plate  IV.  is  an  inclination  map  for  the  year 
1 860,  the  construction  of  which  is  quite  analogous  to  that  of  the  map  of 
declination. 

The  inclination  is  subject  to  secular  variations,  like  the  declination,  as  is 
readily  seen  from  a  comparison  of  maps  of  inclination  for  different  epochs. 
At  Paris,  in  1671,  the  inclination  was  75°  ;  since  then  it  has  been  continually 
decreasing  :  in  1835  it  was  67°  14';  in  1849  67°;  in  1859  66°  14'  ;  and  in 
1874  65°  23'. 

The  following  table  gives  the  alterations  in  the  inclination  at  London, 
from  which  it  will  be  seen  that  since  1723,  in  which  it  was  at  its  maximum, 
it  has  continually  diminished  by  something  more  than  two  minutes  in  each 
year 

Year  Inclination  Year  Inclination 

1576        .        .        .        71°  So'         1828        .        .        .        69°  47' 

1000  .  .  .  72°  1838  ...  69°  if 

1676  .  .  .  73°. 30'  1854  .  .  .  68°  31' 

1723  .  .  .  74°  42'  1859  .  .  .  68°  21' 

1773  .  .'  ,  72°  19'  1874  .  .  .  67°  43' 

1780  .  .  .  72°  8'  1876  .  .  .  67°  39' 

1790  .  .  .  71°  33'  1878  .  .  .  67°  36' 

1800  .  .  .  70°  35'  1880  .  .  .  67°35/ 

1821  70°  3*'  1881  .  .  .  67°  35' 

699.  Inclination  compass. — An  inclination  compass  is  an  instrument 
for  measuring  the  magnetic  inclination  or  dip.  It  consists  of  a  graduated 
horizorbtal  brass  circle,  ;;/  (fig.  576),  supported  on  three  legs,  provided  with 
levelling  screws.  Above  this  circle  there  is  a  plate,  A,  movable  about  a 
vertical  axis,  and  supporting,  by  means  of  two  columns,  a  second  graduated 
circle,  M,  which  measures  the  inclination.  The  needle  rests  on  a  frame,  r, 
and  the  diameter  passing  through  the  two  zeros  of  the  circle,  M,  can  be 
ascertained  to  be  perfectly  horizontal  by  means  of  the  spirit  level,  n. 

To  observe  the  inclination,  the  magnetic  meridian  must  first  be  deter- 
mined, which  is  effected  by  turning  the  plate  A  on  the  circle  m,  until  the 
needle  is  vertical,  which  is  the  case  when  it  is  in  a  plane  at  right  angles  to 
the  magnetic  meridian  (698).  The  plate  A  is  then  turned  90°  on  the  circle 
;«,  by  which  the  vertical  circle,  M,  is  brought  into  the  magnetic  meridian. 


/ 


-700] 


Astatic  Needle  and  Astatic  System. 


The  angle,  dtvz,  which  the  magnetic  needle  makes  with  the  horizontal  dia- 
meter, is  the  angle  of  inclination. 

There  are  here  several  sources  of  error,  which  must  be  allowed  for.  The 
most  important  are  these  : — i.  The  magnetic  axis  of  the  needle  may  not 
coincide  with  its  axis  of  figure  : 
hence  an  error,  which  is  cor 
reeled  by  a  method  of  reversion 
analogous  to  that  already  de- 
scribed (696).  ii.  The  centre  of 
gravity  of  the  needle  may  not 
coincide  with  the  axis  of  suspen- 
sion, and  then  the  angle,  dca,  is 
too  great  or  too  small,  according 
as  the  centre  of  gravity  is  below 
or  above  the  centre  of  suspen- 
sion ;  for  in  the  first  case  the 
action  of  gravity  is  in  the  same 
direction  as  that  of  magnetism, 
and  in  the  second  it  is  in  the 
opposite  direction.  To  correct 
this  error,  the  poles  of  the 
needle  must  be  reversed  by  first 
demagnetising  it,  and  then  im- 
parting a  contrary  magnetism 
to  what  it  had  at  first.  The 
inclination  is  now  redetermined, 
and  the  mean  taken  of  the  re- 
sults oblained  in  the  two  groups 
of  operations,  iii.  The  plane  of  the  ring  may  not  coincide  with  the  true  mag- 
netic meridian.  It  should  be  in  that  plane  when  the  needle  has  its  minimum 
deviation  ;  an  observation  of  this  kind  should  therefore  be  taken  along  with 
that  previously  described,  by  which  the  needle  is  moved  90°  from  its  maxi- 
mum deviation. 

The  dipping-needle  may  be  used  to  determine  the  inclination  in  another 
way.  It  is  first  allowed  to  oscillate  in  the  magnetic  meridian,  and  then  in 
a  plane  at  right  angles  to  it.  If  the  number  of  oscillations  in  a  given  time 
in  the  first  position  be  /*,  and  in  the  second  position  «„  then  in  the  first  position 
the  whole  force  of  the  earth's  magnetism,  E,  acts,  and  in  the  second  posi- 
tion only  the  vertical  component  which  is  E  sin  x,  x  being  the  angle  of  dip. 
Now,  since  the  forces  acting  on  the  needle  are,  from  the  laws  of  the  pen- 
dulum (55),  as  the  squares  of  the  number  of  oscillations,  we  have  —  = 

ji.sm.1     ?i  t" 

- 
from  which  sin  x  =  5 

;r 

700.  Astatic  needle  and  astatic  system.— An  astatic  needle  is  one 
which  is  uninfluenced  by  the  earth's  magnetism.  A  needle  movable  about 
an  axis  in  the  plane  of  the  magnetic  meridian  and  parallel  to  the  inclination 
would  be  one  of  this  kind  ;  for  the  terrestrial  magnetic  couple,  acting  then  in 
the  direction  of  the  axis,  cannot  impart  to  the  needle  any  determinate  direction. 


Fig.  576. 


6o8 


On  Magnetism. 


[700- 


Fig-  577- 


An  astatic  system  is  a  combination  of  two  needles  of  the  same  force 
joined  parallel  to  each  other  with  the  poles  in  contrary  directions,  as  shown 
in  fig.  577.  If  the  two  needles  have  exactly  the 
same  magnetic  force,  the  opposite  action  of  the 
earth's  magnetism  on  the  poles  a'  and  b  and  on 
the  poles  a  and  b'  counterbalance  each  other,  the 
system  is  then  completely  astatic,  and  sets  at 
right  angles  to  the  magnetic  meridian. 

A  single  magnetic  needle  may  also  be  rendered 
astatic  by  placing  a  large  magnet  near  it.  By 
repeated  trials  a  certain  position  and  distance 
can  be  found  at  which  the  action  of  the  magnet 
on  the  needle  just  neutralises  that  of  the  earth's 
magnetism,  and  the  needle  is  free  to  obey  any 
third  force. 

701.  Intensity  of  the  earth's  magnetism. — If  a  magnetic  needle  be 
moved  from  its  position  of  equilibrium  it  will  revert  to  it  after  a  series  of 
oscillations,  which  follows  laws  analogous  to  those  of  the  pendulum  (81).  If 
the  magnet  be  removed  to  another  place,  and  caused  to  oscillate  during  the 
same  length  of  time  as  the  first,  a  different  number  of  oscillations  will  be 
observed.  And  the  intensity  of  the  earth's  magnetism  in  the  two  places 
will  be  respectively  proportional  to  the  squares  of  the  number  of  oscilla- 
tions. 

If  at  M  the  number  of  oscillations  in  a  minute  had  been  25  =  ;z,  and  at 
another  place,  M',  24  -=n,  we  should  have — - 

Intensity  of  the  earth's  magnetism  at  M  =w2  =62jj  =  j.og- 
Intensity  of  the  earth's  magnetism  at  M/     n*     576 

That  is,  if  the  intensity  of  the  magnetism  at  the  second  place  is  taken  as 
unity,  that  of  the  first  is  1-085.  If  the  magnetic  condition  of  the  needle  had 
not  changed  in  the  interval  between  the  two  observations,  this  method  would 
give  the  relation  between  the  intensities  at  the  two  places. 

In  these  determinations  of  the  intensity,  it  would  be  necessary  to  have  the 
oscillations  of  the  dipping-needle,  which  are  produced  by  the  whole  force  of 
the  earth's  magnetism.  These,  however,  are  difficult  to  obtain  with  accuracy, 
and,  therefore,  the  oscillations  of  the  declination  needle  are  usually  taken. 
The  force  which  makes  the  declination  needle  oscillate  is  only  a  portion  of 
the  total  magnetic  force,  and  is  smaller  in  proportion  as  the  inclination  is 
A  greater.  If  a  line  ac  (fig.  578)  =  M  represents  the  total  in- 
tensity, the  angle  z  the  inclination,  then  the  horizontal  com- 
ponent ab  is  M  cos  z.  Hence  to  express  the  intensities'  in  the 
two  places  by  the  oscillations  of  the  declination  needle,  we 
must  substitute  the  values  M  cos  i  and  M'  cos  i'  for  M  and  M' 
in  the  preceding  equation  and  we  have — 

M   cos  i     n 2  TU      *t  2  ,*nc,  ;? 


n"  cos  z 


Fig.  578. 

That  is  to  say,  having  observed  in  two  different  places  the  number  of  oscilla- 
tions, n  and  #',  that  the  same  needle  makes  in  the  same  time,  the  ratio  of  the 


-702]  Magnetic  Observatories.  609 

magnetic  force  in  the  two  places  will  be  found  by  multiplying  the  ratio  of 
the  square  of  the  number  of  oscillations  by  the  inverse  ratio  of  the  cosine  of 
the  angle  of  dip. 

The  magnetic  intensity  increases  with  the  latitude.  Humboldt  found  a 
point  of  minimum  intensity  on  the  magnetic  equator  in  Northern  Peru.  In 
the  following  table  this  has  been  taken  as  the  standard  to  which  the  magnetic 
intensities  of  the  other  places  specified  is  referred  : — 

Magnetic 
Locality  Date  Latitude  Intensity 

St.  Anthony    .         .         .         .  1 802  0-0°  i  -087 

Carthagena     .         .         .         .1801  10-25  N.  I>294 

Naples 1805  40*50  1*274 

Paris 1800  48*52  i'348 

Berlin 1829  52-51  1-366 

Petersburg      ....  1828  59-66  1-410 

Spitzbergen     ....  1823  79'4O  1*567 

According  to  Gauss  the  total  magnetic  action  of  the  earth  is  the  same  as 
that  which  would  be  exerted  if  in  each  cubic  yard  there  were  eight  bar  mag- 
nets each  weighing  a  pound. 

The  lines  connecting  places  of  equal  intensity  are  called  isodynamic  lines. 
They  are  not  parallel  to  the  magnetic  equator,  but  appear  to  have  about 
the  same  direction  as  the  isothermal  lines.  According  to  Kuppfer,  the 
intensity  appears  to  diminish  as  the  height  of  the  place  is  greater  ;  a  needle 
which  made  one  oscillation  in  24"  vibrated  more  slowly  by  o-oi/rat  a  height 
of  i,ooo  feet ;  but,  according  to  Forbes,  the  intensity  is  only  ^^  less  at  a 
height  of  3,000  feet.  There  is,  however,  some  doubt  as  to  the  accuracy 
of  these  observations,  owing  to  the  uncertainty  of  the  correction  for  tem- 
perature. 

The  intensity  varies  in  the  same  place  with  the  time  of  day :  it  attains  its 
maximum  between  4  and  5  in  the  afternoon,  and  is  at  its  minimum  between 
10  and  1 1  in  the  morning. 

It  is  probable,  though  it  has  not  yet  been  ascertained  with  certainty,  that 
the  intensity  undergoes  secular  variations.  From  measurements  made  at 
Kew,  it  appears  that,  on  the  whole,  the  total  force  experiences  a  very  slight 
annual  increase  (692). 

702.  Magnetic  observatories. — During  the  last  few  years  great  attention 
has  been  devoted  to  the  observation  of  the  magnetic  elements,  and  obser- 
vatories for  this  purpose  have  been  fitted  up  in  different  parts  of  the  globe. 
These  observations  have  led  to  the  discovery  that  the  magnetism  of  the  earth 
is  in  a  state  of  constant  fluctuation,  like  the  waves  of  the  sea.  And  in  study- 
ing the  variations  of  the  declination,  &c.,  the  mean  of  a  great  number  of 
observations  must  be  taken,  so  as  to  eliminate  the  irregular  disturbances,  and 
bring  out  the  general  laws. 

The  principle  on  which  magnetic  observations  are  automatically  recorded 
is  as  follows  : — Suppose  that  in  a  dark  room  a  bar  magnet  is  suspended 
horizontally,  and  at  its  centre  is  a  small  mirror  ;  suppose  further  that  a  lamp 
sends  a  ray  of  light  to  this  mirror,  the  inclination  of  which  is  such,  that  the 
ray  is  reflected  and  is  received  on  a  horizontal  drum  placed  underneath  the 
lamp.  The  axis  of  the  drum  is  at  right  angles  to  the  axis  of  the  magnet  ;  it 

D  D  3 


6 io  On  Magnetism.  [702- 

is  covered  with  sensitive  photographic  paper,  and  is  rotated  uniformly  by 
clockwork.  . 

If  now  the  magnet  is  quite  stationary,  and  the  drum  rotates,  the  reflected 
spot  of  light  will  trace  a  straight  line  on  the  paper  with  which  the  revolving 
drum  is  covered.  But  if,  as  is  always  the  case,  the  position  of  the  magnet 
varies  during  the  twenty-four  hours,  the  effect  will  be  to  trace  a  sinuous  line 
on  the  paper.  These  lines  can  afterwards  be  fixed  by  ordinary  photographic 
methods. 

Knowing  the  distance  of  the  mirror  from  the  drum,  and  the  length  of  the 
paper  band  which  comes  under  the  influence  of  the  spot  of  light  in  a  given 
time — twenty-four  hours,  for  instance — the  angular  deflection  at  any  given 
moment  may  be  deduced  by  a  simple  calculation  (522). 

The  observations  made  in  the  English  magnetic  observatories  were 
reduced  by  Sabine,  and  revealed  some  curious  facts  in  reference  to  the 
magnetic  storms  (694).  He  found  that  there  is  a  certain  periodicity  in  their 
appearance  and  that -they  attain  their  greatest  frequency  about  every  ten 
years.  Independently  of  this,  Schwabe,  a  German  astronomer,  who  had 
studied  the  subject  many  years,  has  found  that  the  spots  on  the  sun,  seen  on 
looking  at  it  through  a  coloured  glass,  vary  in  their  number,  size,  and  fre- 
quency, but  attain  their  maximum  between  every  ten  or  eleven  years.  Now 
Sabine  established  the  interesting  fact  that  the  period  of  their  greatest 
frequency  coincides  with  the  period  of  greatest  magnetic  disturbance.  Other 
remarkable  connections  between  the  sun  and  terrestrial  magnetism  have  been 
observed ;  one,  especially,  of  recent  occurrence  has  attracted  considerable 
attention.  It  was  the  flight  of  a  large  luminous  mass  across  a  vast  sun-spot, 
while  a  simultaneous  perturbation  of  the  magnetic  needle  was  observed  in 
the  observatory  at  Kew  :  subsequent  examination  of  magnetic  observations 
in  various  parts  of  the  world  showed  that  within  a  few  hours  one  of  the  most 
violent  magnetic  storms  ever  known  had  prevailed. 

Magnetic  storms  are  nearly  always  accompanied  by  the  exhibition  of  the 
aurora  borealis  in  high  latitudes  ;  that  this  is  not  universal  may  be  due  to 
the  fact  that  many  auroras  escape  notice.  The  converse  of  this  is  true, 
that  no  great  display  of  the  aurora  takes  place  without  a  violent  magnetic 
storm. 

The  centre  or  focus  towards  which  the  rays  of  the  aurora  converge  lies 
approximately  in  the  prolongation  of  the  direction  of  the  dipping-needle. 


-704] 


The  Torsion  Balance. 


611 


CHAPTER    III. 

LAWS   OF   MAGNETIC  ATTRACTIONS   AND   REPULSIONS. 

703.  x,aw  of  decrease  with  distance. — Coulomb  discovered  the  remark- 
able law  in  reference  to  magnetism,  that  magnetic  attractions  and  repul- 
sions are  inversely  as  the  squares  of  the  distances.     He  proved  this  by 
means  of  two  methods  : — (i.)  that  of  the  torsion  balance,  and  (ii.)  that  of 
oscillation. 

704.  i.  The  torsion  balance. — This  apparatus  depends  on  the  principle 
that,  when  a  wire  is  twisted  through  a  certain  space,  the  angle  of  torsion  is 
proportional  to  the  force  of  torsion 

(90).  It  consists  (fig.  529)  of  a 
glass  case  closed  by  a  glass  top, 
with  an  aperture  near  the  edge, 
to  allow  the  introduction  of  a  mag- 
net, A.  In  another  aperture  in 
the  centre  .of  the  top  a  glass  tube 
fits,  provided  at  its  upper  extremity 
with  a  micrometer.  This  consists 
of  two  circular  pieces  :  d,  which  is  ' 
fixed,  is  divided  on  the  edge  into 
360°,  while  on  one  e,  which  is  move- 
able,  there  is  a  mark,  c,  to  indicate 
its  rotation.  D  and  E  represent 
the  two  pieces  of  the  micrometer 
on  a  larger  scale.  On  E  there 
are  two  uprights  connected  by  a 
horizontal  axis,  on  which  is  a  very 
fine  silver  wire  supporting  a  mag- 
netic needle,  ab.  On  the  side  of  Fis-  579- 
the  case  there  is  a  graduated  scale,  which  indicates  the  angle  of  the  needle 
ad,  and  hence  the  torsion  of  the  wire. 

When  the  mark  c  of  the  disc  E  is  at  zero  of  the  scale,  D,  the  case  is  so 
arranged  that  the  wire  supporting  the  needle  and  the  zero  of  the  scale  in  the 
case  are  in  the  magnetic  meridian.  The  needle  is  then  removed  from  its 
stirrup,  and  replaced  by  an  exactly  similar  one  of  copper,  or  any  unmagnetic 
substance  ;  the  tube,  and  with  it  the  pieces  D  and  E,  are  then  turned  so  that 
the  needle  stops  at  zero  of  the  graduation.  The  magnetic  needle,  ab,  being 
now  replaced,  is  exactly  in  the  magnetic  meridian,  and  the  wire  exerts  no 
torsion. 

Before  introducing  the  magnet,  A,  it  is  necessary  to  investigate  the  action 


612  On  Magnetism.  [704- 

of  the  earth's  magnetism  on  the  needle  ab,  when  the  latter  is  removed  out  of 
the  magnetic  meridian.  This  will  vary  with  the  dimensions  and  force  of  the 
needle,  with  the  dimensions  and  nature  of  the  particular  wire  used,  and  with 
the  intensity  of  the  earth's  magnetism  in  the  place  of  observation.  Accord- 
ingly, the  piece  E  is  turned  until  ab  makes  a  certain  angle  with  the  magnetic 
meridian.  Coulomb  found  in  his  experiments  that  E  had  to  be  turned  36° 
in  order  to  move  the  needle  through  i° ;  that  is,  the  earth's  magnetism  was 
equal  to  a  torsion  of  the  wire  corresponding  to  35°.  As  the  force  of  torsion 
is  proportional  to  the  angle  of  torsion,  when  the  needle  is  deflected  from  the 
meridian  by  2,  3  ...  degrees,  the  directive  action  of  the  earth's  magnetism 
is  equal  to  2,  3  ...  times  35°. 

The  action  of  the  earth's  magnetism  having  been  determined,  the  magnet 
A  is  placed  in  the  case  so  that  similar  poles  are  opposite  each  other.  In  one 
experiment  Coulomb  found  that  the  pole  a  was  repelled  through  24°.  Now 
the  force  which  tended  to  bring  the  needle  into  the  magnetic  meridian  was 
represented  by  24°+ 24  x  35  =  864,  of  which  the  part  24°  was  due  to  the 
torsion  of  the  wire,  and  24  x  35°  was  the  equivalent  in  torsion  of  the  directive 
force  of  the  earth's  magnetism.  As  the  needle  was  in  equilibrium,  it  is  clear 
that  the  repulsive  force  which  counterbalanced  those  forces  must  be  equal  to 
864°.  The  disc  was  then  turned  until  ab  made  an  angle  of  12°.  To  effect 
this,  eight  complete  rotations  of  the  disc  were  necessary.  The  total  force 
which  now  tended  to  bring  the  needle  into  the  magnetic  meridian  was  com- 
posed of: — ist,  the  12°  of  torsion  by  which  the  needle  was  distant  from  its 
starting  point ;  2nd,  of  8  x  360°  =  2880,  the  torsion  of  the  wire  ;  and  3rd,  the 
force  of  the  earth's  magnetism,  represented  by  a  torsion  of  12  x  35°.  Hence 
the  forces  of  torsion  which  balance  the  repulsive  forces  exerted  at  a  distance 
of  24°  and  of  12°  are— 

24°        ....  864 

12°  .  3312 

Now,  3312  is  very  nearly  four  times  864  ;  hence,  for  half  the  distance  the 
repulsive  force  is  four  times  as  great. 

705.  ii.  Method  of  oscillations. — A  magnetic  needle  oscillating  under 
the  influence  of  the  earth's  magnetism  may  be  considered  as  a  pendulum, 
and  the  laws  of  pendulum  motion  apply  to  it  (55).  The  method  of  oscillations 
consists  in  causing  a  magnetic  needle  to  oscillate  first  under  the  influence 
of  the  earth's  magnetism  alone,  and  then  successively  under  the  combined  in- 
fluence of  the  earth's  magnetism  and  of  a  magnet  placed  at  unequal  distances. 

The  following  determination  by  Coulomb  will  illustrate  the  use  of  the 
method.  A  magnetic  needle  was  used  which  made  15  oscillations  in  a 
minute  under  the  influence  of  the  earth's  magnetism  alone.  A  magnetic  bar 
about  2  feet  long  was  then  placed  vertically  in  the  plane  of  the  magnetic 
meridian,  so  that  its  north  pole  was  downwards  and  its  south  pole  presented 
to  the  north  pole  of  the  oscillating  needle.  He  found  that  at  a  distance  of  4 
inches  the  needle  made  41  oscillations  in  a  minute,  and  at  a  distance  of  8 
inches  24  oscillations.  Now,  from  the  laws  of  the  pendulum  (55),  the 
intensity  of  the  forces  are  inversely  as  the  squares  of  the  times  of  oscillations. 
Hence,  if  we  call  M  the  force  of  the  earth's  magnetism,  ;«the  attractive  force 
of  the  magnet  at  the  distance  of  4  inches,  mf  at  the  distance  of  8  inches,  we 
have 


-706]  Magnetic  Curves.  613 

M  :  M  4  m  =  1 5-  :  41-,  and 
M  :  M  +  /w'=i52  :  24, 
eliminating  M 

AV  :  ;//'  =  41°  —  1 52  :  24-  —  1 5-  -  1456  1351=4:  i  nearly, 
or  ;;/  :  /;/'  =  4  :  i. 

In  other  words,  the  force  acting  at  4  inches  is  quadruple  that  which  acts  at 
double  the  distance. 

The  above  results  do  not  quite  agree  with  the  numbers  required  by  the 
law  of  inverse  squares.  But  this  could  only  be  expected  to  apply  in  the  case 
in  which  the  repulsive  or  attractive  force  is  exerted  between  two  points,  and 
not,  as  is  here  the  case,  between  the  resultant  of  a  system  of  points.  And  it 
is  to  this  fact  that  the  discrepancy  between  the  theoretical  and  observed 
results  is  due. 

When  a  magnet  acts  upon  a  mass  of  soft  iron,  the  law  of  the  variation 
with  the  distance  is  modified.  The  attraction  in  this  case  is  inversely  pro- 
portional to  the  distance  between  the  magnet  and  the  iron. 

\Yhen  the  distance  between  the  magnet  and  the  iron  is  small,  Tyndall 
found  that  the  attraction  is  directly  proportional  to  the  square  of  the  strength 
of  the  magnet  ;  but  when  the  iron  and  the  magnet  are  in  contact,  then  the 
attraction  is  directly  proportional  to  the  strength  of  the  magnet. 


Fig.  580. 

706.  Magnetic  curves. —  If  a  stout  sheet  of  paper  stretched  on  a  frame 
be  held  over  a  horse-shoe  magnet,  and  then  some  very  fine  iron  filings  be 
strewn  on  the  paper,  on  tapping  the  frame  the  filings  will  be  found  to 
arrange  themselves  in  thread-like  curved  lines,  stretching  from  pole  to  pole 
(fig.  580).  These  lines  form  what  are  called  magnetic  curves.  The  direction  of 
the  curve  at  any  point  represents  the  direction  of  the  magnetism  at  this  point. 

To  render  these  curves  permanent,  the  paper  on  which  they  are  formed 
should  be  v/axed  ;  if  then  a  hot  iron  plate  be  held  over  them,  this  melts  the 
wax,  which  rises  by  capillary  attraction  (132)  between  the  particles  of  filings, 
and  on  subsequent  cooling  connects  them  together. 

These  curves  are  a  graphic  representation  of  the  law  of  magnetic  attrac- 
tion and  repulsion  with  regard  to  distance  ;  for  under  the  influence  of  the 


614 


On  Magnetism. 


[706- 


two  poles  of  the  magnet,  each  'particle  itself  becomes  a  minute  magnet,  the 
poles  of  which  arrange  themselves  in  a  position  dependent  on  the  resultant 
of  the  forces  exerted  upon  them  by  the  two  poles,  and  this  resultant  varies 
with  the  distance  of  the  two  poles  respectively.  A  small  magnetic  needle 
placed  in  any  position  near  the  magnet  will  take  a  direction  which  is  the 
tangent  to  the  curve  at  this  place. 

707.  Magnetic   field.  —  The  space  in  the  immediate  neighbourhood  of 
any  magnet  undergoes  some  change,  in  consequence  of  the  presence  of  this 
magnet,  and  such  a  space  is  spoken  of  as  a  magnetic  field  ;  the  effect  pro» 
duced  by  the  magnet  is  often  said  to  be  due  to  the  magnetic  field.     Magnets 
of  different  powers  produce  magnetic  fields  of  different  intensity. 

The  direction  which  represents  the  resultant  of  the  magnetic  forces  in  a 
magnetic  field  is  spoken  of  as  the  direction  of  the  lines  of  force  of  this  field. 
In  the  above  figure  the  magnetic  curves  represent  the  direction  of  the  lines 
of  force  in  the  field  due  to  the  two  poles. 

A  uniform  magnetic  field  is  one  in  which  the  lines  of  force  are  parallel. 
This  is  practically  the  case  with  a  small  portion  of  a  field  at  some  distance 
from  a  long  thin  magnet  of  uniform  magnetisation.  The  dipping-needle, 
when  free  to  oscillate  in  a  vertical  plane  in  the  magnetic  meridian,  represents 
the  direction  of  the  lines  of  force  due  to  the  terrestrial  magnetic  field.  The 
field  due  to  this  in  any  one  place  is  uniform. 

708.  Total  action  of  two  magnets  on  each  other.  —  In  the  above  case 
of  the  torsion  balance  one  pole  of  the  magnet  to  be  tested  was  at  so  great 
a  distance  that  it  could  not  appreciably  modify  the  influence  of  the  other. 
When,  however,  the  conditions  are  such  that  both  poles  act,  then  they  follow 
a  different  law,  as  will  now  be  demonstrated. 

Let  ns  (fig.  581)  be  a  small  magnetic  needle,  free  to  move  in  a  horizontal 
plane,  and  let  NS  be  a  bar  magnet  placed  at  right  angles  to  the  magnetic 
meridian,  at  a  distance  which  is  great  compared  with  its 
own  dimensions,  and  so  that  the  straight  line  drawn  through 
its  middle  point  and  that  of  the  needle  coincides  with  the 
magnetic  meridian.  The  two  poles  S  and  s  will  repel  each 
other  in  the  direction  sa  :  if  mm,  is  the  repellent  force 
which  these  two  poles  would  exert  at  the  unit  distance,  then 

mn*i  is  the  force  which  they   would  exert  at  the  distance 

Sj  =  r  ;  let  this  force  be  represented  in  direction  and  strength 
by  the  line  sa.  Similarly,  the  pole  N  will  act  on  j,  with  a 
force  represented  by  the  line  sc  ;  S  and  N  being  at  the  same 
distance  r  from  sy  sa  and  sc  are  equal,  and  their  resultant 
may  be  represented  by  the  line  sb.  From  the  similarity  of 
the  triangles  bsa  and  NSj  we  have  the  proportion  Sj  :  SN  = 
-as  :  bs  ;  if  /  is  the  value  of  the  resultant  &r,  that  is  the  total 
action  of  the  magnet  SN  on  the  pole  j,  and  if  /  be  half  the 

length  of  the  magnet  SN,  we  have  r  :  2  /=  -        :/  from 


Fig.  581. 


which  /=  ;  that  is,  the  total  action  of  the  magnet  NS  upon  another  is 

inversely  as  the  cube  of  the  distance  r. 


-709]      Determination  of  Magnetism  in  Absolute  Measure.      615 

If  the  two  magnets  be  placed  as  represented  in  fig.  582,  the  needle 
being  in  the  magnetic  meridian,  and  the  deflecting  magnet  at  right  angles 
thereto,  and  so  that  the  prolongation  of  its  axis  bisects  the  needle,  then  if 
;//;>>/!  is  the  force  with  which  the  pole  N  attracts  the  pole  s  at  the  unit  dis- 
tance, ;;/  and  ;;/,  being  the  strength  of  the  poles  in  the  bar  magnet,  and  the 
magnetic  needle  respectively  ;  the  attracting  force  at  the  distance  N.y  will 

be  /"-'    ,  /  being  as  before  the  half- 

(r  +  /) 

length  of  the  magnet,  and  r  the  dis- 
tance of  the  pole  s  from  the  middle 
of  the  magnet  NS  ;  in  like  manner 
the  repellent  force  with  which  S  acts 

upon  s  will  be  ~  ^.     If  ns  is  small 

v    —    / 

compared  with  the  distance  of  the  bar  magnet  NS,  the  direction  of  these 
forces  may  be  assumed  to  be  parallel,  and  at  right  angles  to  ns.     Since  S 
is  nearer  than  N  the  repulsion  will  predominate,  and  the  total  force  with 
which  the  magnet  NS  acts  on  the  pole  s  is 
F_  mm,   _ 


which,  assuming  that  /  is  so  small  in  comparison  with  r  that  its  square  and 
higher  powers  may  be  neglected,  gives  approximately 

-p  _  4  mm,  I 
-75— 

so  that  compared  with  the  first  position  of  the  magnet 

F-2/ 

709.  Determination  of  magnetism  in  absolute  measure.  —  The  com- 
parisons of  the  intensity  of  the  earth's  magnetism  in  different  places  (701)  are 
only  relative.  Of  late  years  much  attention  has  been  devoted  to  the  method 
of  expressing  not  only  this,  but  all  other  magnetic  forces  in  what  is  called 
absolute  measure.  This  term  is  used  as  opposed  to  relative,  and  does  not 
imply  that  the  measure  is  absolutely  accurate,  or  that  the  units  of  comparison 
employed  are  of  perfect  construction  ;  it  means  that  the  measurements, 
instead  of  being  a  simple  comparison  with  an  arbitrary  quantity  of  the  same 
kind  as  that  measured,  are  referred  to  the  fundamental  units  of  time,  space, 
and  mass  (21). 

The  manner  in  which  this  oetermination  is  made  in  the  case  of  magnetism, 
depends  essentially  on  the  observation  of  the  oscillation  of  a  horizontal  bar 
magnet  under  the  influence  of  the  earth's  magnetism  ;  and  in  the  second 
place,  on  observing  the  deflection  of  a  magnetic  needle  under  the  influence 
of  this  same  magnet. 

When  a  bar  magnet  suspended  by  a  thread  without  torsion,  free  to  oscil- 
late in  a  horizontal  plane,  is  deflected  from  its  position  of  equilibrium  and 
then  left  to  itself,  it  vibrates  backwards  and  forwards  through  its  position  of 
equilibrium,  making  oscillations  which,  if  small,  are  isochronous  like  those  of 
the  pendulum.  The  number  of  these  oscillations  in  a  given  time  depends  on  the 
mass  and  dimensions  of  the  bar,  on  its  magnetic  power,  and  on  the  intensity  of 


6i6  On  Magnetism.  [709 

the  earth's  magnetism  in  the  place  of  observation.    The  time,  /,  of  a  complete 

/   /£ 

oscillation  of  such  a  magnet  is  represented  by  the  formula  /  =  27rA  /—— -  ; 

V    -H-  M 

where  k  is  the  moment  of  inertia  of  the  magnet ;  that  is,  the  mass  which  must 
be  concentrated  at  the  unit  of  distance  from  the  centre  of  suspension,  to 
present  the  same  resistance  to  change  of  angular  velocity  about  this  centre 
as  the  magnet  itself  actually  does.  The  moment  of  inertia  of  a  magnet 
may  be  determined  theoretically  if  it  be  homogeneous  in  structure,  and  of  a 
regular  geometrical  shape  ;  or  it  may  be  determined  experimentally  by  first 
observing  the  time  of  oscillation  of  the  magnet  under  the  influence  of  the 
earth's  magnetism,  and  then  the  time  when  it  has  been  loaded  with  a  mass 
the  inertia  of  which  is  known,  and  which  does  not  alter  the  magnetic  moment 
of  the  bar.  M  is  the  magnetic  moment  of  the  bar  itself,  and  H  is  the  force 
of  the  earth's  manetism.  Hence 

(i). 


This  expression  gives  the  force  which,  applied  in  opposite  directions  at 
the  ends  of  a  lever  of  unit  length,  placed  at  right  angles  to  the  direction  of 
this  force,  would  have  the  same  effect  in  tending  to  turn  the  lever,  as  the 
magnetic  force  of  the  earth  has  in  tending  to  turn  the  magnet  about  a  vertical 
axis  when  it  is  set  at  right  angles  to  the  magnetic  meridian. 

Now  the  value  of  HM  depends  on  the  nature  of  the  bar,  and  on  the  force 
of  the  earth's  magnetism  in  the  place  in  question.  If  the  bar  were  magne- 
tised more  or  less  strongly,  or  if  the  same  bar  were  removed  to  a  different 
locality,  the  product  would  have  a  different  value.  We  must,  therefore,  find 
some  independent  relation  between  H  and  M,  which  will  give  rise  to  a  new 
equation,  and  thus  M,  the  magnetic  moment  of  the  bar,  would  be  got  rid  of, 
and  an  absolute  value  be  obtained  for  H. 

Such  a  relation  exists  in  the  deflection  from  the  magnetic  meridian,  which 
a  bar  magnet  produces  in  a  magnetic  needle. 

If  in  the  formula  in  the  preceding  article  we  put  M  =  2ml,  then  2     ;;*  = 

the  +  or  —  force  acting  on  either  pole  of  the  magnetic  needle,  and,  as  both 
poles  are  acted  on,  the  magnet  will  be  subject  to  the  action  of  a  couple,  the 

moment  of  which  will  be  expressed  by  --|—  2/'  cos  a  ;  where  a  is  the  angle 

of  deflection,  /'  the  half-length  of  the  small  magnetic  needle  ;  let  M'  =  2m' I'. 
In  like  manner  the  earth's  magnetism  will  act  upon  the  magnetic  needle 
with  a  couple  the  moment  of  which  is  expressed  by  H;;z'  2/'  sin  a  =  HM' 
sin  a.  Now  when  the  needle  is  in  equilibrium  these  forces  are  equal ;  that 
is — 

2MaM/  cos  a-HM'  sina, 

from  which  ^=-  =  r*  tan  a (2). 

Jri 

Combining  (i)  and  (2)  we  get  the  expression 


TT  77  /  k 

~/VVtan« 


709]        Determination  of  Magnetism  in  Absolute  Measure.      617 

an  expression  which  involves  no  other  physical  units  than  those  of  length 
(involved  in  k  and  r),  mass  (involved  in  £),  and  time  (involved  in  /),  so  that 
the  value  of  H  can  be  expressed  in  absolute  measure. 

The  value  for  H  in  this  expression  only  gives  the  horizontal  compo- 
nent of  the  earth's  magnetism  ;  the  total  force  is  obtained  by  dividing  the 
value  of  H  by  the  cosine  of  the  angle  of  dip  for  the  place  and  time  of  obser- 
vation. 

The  numerical  value  of  H  will  depend,  moreover,  on  the  units  taken.  On 
the  centimctre-gramme-second  system  the  unit  offeree  is  called  a  dyne.  It  is 
the  force  which  acting  upon  a  gramme  for  a  second  generates  a  velocity  of  a 
centimetre  per  second.  The  value  of  H  at  Greenwich  for  the  year  1877,  ex- 
pressed in  this  unit,  is  0-18079  of  a  dyne  ;  that  is,  the  horizontal  component 
of  the  earth's  magnetism  at  this  place  acting  on  the  unit  of  magnetism,  asso- 
ciated with  one  gramme  of  matter,  would  produce  a  velocity  of  0-18079 
c  entimetres  at  the  end  of  a  second.  The  angle  of  dip  at  this  time  and  place 
being  67°  37',  we  get  the  total  force  =  0-4745  units.  If  British  units — namely, 
the  foot,  grain,  second — be  employed,  the  unit  of  force  is  that  which  by  acting 
for  a  second  on  a  grain  gives  to  it  a  velocity  of  a  foot  per  second,  and  the 
unit  magnetic  pole  is  such  that  if  placed  one  foot  from  a  second  equal  pole 
it  will  repel  it  with  a  force  equal  to  the  unit  just  defined.  To  convert  the 
value  of  H  when  expressed  in  centimetres,  grammes,  and  seconds  into  the 
equivalent  value  referred  to  British  units,  we  must  multiply  by  21-69.  ^n  like 
manner  to  convert  magnetic  forces  referred  to  British  units  into  the  corre- 
sponding values  expressed  in  centimetres,  grammes,  and  seconds  we  must 

multiply  by  0*0461  =  ^r~- 


6 1 8  On  Magnetism.  [710- 


CHAPTER   IV. 

PROCESSES   OF  MAGNETISATION. 

710.  Magnetisation. — The  various  sources  of  magnetism  are  the   in- 
fluence of  natural  or  artificial  magnets,  terrestrial  magnetism,  and  electricity. 
This  last  method  will  be  described  under  voltaic  electricity.    The  three  prin- 
cipal methods  of  magnetisation  by  magnets  are  known  by  the  technical  names 
of  single  touch,  separate  touch,  and  double  touch. 

711.  Method  of  single  touch. — This   consists  in  moving  the  pole  of  a 
powerful  magnet  from  one  end  to  the  other  of  the  bar  to  be  magnetised,  and 
repeating  this  operation  several  times  always  in  the  same  direction.     The 
neutral  magnetism  is  thus  gradually  decomposed  throughout  all  the  length  of 
the  bar,  and  that  end  of  the  bar  which  was  touched  last  by  the  magnet  is  of 
opposite  polarity  to  the  end  of  the  magnet  by  which  it  has  been  touched. 
This  method  only  produces  a  feeble  magnetic  power,  and  is,  accordingly,  only 
used  for  small  magnets.     It  has  further  the  disadvantage  of  frequently  deve- 
loping consequent  poles. 

712.  Method  of  separate  touch. — This  method,  which  was  first  used  by 
Dr.  Knight  in  1745,  consists  in  placing  the  two  opposite  poles  of  two  magnets 
of  equal  force  in  the  middle  of  the  bar  to  be  magnetised,  and  in  moving  each 
of  them  simultaneously  towards  the  opposite  ends  of  the  bar.     Each  magnet 
is  then  placed  in  its  original  position,  and  the  operation  repeated.     After 
several  frictions  on  both  faces  of  the  bar  it  is  magnetised. 

In  Knight's  method  the  magnets  are  held  vertically.  Duhamel  improved 
the  method  by  inclining  the  magnets,  as  represented  in  fig.  583  ;  and  still 
more,  by  placing  the  bar  to  be  magnetised  on  the  opposite  poles  of  two  fixed 
magnets,  the  action  of  which  strengthens  that  of  the  movable  magnets.  The 
relative  position  of  the  poles  of  the  magnets  is  indicated  in  the  figure.  This 
method  produces  the  most  regular  magnets. 

713.  Method  of  double  touch. — In  this  method,  which  was  invented  by 
Mitchell,  the  two  magnets  are  placed  with  their  poles  opposite  each  other  in 
the  middle  of  the  bar  to  be  magnetised.     But,  instead  of  moving  them  in 
opposite  directions  towards  the  two  ends,  as  in  the  method  of  separate  touch, 
they  are  kept  at  a  fixed  distance  by  means  of  a  piece  of  wood  placed  between 
them  (fig.  583),  and  are  simultaneously  moved  first  towards  one  end,  then 
from  this  to  the  other  end,  repeating  this  operation  several  times,  and  finish- 
ing in  the  middle,  taking  care  that  each  half  of  the  bar  receives  the  same 
number  of  frictions. 

Epinus,  in  1758,  improved  this  method  by  supporting  the  bar  to  be  mag- 
netised, as  in  the  method  of  separate  touch,  on  the  opposite  poles  of  two 
powerful  magnets,  and  by  inclining  the  bars  at  an  angle  of  15°  to  20°.  In 


-715] 


Magnetism  of  Iron  Ships. 


619 


practice,  instead  of  two  bar  magnets,  it  is  usual  to  employ  a  horse-shoe 
magnet,  which  has  its  poles  conveniently  close  together. 

By  this  method  of  double  touch,  powerful  magnets  are  obtained,  but  they 


Fig.  583- 

have  frequently  consequent  poles.     As  this  would  be  objectionable  in  com- 
pass needles,  these  are  best  magnetised  by  separate  touch. 

714.  Magnetisation  by  the  action  of  tne   earth. — The  action  of  the 
earth  on  magnetic  substances  resembles  that  of  a  magnet,  and  hence  the 
terrestrial  magnetism  is  constantly  tending  to  separate  the  two  magnetisms 
which  are  in  the  neutral  state  in  soft  iron  and  in  steel.     But,  as  the  coercive 
force  is  very  considerable  in  the  latter  substance,  the  action  of  the  earth  is 
inadequate  to  produce  magnetisation,  except  when  continued  for  a  long  time. 
This  is  not  the  case  with  perfectly  soft  iron.     When  a  bar  of  this  metal  is 
held  in  the  magnetic  meridian  parallel  to  the  inclination,  the  bar  becomes  at 
once  endowed  with  feeble  magnetic  polarity.    The  lower  extremity  is  a  north 
pole,  and  if  the  north  pole  of  a  small  magnetic  needle  be  approached,  it  will 
be  repelled.     This  magnetism  is  of  course  unstable,  for  if  the  bar  be  turned 
the  poles  are  inverted,  as  pure  soft  iron  is  destitute  of  coercive  force. 

\Vhile  the  bar  is  in  this  position,  a  certain  amount  of  coercive  force  may 
be  imparted  to  it  by  giving  it  several  smart  blows  with  a  hammer,  and  the 
bar  retains  for  a  short  time  the  magnetism  which  it  has  thus  obtained.  But 
the  coercive  force  thus  developed  is  very  small,  and  after  a  time  the  mag- 
netism disappears. 

If  a  bar  of  soft  iron  be  twisted  while  held  vertically,  or,  better,  in  the 
plane  of  the  dip,  it  acquires  a  feeble  permanent  magnetism. 

It  is  this  magnetising  action  of  the  earth  which  develops  the  magnetism 
frequently  observed  in  steel  and  iron  instruments,  such  as  fire-irons,  rifles, 
lamp-posts,  railings,  gates,  lightning-conductors,  £c.,  which  remain  for  some 
time  in  a  more  or  less  inclined  position.  They  become  magnetised  with  their 
north  pole  downward,  just  as  if  placed  over  the  pole  of  a  powerful  magnet. 
The  magnetism  of  native  black  oxide  of  iron  has  doubtless  been  produced  by 
the  same  causes  ;  the  very  different  magnetic  power  of  different  specimens 
being  partly  attributable  to  the  different  positions  of  the  veins  of  ore  with 
regard  to  the  line  of  dip.  The  ordinary  irons  of  commerce  are  not  quite  pure, 
and  possess  a  feeble  coercive  force  ;  hence  a  feeble  magnetic  polarity  is 
generally  found  to  be  possessed  by  the  tools  in  a  smith's  shop.  Cast  iron, 
too,  has  usually  a  great  coercive  force,  and  can  be  permanently  magnetised. 
The  turnings,  also,  of  wrought  iron  and  of  steel  produced  by  the  powerful 
lathes  of  our  ironworks  are  found  to  be  magnetised. 

715.  Magnetism  of  iron  snips. — The  inductive  action    of  terrestrial 
magnetism  upon  the  masses  of  iron  always  found  in  ships  exerts  a  disturb- 


62O  On  Magnetism.  [715- 

ing  action  upon  the  compass  needle.  The  local  attraction,  as  it  is  called, 
may  be  so  considerable  as  to  render  the  indications  of  the  needle  almost 
useless  if  it  be  not  guarded  against.  A  full  account  of  the  manner  in 
which  local  attraction  is  produced,  and  in  which  it  is  compensated,  is  in- 
consistent with  the  limits  of  this  book,  but  the  most  important  points  are 
the  following  : — 

i.  A  vertical  mass  of  soft  iron  in  the  vessel,  say  in  the  bows,  would 
become  magnetised  under  the  influence  of  the  earth  ;  in  the  northern  hemi- 
sphere, the  lower  end  would  be  a  north  pole,  and  the  upper  end  a  south 
pole  ;  and  as  the  latter  may  be  assumed  to  be  nearer  the  north  pole  of  the 
compass  needle,  it  would  act  upon  it.  So  long  as  the  vessel  was  sailing  in 
the  magnetic  meridian  this  would  have  no  effect ;  but  in  any  other  direction 
the  needle  would  be  drawn  out  of  the  magnetic  meridian,  and  a  little  con- 
sideration will  show  that  when  the  ship  was  at  right  angles  to  the  magnetic 
meridian  the  effect  would  be  greatest.  This  vertical  induction  would  dis- 
appear twice  in  swinging  the  ship  round,  and  would  be  at  its  maximum 
twice  ;  hence  the  deviation  due  to  this  cause  is  known  as  semicircular 
deviation. 

ii.  Horizontal  masses  again,  such  as  deck-beams,  are  also  acted  upon 
inductively  by  the  earth's  magnetism,  and  their  induced  magnetism  exerts 
a  disturbing  influence  upon  the  magnetic  needle.  The  effect  of  this  hori- 
zontal induction  will  disappear  when  the  ship  is  in  the  magnetic  meridian 
and  also  when  it  is  at  right  angles  thereto.  In  positions  intermediate  to  the 
above  the  disturbing  influence  will  attain  its  maximum.  Hence  in  swinging 
a  ship  round  there  would  be  four  positions  of  the  ship's  head  in  which  the 
influence  would  be  at  a  maximum,  and  four  in  which  it  would  be  at  a  mini- 
mum. The  effect  of  horizontal  induction  is  accordingly  spoken  of  as  quad- 
rantal  deviation. 

The  influence  of  both  these  causes,  vertical  and  horizontal  induction, 
may  be  remedied  in  the  process  of  '  swinging  the  ship.'  This  consists  in 
comparing  the  indications  of  the  ship's  compass  with  those  of  a  standard 
compass  placed  on  shore.  The  ship  is  then  swung  round  in  various  posi- 
tions, and  by  arranging  small  vertical  and  horizontal  masses  of  soft  iron  in 
proximity  to  the  steering  compass,  positions  are  found  for  them  in  which  the 
inductive  action  of  the  earth  upon  them  quite  neutralises  the  influence  of  the 
earth's  magnetism  upon  the  ship  ;  and  in  all  positions  of  the  ship,  the  com- 
pass points  in  the  same  direction  as  the  one  on  shore. 

iii.  The  extended  use  of  iron  in  ship-building,  more  especially  when  the 
frames  are  entirely  of  iron,  has  increased  the  difficulty.  In  the  process  of 
building  a  ship,  the  hammering  and  other  mechanical  operations  to  which 
it  is  subject,  while  under  the  influence  of  the  earth's  magnetism,  will  cause 
it  to  become  to  a  certain  extent  permanently  magnetised.  The  distribution 
of  the  magnetism,  the  direction  of  its  magnetic  axis,  will  depend  on  the 
position  in  which  it  has  been  built ;  it  may  or  may  not  coincide  with  the 
direction  of  the  keel.  The  vessel  becomes  in  short  a  huge  magnet,  and  will 
exert  an  influence  of  its  own  upon  the  compass  quite  independently  of  ver- 
tical or  horizontal  induction.  The  influence  is  semicircular ;  that  is,  it  dis- 
appears when  the  magnetic  axis  of  the  ship  is  in  the  magnetic  meridian,  and 
is  greatest  at  right  angles  to  it.  It  may  be  compensated  by  two  permanent 


-717]  Magnetic  Battery.  62 1 

magnets  placed  near  the  compass  in  suitable  positions  found  by  trial  during 
the  process  of  swinging  the  ship.  Supposing  the  inherent  magnetism  of  the 
ship  to  have  the  power  of  drawing  the  compass  a  point  to  the  east,  the  com- 
pensating magnets  may  be  so  arranged  as  to  tend  to  draw  it  a  point  to  the 
west,  and  thus  keep  it  in  the  magnetic  meridian.  If,  however,  the  inherent 
magnetism  be  destroyed,  from  whatever  cause,  it  is  clear  that  the  magnets 
will  now  draw  it  aside  a  point  too  much  to  the  west.  This  is  the  source  of  a 
new  difficulty.  It  has  been  found  that  a  ship  which  at  the  time  of  sailing 
was  properly  compensated,  would,  on  returning  from  a  long  voyage,  have  its 
compasses  over-compensated.  The  buffeting  which  the  ship  had  experienced 
had  destroyed  its  inherent  magnetism,  and  numerous  instances  are  known 
where  the  loss  of  a  vessel  can  be  directly  traced  to  this  cause.  Fortunately, 
it  has  been  found  that  after  some  time  a  ship's  magnetic  condition  is  virtu- 
ally permanent,  and  is  unaltered  by  any  further  wear  and  tear.  The  magne- 
tism which  it  then  retains  is  called  its  permanent  magnetism,  in  opposition 
to  the  sub-permanent  which  it  loses. 

The  difficulty  of  adequately  compensating  compasses,  which  is  greatly 
increased  by  the  armour-plated  and  turret  ships  now  in  use,  has  induced  one 
school  to  throw  over  any  attempt  at  correction  ;  but  by  careful  observation 
of  the  magnetic  condition  of  a  ship,  and  tabulating  the  errors  to  construct  a 
table,  and  comparing  this  with  the  indications  of  the  compass  at  any  one 
time,  the  true  course  can  be  made  out. 

In  the  Royal  Navy,  the  plan  now  adopted  is  to  combine  both  methods  : 
compensate  the  errors  to  a  considerable  extent,  and  then  construct  a  table 
of  the  residual  errors. 

716.  Magnetic  saturation. — Experiment  has  shown  that  to  a  certain 
extent  the  magnetic  force  which  can  be  imparted  to  a  steel  bar  increases  with 
the  magnetising  force  used.     It  depends  also  on  the  number  of  strokes  or 
movements  of  the  magnetising  magnets  or  coils  ;  on  the  form  and  dimensions 
of  the  bar,  on  its  density,  on  the  quantity  of  carbon  it  contains,  on  its  hard- 
ness, and  on  the  manner  in  which  it  is  tempered.     Yet  there  is  a  limit  to  the 
magnetic  force  which  can  be  imparted  to  iron  or  steel,  and  when  this  is  at- 
tained, the  bar  is  said  to  be  saturated  or  magnetised  to  saturation.     A  bar 
may  indeed  be  magnetised  beyond  this  point,  but  this  excess  is  temporary ; 
it  gradually  diminishes  until  the  magnet  has  sunk  to  its  point  of  saturation. 

This  is  intelligible,  for  the  magnetisms  once  separated  tend  to  reunite, 
and  when  their  attractive  force  is  equal  to  that  which  opposes  their  separa- 
tion— that  is,  the  coercive  force  of  the  metal — equilibrium  is  attained,  and 
the  magnet  is  saturated.  Hence,  more  magnetism  ought  to  be  developed 
in  bars  than  they  can  retain,  in  order  that  they  may  decline  to  their  perma- 
nent state  of  saturation.  To  increase  the  magnetism  of  an  unsaturated  bai, 
a  less  feeble  magnet  must  not  be  used  than  that  by  which  it  was  originally 
magnetised. 

717.  Magnetic  battery. — A  magnetic  battery  or  magazine  consists  of 
a  number  of  magnets  joined  together  by  their  similar  poles.     Sometimes 
they  have  the  form  of  a  horse-shoe,  and  sometimes  a  rectilinear  form.     The 
batter)'  represented  in  fig.  584  consists  of  five  superposed  steel  plates.     That 
in  fig.  585  consists  of  twelve  plates,  arranged  in  three  layers  of  four  each. 
The  horse-shoe  form  is  best  adapted  for  supporting  a  weight,  for  then  both 


622 


On  Magnetism.  [717- 

In  both  the  bars  are  magnetised  separately,  and 


poles  are  used  at  once. 

then  fixed  by  screws. 

The  force  of  a  magnetic  battery  consisting  of  n  similar  plates  equally 

magnetised,  is  not  n  times  as  great  as  that  of  a  single  one,  but  is  somewhat 

smaller.  These  magnets  mutually  en- 
feeble each  other  ;  manifestly  because, 
for  instance,  each  north  pole  evokes 
south  magnetism  in  the  adjacent  north 
pole,  and  thereby  diminishes  some  of  its 
north  polarity.  The  magnetism  of  a 
plate  which  has  formed  part  of  such  a 
battery  will  be  found  to  be  materially 
less  than  it  was  originally. 

Thus  Jamin  found  that  six  equal  plates 
which  had  each  the  portative  force  18 
kilos,  only  lifted  64  kilos  when  arranged 
as  a  battery,  instead  of  108  ;  and  when 
removed  from  the  battery,  each  of  them 
had  only  the  portative  force  9  to  10  kilos. 
The  force  is  increased  by  making  the 
lateral  plates  I  or  2  centimetres  shorter 
than  the  one  in  the  middle  (fig.  584). 

718.  Armatures. — When  even  a  steel 
bar  is  at  its  limit  of  saturation,  it  gradu- 
ally loses  its  magnetism.  To  prevent 
this,  armatures  or  keepers  are  used  ; 


Fig.  .584- 


these  are  pieces  of  soft  iron,  A  and  B  (fig.  585),  which  are  placed  in  contact 
with  the  poles.  Acted  on  inductively,  they  become  powerful  temporary 
magnets,  possessing  opposite  polarity  to  that  of  the  inducing  pole  ;  they 


Fig   585- 


thus  react  in  turn  on  the  permanent  magnetism  of  the  bars,  preserving  and 
even  increasing  it. 

When  the  magnets  are  in  the  form  of  bars,  they  are  arranged  in  pairs, 
as  shown  in  fig.  586,  with  opposite  poles  in  juxtaposition,  and  the  circuit  is 


Fig.  586. 


completed  by  two  small  bars  of  soft  iron,  AB.  Movable  magnetic  needles, 
if  not  clamped  down,  set  spontaneously  towards  the  magnetic  poles  of  the 
earth,  the  influence  of  which  acts  as  a  keeper. 


-719]  Portative  Force.     Power  of  Magnets.  623 

A  horse-shoe  magnet  has  a  keeper  attached  to  it,  which  is  usually  ar- 
ranged so  as  to  support  a  weight.  The  keeper  becomes  magnetised  under 
the  influence  of  the  two  poles,  and  adheres  with 
great  force  :  the  weight  which  it  can  support  being 
more  than  double  that  which  a  single  pole  would 
hold. 

In  respect  to  this  weight,  a  singular  and  hitherto 
inexplicable  phenomenon  has  been  observed.  When 
contact  is  once  made,  and  the  keeper  is  charged  with 
its  maximum  weight,  any  further  addition  would 
detach  it  ;  but  if  left  in  contact  for  a  day,  an  addi- 
tional weight  may  be  added  without  detaching  it,  and 
by  slightly  increasing  the  weight  every  day  it  may 
ultimately  be  brought  to  support  a  far  greater  load 
than  it  would  originally.  But  if  contact  be  once 
broken,  the  weight  it  can  now  support  does  not  much 
exceed  its  original  charge. 

It  is  advantageous  that  the  surface  of  the  magnet 
and  armatures  which  are  in  contact  should  not  be  Fis-  587. 

plane  but  slightly  cylindrical,  so  that  they  touch  along  a  line. 

In  providing  a  natural  magnet  with  a  keeper,  the  line  joining  the  two 
poles  is  first  approximately  determined  by  means  of  iron  filings.  Two  poles 
of  soft  iron  (fig.  587),  each  terminating  in  a  massive  shoe,  are  then  applied 
to  the  faces  corresponding  to  the  poles.  Under  the  influence  of  the  natural 
magnet,  these  plates  become  magnetised,  and  if  the  letters  A  and  B  repre- 
sent the  position  of  the  poles  of  the  natural  magnet,  the  poles  of  the  arma- 
ture are  a  and  b. 

719.  Portative  force.  Power  of  magnets.  —  The  portative  force  is 
the  greatest  weight  which  a  magnet  can  support.  Hacker  found  that  the 
portative  force  of  a  saturated  horse-shoe  magnet,  which,  by  repeatedly  de- 
taching the  keeper,  had  become  constant,  may  be  represented  by  the  formula 


in  which  P  is  the  portative  force  of  the  magnet,^  its  own  weight,  and  a  a 
coefficient  which  varies  with  the  nature  of  the  steel  and  the  mode  of  mag- 
netising. Hence  a  magnet  which  weighs  1,000  ounces  only  supports  25 
times  as  much  as  one  weighing  8  ounces  or  y|s  as  heavy,  and  125  such  bars 
would  support  as  much  as  one  which  is  as  heavy  as  all  together.  It  appears 
immaterial  whether  the  section  of  the  bar  is  quadratic  or  circular,  and  the 
distance  of  the  legs  is  of  inconsiderable  moment  ;  it  is  important,  however, 
that  the  magnet  be  suspended  vertically,  and  that  the  load  be  exactly  in  the 
middle.  In  Hacker's  magnets  the  value  of  a  was  10-33,  while  in  Logemann's 
it  was  23.  By  arranging  together  several  thin  magnetised  plates  Jamin 
constructed  bar  magnets  which  support  1  5  times  their  own  weight. 

The  strength  of  two  bar  magnets  may  be  compared  by  the  following 
simple  method,  which  is  known  as  Kiilp's  compensation  method:  —  A  small 
magnetic  compass  needle  is  placed  in  the  magnetic  meridian.  One  pole  of 
one  of  the  magnets  to  be  tested  is  then  placed  at  right  angles  to  the  mag- 
netic meridian  in  the  same  plane  as  the  needle,  and  so  that  its  axis  prolonged 


624  On  Magnetism.  [719- 

would  bisect  the  needle.  The  compass  needle  is  thereby  deflected  through 
a  certain  angle.  The  similar  pole  of  the  other  magnet  is  then  placed 
similarly  on  the  other  side  of  the  needle,  and  a  position  found  for  it  in 
which  it  exactly  neutralises  the  action  of  the  first  magnet  ;  that  is,  when 
the  needle  is  again  in  the  magnetic  meridian.  If  the  magnets  are  not  too 
long,  compared  with  their  distance  from  the  needle,  their  strengths  are  ap- 
proximately as  the  cubes  of  the  distance  of  the  acting  poles  from  the  mag- 
netic needle. 

720.  Circumstances  which  influence  the  power  of  magnets. — All  bars 
do  not  attain  the  same  state  of  saturation,  for  their  coercive  force  varies 
Twisting  or  hammering  imparts  to  iron  or  steel  a  considerable  coercive  force 
But  the  most  powerful  of  these  influences  is  the  operation  of  tempering  (95). 
Coulomb  found  that  a  steel  bar  tempered  at  dull  redness  and  magnetised  to 
saturation,  made  ten  oscillations  in  93  seconds.  The  same  bar  tempered  at 
a  cherry -red  heat,  and  similarly  magnetised  to  saturation,  only  took  63 
seconds  to  make  ten  oscillations. 

Hence  it  would  seem,  that  the  harder  the  steel  the  greater  is  its  coercive 
force  ;  it  receives  magnetism  with  much  greater  difficulty,  but  retains  it  more 
effectually.  It  appears  from  Jamin's  experiments  that  no  general  rule  of  this 
kind  can  be  laid  down  ;  for  each  specimen  of  steel  there  seems,  according 
to  the  proportion  of  carbon  which  it  contains,  to  be  a  certain  degree  of 
tempering  which  is  most  favourable  for  the  development  of  permanent 
magnetisation. 

Very  hard  steel  bars  have  the  disadvantage  of  being  very  brittle,  and  in 
the  case  of  long  thin  bars  a  hard  tempering  is  apt  to  produce  consequent 
*poles.  Compass  needles  are  usually  tempered  at  the  blue  heat — that  is,  about 
300°  C. — by  which  a  high  coercive  force  is  obtained  without  great  fragility. 
Steel  is  magnetised  with  difficulty  even  when  placed  for  some  time  in  a  coil 
through  which  a  powerful  current  is  passing  ;  iron  under  these  circum- 
stances is  magnetised  at  once.  If  a  short  coil  covering  only  a  portion  of  the 
steel  bars  be  moved  backwards  and  forwards  the  magnetisation  is  more 
complete. 

The  hardness  of  steel,  and  the  proportion  of  carbon  which  it  contains,  exert 
an  important  influence  on  the  degree  to  which  it  can  be  magnetised.  For 
the  same  degree  of  hardness,  the  magnetisation  increases  with  the  proportion 
of  carbon  in  the  steel,  and  more  markedly  the  smaller  this  proportion  ;  with 
the  same  proportion  of  carbon  it  increases  with  the  hardness  of  the  steel.  It 
appears  that  the  compound  of  iron  and  carbon  in  steel  is  the  carrier  of  the 
permanent  magnetism,  and  the  interjacent  particles  of  iron  the  carriers  of 
the  temporary  magnetism.  Holtz  magnetised  plates  of  English  corset  steel 
to  saturation  and  determined  their  magnetic  moment  ;  they  were  then  placed 
in  dilute  hydrochloric  acid,  by  which  the  iron  was  eaten  away,  and  the 
magnetic  moment  determined  when  the  plate  had  been  magnetised  to  satura- 
tion after  each  such  treatment.  It  was  thus  found  that,  with  a  diminution 
in  the  proportion  of  iron,  there  was  an  increase  in  the  magnetic  moment  for 
the  unit  of  weight.  Holtz  found,  however,  that  pure  iron  prepared  by  elec- 
trolysis can  acquire  permanent  magnetism. 

Jamin  investigated  the  distribution  of  force  in  magnets  by  suspending 
from  one  arm  of  a  delicate  balance  a  small  iron  ball,  and  then  ascertaining 


-720]  Power  of  Magnets.  62$ 

what  force  applied  at  the  other  arm,  was  required  to  detach  the  ball  when 
placed  in  contact  with  various  positions  of  the  magnet  to  be  investigated. 

Taking  thus  a  thin  plate  magnetised  to  saturation,  it  was  found  that  the 
magnetism  increased  with  the  thickness,  but  did  not  materially  vary  with 
the  breadth  of  the  plate.  The  magnetic  force  was  developed  almost  ex- 
clusively at  the  ends.  The  curve  representing  the  magnetic  force  (721) 
was  convex  towards  the  poles  at  the  ends.  If  now  several  similar  plates  are 
superposed,  the  corresponding  curves  become  steeper  and  prolonged  towards 
the  middle  ;  the  magnetic  force  thus  becomes  increased.  When  the  curves 
run  into  each  other  in  the  middle  the  maximum  of  the  combination  is  reached  ; 
any  additional  plates  produce  no  increase  in  the  strength.  Steel  bars  may 
also  be  magnetised  so  as  to  show  the  same  curves,  and  such  bars  and  com- 
binations of  plates  are  called  by  Jamin  normal  magnets. 

Jamin  found  that  magnetisation  extends  deeper  in  a  bar  than  has  been 
usually  supposed  ;  in  soft  and  annealed  steel  it  penetrates  deeply.  The 
depth  diminishes  with  the  hardness  of  the  steel  and  the  proportion  of  carbon 
it  contains.  If  plates  of  varying  thickness  are  so  thin  that  the  magnetisation 
can  entirely  penetrate  them,  the  thicker  of  these  plates  are  more  strongly  mag- 
netised by  the  same  force,  for  the  magnetisation  extends  through  a  thicker 
layer  than  the  thinner  ones ;  if,  however,  the  plates  are  very  thick,  they  are 
magnetised  to  the  same  extent  by  one  and  the  same  force.  With  equal  bars 
the  thickness  of  the  magnetic  layer  varies  with  the  strength  of  the  magnetising 
force.  Jamin  proved  this  by  placing  the  plates  in  sulphuric  acid  ;  he  found 
magnetism  in  bars  which  had  been  exposed  to  the  stronger  force,  while  those 
which  had  been  more  feebly  magnetised  showed  none  when  they  had  been 
eaten  away  by  the  acid  to  the  same  extent.  He  thus  showed  that  the 
magnetism  which  had  penetrated  was  as  strong  as  that  on  the  surface. 

Xoltz  has  made  some  experiments  on  the  influence  of  solid  bars  as  against 
hollow  tubes  in  the  construction  of  permanent  steel  magnets.  The  latter 
are  to  be  preferred  ;  they  are  decidedly  cheaper,  as  they  need  not  be  bored, 
but  may  be  bent  from  steel  plates.  A  bar  and  a  tube  of  the  same  steel, 
125  mm.  in  length  by  13  mm.  diameter,  and  the  tube  175  mm.  thick,  were 
magnetised  to  saturation,  and  their  magnetic  moments  determined  by  the 
method  of  oscillation  (705)  the  tube  being  loaded  with  copper.  The  mag- 
netism of  the  tube  was  to  that  of  the  bar  as  i'6  :  i.  The  tubes  also  retained 
their  magnetisation  better.  After  the  lapse  of  six  months  the  ratio  of  the 
magnetisation  of  the  tube  was  to  that  of  the  bar  as  27  :  i.  A  magnetised 
steel  tube  filled  with  a  soft  iron  core  had  scarcely  any  directive  force. 

Temperature. — Increase  of  temperature  always  produces  a  diminution  of 
magnetic  force.  If  the  changes  of  temperature  are  small,  those  of  the  atmo- 
sphere for  instance,  the  magnet  is  not  permanently  altered.  Kuppfer  allowed 
a  magnet  to  oscillate  at  different  temperatures,  and  found  a  definite  decrease 
in  its  power  with  increased  temperature,  as  indicated  by  its  slower  oscillations. 
In  the  case  of  a  magnet  2£  inches  in  length,  he  observed  that  with  an  increase 
of  each  degree  of  temperature  the  duration  of  800  oscillations  was  0-4" 
longer.  If  n  be  the  number  of  oscillations  at  zero,  and  n^  the  number  at  /, 
then 

n  =  nl  (\-ct], 

where  c  is  a  constant  depending  in  each  case  on  the  magnet  used.     This 

E  E 


626  On  Magnetism.  [720- 

formula  has  an  important  application  in  the  correction  of  the  observations  of 
magnetic  intensity  which  are  made  at  different  places  and  at  different  tem- 
peratures, and  which,  in  order  to  be  comparable,  must  first  be  reduced  to  a 
uniform  temperature. 

When  a  magnet  has  been  more  strongly  heated,  it  does  not  regain  its 
original  force  on  cooling  to  its  original  temperature,  and  when  it  has  been 
heated  to  redness,  it  is  demagnetised.  This  was  first  shown  by  Coulomb, 
who  took  a  saturated  magnet,  progressively  heated  it  to  higher  tem- 
peratures, and  noted  the  number  of  oscillations  after  each  heating. 
The  higher  the  temperature  to  which  it  had  been  heated  the  slower  its 
oscillations. 

A  magnet  heated  to  bright  redness  loses  its  magnetism  so  completely 
that  it  is  quite  indifferent,  not  only  towards  iron,  but  also  towards  another 
magnet,  and  this  holds  so  long  as  this  high  temperature  continues.  Incan- 
descent iron  also  does  not  possess  the  property  of  being  attracted  by  the 
magnet.  Hence  there  is  in  the  case  of  iron  a  magnetic  limit,  beyond  which 
it  is  unaffected  by  magnetism.  Such  a  magnetic  limit  exists  in  the  case  of 
other  magnetic  metals.  With  cobalt,  for  instance,  it  is  far  beyond  a  white 
heat,  for  at  the  highest  temperatures  hitherto  examined  it  is  still  magnetic  ; 
the  magnetic  limit  of  chromium  is  somewhat  below  red  heat ;  that  of  nickel 
at  about  350°  C.  and  of  manganese  at  about  15°  to  20°  C. 

A  change  of  temperature  whether  from  16°  to  100°,  or  from  100°  to  16°, 
increases  the  strength  of  temporary  or  induced  magnetism  both  in  the  case 
of  iron  and  of  steel. 

Percussion  and  Torsion. — When  a  steel  bar  is  hammered  while  being 
magnetised  it  acquires  a  much  higher  degree  of  magnetisation  than  it  would 
without  this  treatment.  Conversely  when  a  magnet  is  let  fall,  or  is  otherwise 
violently  disturbed,  it  loses  much  of  its  magnetisation.  Torsion  exerts  a 
great  influence  on  the  magnetisation  of  a  bar,  and  the  interesting  phenomenon 
has  been  observed  that  torsion  influences  magnetism  in  the  same  manner 
as  magnetism  does  torsion.  Thus  the  permanent  magnetisation  of  a  steel  bar 
is  diminished  by  torsion,  but  not  proportionally  to  the  increase  of  torsion. 
In  like  manner  the  torsion  of  twisted  iron  wires  is  diminished  by  their  being 
magnetised,  though  less  so  than  in  proportion  to  their  magnetisation.  Re- 
peated torsions  in  the  same  direction  scarcely  diminish  magnetisation,  but 
a  torsion  in  the  opposite  direction  produces  a  new  diminution  of  the  magne- 
tism. In  a  perfectly  analogous  manner,  repeated  magnetisations  in  the  same 
sense  scarcely  diminish  torsion,  but  a  renewed  magnetisation  in  the  opposite 
direction  does  so. 

721.  Distribution  of  free  magnetism. — Coulomb  investigated  the  dis- 
tribution of  magnetic  force  by  placing  a  large  magnet  in  a  vertical  position 
in  the  magnetic  meridian  ;  he  then  took  a  small  magnetic  needle,  and,  having 
ascertained  the  number  of  its  oscillations  under  the  influence  of  the  earth's 
magnetism  alone,  he  presented  it  to  different  parts  of  the  magnet.  The 
oscillations  were  fewer  as  the  needle  was  nearer  the  middle  of  the  bar,  and 
when  they  had  reached  that  position  their  number  was  the  same  as  under 
the  influence  of  the  earth's  magnetism  alone.  For  saturated  bars  of  more 
than  7  inches  in  length  the  distribution  could  always  be  expressed  by  a 
curve  whose  abscissae  were  the  distances  from  the  ends  of  the  magnet,  and 


-722]  Mayer's  Floating  Magnets.  627 

whose  ordinates  were  the  force  of  magnetism  at  these  points.  With  magnets 
of  the  above  dimensions  the  poles  are  at  the  same  distance  from  the  end  ; 
Coulomb  found  the  distance  to  be  r6  inch  in  a  bar  8  inches  long.  He  also 
found  that,  with  shorter  bars,  the  distance  of  the  poles  from  the  end  is  |  of 
the  length  ;  thus  with  a  bar  of  three  inches  it  would  be  half  an  inch.  These 
results  presuppose  that  the  other  dimensions  of  the  bar  are  very  small  as 
compared  with  its  length,  that  it  has  a  regular  shape,  and  is  uniformly 
magnetised.  When  these  conditions  are  not  fulfilled,  the  positions  of  the 
poles  can  only  be  determined  by  direct  trials  with  a  magnetic  needle.  With 
lozenge-shaped  magnets  the  poles  are  nearer  the  middle.  Coulomb  found 
that  these  lozenge-shaped  bars  have  a  greater  directive  force  than  rectangular 
bars  of  the  same  weight,  thickness,  and  hardness. 

722.  Mayer's  floating:  magnets. — The  reciprocal  action  of  magnetic 
poles  may  be  conveniently  illustrated  by  an  elegant  method  devised  by 
Prof.  A.  M.  Mayer.  Steel  sewing-needles  are  magnetised  so  that  their 
points  are  north  poles,  and  their  eyes,  which  are  thus  south  poles,  just 
project  through  minute  cork  discs,  so  that  when  placed  in  water  the  magnets 
float  in  a  vertical  position.  If  the  north  pole  of  a  strong  magnet  is  brought 
near  a  number  of  these  floating  magnets  they  are  attracted  by  it,  and  take  up 
definite  positions,  forming  figures  which  depend  on  the  reciprocal  repulsion 
of  the  floating  magnets,  and  on  their  number.  Some  of  them  are  repre- 
sented in  fig.  588.  The  more  complex  produce  more  than  one  arrange- 

6a  63 


* • 


ment  which  are  not  equally  stable,  the  letters  <?,  £,  and  c  indicating  the  de- 
creasing order  of  stability.  A  slight  shock  often  causes  one  form  to  pass 
into  another  and  more  stable  form. 

These  figures  not  only  illustrate  magnetic  actions,  but  they  suggest  an 
image  of  the  manner  in  which  alteration  of  molecular  groupings  may  give 
rise  to  physical  phenomena,  such  as  those  of  superfusion  (345). 


£  £  2 


628  Fnctional  Electricity.  [723- 


BOOK   IX. 

FRICTIONAL  ELECTRICITY. 


CHAPTER    I. 
FUNDAMENTAL  PRINCIPLES. 

723.  Electricity.     Its  nature. — Electricity  is  a  powerful  physical  agent 
which  manifests  itself  mainly  by  attractions  and  repulsions,  but  also  by 
luminous  and  heating  effects,  by  violent  commotions,  by  chemical  decomposi- 
tions, and  many  other  phenomena.     Unlike  gravity,  it  is  not  inherent  in 
bodies,  but  it    is  evoked  in  them  by  a  variety  of  causes,  among  which  are 
friction,  pressure,  chemical  action,  heat  and  magnetism. 

Thales,  6  B.C.,  knew  that  when  amber  was  rubbed  with  silk,  it  acquired 
the  property  of  attracting  light  bodies  ;  and  from  the  Greek  form  of  this 
word  (j/Af/crpoi/)  the  term  electricity  has  been  derived.  This  is  nearly  all 
the  knowledge  left  by  the  ancients  ;  it  was  not  until  towards  the  end  of  the 
sixteenth  century  that  Dr.  Gilbert,  physician  to  Queen  Elizabeth,  showed 
that  this  property  was  not  limited  to  amber,  but  that  other  bodies,  such  as 
sulphur,  wax,  glass,  &c.,  also  possessed  it  in  a  greater  or  less  degree. 

724.  Development  of  electricity  by  friction. — When  a  glass  rod,  or  a 
stick  of  sealing-wax,  or  shellac,  is  held  in  the  hand,  and  is  rubbed  with  a 
piece  of  flannel  or  with  the  skin  of  a  cat,  the  parts  rubbed  will  be  found  to 
have  the  property  of  attracting  light  bodies,  such  as  pieces  of  silk,  wool, 
feathers,  paper,  bran,  gold  leaf,  &c.,  which,  after  remaining  a  short  time  in 
contact,  are  again  repelled.     In  order  to  ascertain  whether  bodies  are  electri- 
fied or  not,  instruments  called  electroscopes  are  used.     The  simplest  of  these, 
the  electric  pendulum  (fig.  589),  consists  of  a  pith  ball  attached  by  means  of 
a  silk  thread  to  a  glass  support.     When  an  electrified  body  is  brought  near 
the  pith  ball,  the  latter  is  instantly  attracted,  but  after  momentary  contact  is 
again  repelled  (fig.  590). 

A  solid  body  may  also  be  electrified  by  friction  with  a  liquid  or  with  a 
gas.  In  the  Torricellian  vacuum  a  movement  of  the  mercury  against  the 
sides  of  the  glass  produces  a  disengagement  of  electric  light  visible  in  the 
dark  ;  a  tube  exhausted  of  air,  but  containing  a  few  drops  of  mercury,  be- 
comes also  luminous  when  agitated  in  the  dark. 

If  a  quantity  of  mercury  in  a  dry  glass  vessel  be  connected  with  a  gold- 
leaf  electroscope  by  a  wire,  and  a  dry  glass  rod  be  immersed  in  it,  no  indica- 


-725] 


Conductors  and  Nonconductors. 


629 


tions  are  observed  during  the  immersion,  but  on  smartly  withdrawing  the 
rod,  the  leaves  increasingly  diverge,  attaining  their  maximum  when  the  rod 
leaves  the  mercury. 

Some  substances,  particularly  metals,  do  not  seem  capable  of  receiving 
the  electric  excitement.  When  a  rod  of  metal  is  held  in  the  hand,  and 
rubbed  with  silk  or  flannel,  no  electrical  effects  are  produced  in  it ;  and  bodies 


Fig.  589- 


Fig.  590. 


were  divided  by  Gilbert  into  ideoelectrics,  or  those  which  become  electrical 
by  friction  ;  and  anelectrics,  or  those  which  do  not  possess  this  property. 
These  distinctions  no  longer  obtain  in  any  absolute  sense  ;  under  appropriate 
conditions,  all  bodies  may  be  electrified  by  friction  (726). 

725.  Conductors  and  nonconductors. — When  a  dry  glass  rod,  rubbed 
at  one  end,  is  brought  near  an  electroscope,  that  part  only  will  be  electrified 
which  has  been  rubbed  ;  the  other  end  will  produce  neither  attraction  nor 
repulsion.  The  same  is  the  case  with  a  rod  of  shellac  or  of  sealing-wax. 
In  these  bodies  electricity  does  not  pass  from  one  part  to  another— they  do 
not  conduct  electricity.  Experiment  shows,  that  when  a  metal  has  received 
electricity  in  any  of  its  parts,  the  electricity  instantly  spreads  over  its  entire 
surface.  Metals  are  hence  said  to  be  good  conductors  of  electricity. 

Bodies  have,  accordingly,  been  divided  into  conductors  and  nonconductors 
or  insulators.  This  distinction  is  not  absolute,  and  we  may  advantageously 
consider  bodies  as  offering  a  resistance  to  the  passage  of  electricity  which 
varies  with  the  nature  of  the  substance.  Those  bodies  which  offer  little 
resistance  are  thus  conductors,  and  those  which  offer  great  resistance  are  non- 
conductors or  insulators  :  electrical  conductivity  is  accordingly  the  inverse 
of  electrical  resistance.  There  is  no  such  thing  as  an  absolute  nonconductor 
of  electricity,  any  more  than  there  is  an  absolute  nonconductor  of  heat. 
We  are  to  consider  that  between  conductors  and  nonconductors  there  is  a 
quantitative  and  not  a  qualitative  difference  ;  there  is  no  conductor  so  good 


630 


Frictional  Electricity. 


[725- 


but  that  it  offers  some  resistance  to  the  passage  of  electricity,  nor  is  there 
any  substance  which  insulates  so  completely  but  that  it  allows  some  electri- 
city to  pass.  The  transition  from  conductors  to  nonconductors  is  gradual, 
and  no  line  of  sharp  demarcation  can  be  drawn  between  them. 

In  this  sense  we  are  to  understand  the  following  table,  in  which  bodies 
are  classed  as  conductors,  semiconductors,  and  nonconductors  ;  those  bodies 
being  conveniently  designated  as  conductors  which,  when  applied  to  a 
charged  electroscope,  discharge  it  almost  instantaneously  ;  semiconductors 
being  those  which  discharge  it  in  a  short  but  measurable  time,  a  few  seconds, 
for  instance  ;  while  nonconductors  effect  no  perceptible  discharge  in  the 
course  of  a  minute. 


Conductors. 


Semiconductors. 


Nonconductors. 


Metals. 

Alcohol  and  ether. 

Dry  oxides. 

Well-burnt  charcoal. 

Powdered  glass. 

Ice  at  -25°  C. 

Graphite. 

Flour  of  sulphur. 

Lime. 

Acids. 

Dry  wood. 

Caoutchouc. 

Aqueous  solutions. 

Paper. 

Air  and  dry  gases. 

Water. 

Ice  at  o°. 

Dry  paper. 

Snow. 

Silk. 

Vegetables. 

Diamond  and  precious  stones. 

Animals. 

Glass.    • 

Soluble  salts. 

Wax. 

Linen. 

Sulphur. 

Cotton. 

Resins. 

Amber. 

Shellac. 

This  list  is  arranged  in  the  order  of  decreasing  conductivity,  or,  what  is  the 
same  thing,  of  increasing  resistance.  The  arrangement,  however,  is  not  in- 
variable. Conductivity  depends  on  many  physical  conditions.  Glass,  for 
example,  which  does  not  conduct  at  any  ordinary  temperature^  does  so  at  a 
red  heat.  Shellac  and  resin  do  not  insulate  so  well  when  they  are  heated. 
Water,  which  is  a  good  conductor,  conducts  but  little  in  the  state  of  ice  at 
o°,  and  very  badly  at  —25°.  Powdered  glass  and  flour  of  sulphur  conduct 
very  well,  while  in  large  masses  they  are  nonconductors  ;  probably  because 
in  a  state  of  powder  each  particle  becomes  covered  with  a  film  of  moisture 
that  acts  as  a  conductor.  The  nonconducting  power  of  glass  depends  also 
on  its  chemical  composition. 

According  to  Said  Effendi,  if  the  conducting  power  of  water  be  taken  at 
1,000,  the  conducting  power  of  petroleum  is  72  ;  alcohol  49  ;  ether  40  ; 
turpentine  23  ;  and  benzole  16.  Domalip  obtained  the  following  numbers 
for  the  respective  conductivities:  W7ater  144;  ether  6-3;  turpentine  1-9; 
and  benzole  I. 

726.  Insulating:  bodies.  Common  reservoir.— Bad  conductors  are 
called  insulators,  for  they  are  used  as  supports  for  bodies  in  which  electricity 
is  to  be  retained.  A  conductor  remains  electrified  only  so  long  as  it  is  sur- 
rounded by  insulators.  If  this  were  not  the  case,  as  soon  as  the  electrified 


-727]  Distinction  of  the  two  kinds  of  Electricity.  631 

body  came  in  contact  with  the  earth,  which  is  a  good  conductor,  the  electri- 
city would  pass  into  the  earth  and  diffuse  itself  through  its  whole  extent. 
On  this  account,  the  earth  has  been  named  the  common  reset  voir.  A  body 
is  insulated,  by  being  placed  on  a  support  with  glass  feet,  or  on  a  resinous 
cake,  or  by  being  suspended  by  silk  threads.  No  bodies,  howqver,  insulate 
perfectly  ;  all  electrified  bodies  lose  their  electricity  more  or  less  rapidly 
by  means  of  the  supports  on  which  they  rest.  Glass  is  always  somewhat 
hygroscopic,  and  the  aqueous  vapour  which  condenses  on  it  affords  a 
passage  for  the  electrictity  ;  the  insulating  power  of  glass  is  materially  im- 
proved by  coating  it  with  shellac  or  copal  varnish.  Dry  air  is  a  good  insu- 
lator ;  but  when  the  air  contains  moisture  it  conducts  electricity,  and  this  is 
the  principal  source  of  the  loss  of  electricity.  Hence  it  is  necessary,  in 
electrical  experiments,  to  rub  the  supports  with  cloths  dried  at  the  fire,  and 
to  surround  electrified  bodies  by  glass  vessels,  containing  substances  which 
absorb  moisture,  such  as  chloride  of  calcium,  or  pumice  soaked  with  sulphuric 
acid. 

From  their  great  conductivity  metals  do  not  seem  to  become  electrified 
by  friction.     But  if  they  are  insulated,  and  then  rubbed,  they  give  good  indi- 
cations.    This  may  be  seen  by  the  fol- 
lowing experiment  (fig.    591).      A   brass  eT~  LM» —- ^— » 

tube  is  provided  with  a  glass  handle  by 
which  it  is  held,  and  then  rubbed  with  Flg-  59I> 

silk  or  flannel.  On  approaching  the  metal  to  an  electrical  pendulum  (fig. 
589).  the  pith  ball  will  be  attracted.  If  the  metal  is  held  in  the  hand  electri- 
city is  indeed  produced  by  friction — but  it  immediately  passes  through  the 
body  into  the  ground. 

If,  too,  the  cap  of  a  gold-leaf  electroscope  be  briskly  flapped  with  a  dry 
silk  handkerchief,  the  gold  leaves  will  diverge. 

727.  Distinction  of  tne  two  kinds  of  electricity. — If  electricity  be 
developed  on  a  glass  rod  by  friction  with  silk,  and  the  rod  be  brought  near 
an  electrical  pendulum,  the  ball  will  be  attracted  to  the  glass,  and  after 
momentary  contact  will  be  again  repelled.  By  this  contact  the  ball  becomes 
electrified,  and  so  long  as  the  two  bodies  retain  their  electricity,  repulsion 
follows  whenever  they  are  brought  near  each  other.  If  a  stick  of  sealing-wax 
electrified  by  friction  with  flannel  or  silk  be  approached  to  another  electrical 
pendulum,  the  same  effects  will  be  produced — the  ball  will  fly  towards  the 
wax,  and  after  contact  will  be  repelled.  Two  bodies,  which  have  been 
charged  with  electricity,  repel  one  another.  But  the  electricities  respectively 
developed  in  the  preceding  cases,  are  not  the  same.  If,  after  the  pith  ball 
had  been  touched  with  an  electrified  glass  rod,  an  electrified  stick  of  sealing- 
wax,  and  then  an  electrified  glass  rod,  be  alternately  approached  to  it,  the 
pith  ball  will  be  attracted  by  the  former  and  repelled  by  the  latter.  Simi- 
larly, if  the  pendulum  be  charged  by  contact  with  the  electrified  sealing- 
wax,  it  will  be  repelled  when  this  is  approached  to  it,  but  attracted  by  the 
approach  of  the  excited  glass  rod. 

On  experiments  of  this  nature,  Dufay  first  made  the  observation  that 
there  are  two  different  electricities  :  the  one  developed  by  the  friction  of 
glass,  the  other  by  the  friction  of  resin  or  shellac.  To  the  first  the  name 
I'itreons  electricity  is  given ;  to  the  second  the  name  resinous  electricity. 


632  Frictional  Electricity.  [728- 

728.  Theories  of  electricity. — Two  theories  have   been  proposed   to 
account  for  the  different  effects  of  electricity.     Franklin  supposed  that  there 
exists  a  peculiar,  subtle,  imponderable  fluid,  which  acts  by  repulsion  on  its 
own  particles,  and  pervades  all  matter.     This  fluid  is  present  in  every  sub- 
stance in  a  quantity  peculiar  to  it,  and  when  it  contains  this  quantity  it  is  in 
the  natural  state,  or  in  a  state  of  equilibrium.     By  friction  certain  bodies 
acquire  an  additional  quantity  of  the  fluid,  and  are   said  to  be  positively 
electrified ;  others  by  friction  lose  a  portion,  and  are  said  to  be  negatively 
electrified.     The  former  state  corresponds  to  vitreous  electricity,  and  the 
latter  to   resinous  electricity.     Positive  electricity   is   represented   by   the 
sign   +  ,  and  negative  electricity  by  the  sign  —  ;   a  designation  based  on 
the  algebraical  principle,  that  when  a  plus  quantity  is  added  to  an  equal 
minus  quantity  zero  is  produced.     So  when  a  body  containing  a  quantity  of 
positive  electricity  is  touched  with  a  body  possessing  an  equivalent  quantity 
of  negative  electricity,  a  neutral  or  zero  state  is  produced. 

The  theory  of  Symmer  assumes  that  every  substance  contains  an  indefinite 
quantity  of  a  subtle,  imponderable  matter,  which  is  called  the  electric  fluid. 
This  fluid  is  formed  by  the  union  of  two  fluids — \hepositive  and  the  negative. 
When  they  are  combined  they  neutralise  one  another,  and  the  body  is  then 
in  the  natural  or  neutral  state.  By  friction,  and  by  several  other  means, 
the  two  fluids  may  be  separated,  but  one  of  them  can  never  be  excited 
without  a  simultaneous  production  of  the  other.  There  may,  however,  be  a 
greater  or  less  excess  of  the  one  or  the  other  in  any  body,  and  it  is  then  said 
to  be  electrified  positively  or  negatively.  As  in  Franklin's  theory,  vitreous 
corresponds  to  positive  and  resinous  to  negative  electricity.  This  distinction 
is  merely  conventional  :  it  is  adopted  for  the  sake  of  convenience,  and  there 
is  no  other  reason  why  resinous  electricity  should  not  be  called  positive 
electricity. 

Fluids  of  the  same  name  repel  one  another,  and  fluids  of  opposite  kinds 
attract  each  other.  The  fluids  can  circulate  freely  on  the  surface  of  certain 
bodies,  which  are  called  conductors,  but  remain  confined  to  certain  parts  of 
others,  which  are  called  nonconductors. 

It  must  be  added  that  this  theory  is  quite  hypothetical ;  but  its  general 
adoption  is  justified  by  the  convenient  explanation  which  it  gives  of  electrical 
phenomena. 

729.  Action  of  electrified  bodies  on  each  other. — Admitting  the  two- 
fluid  hypothesis,  the  phenomena  of  attraction  and  repulsion  may  be  enunciated 
in  the  following  law  : — 

Two  bodies  charged  with  the  same  electricity  repel  each  other;  two  bodies 
charged  with  opposite  electricities  attract  each  other. 

These  attractions  and  repulsions  take  place  in  virtue  of  the  action  which 
the  two  electricities  exert  on  themselves,  and  not  in  virtue  of  their  action  on 
the  particles  of  matter. 

730.  I,aw  of  the  development  of  electricity  by  friction. — Whenever 
two  bodies  are  rubbed  together,  the  neutral  electricity  is  decomposed.     Two 
electricities  are  developed  at  the  same  time  and  in  equal  quantities — one 
body  takes  positive  and  the  other  negative  electricity.     This  may  be  proved 
by  the  following  experiment  devised  by  Faraday  : — A  small  flannel  cap 
provided  with  a  silk  thread  (fig.  592)  is  fitted  on  the  end  of  a  stout  rod  of 


-731]    Development  of  Electricity  by  Pressure  and  Cleavage.    633 

shellac,  and  rubbed  round  a  few  times.  When  the  cap  is  removed  by  means 
of  a  silk  thread,  and  presented  to  a  pith-ball  pendulum  charged  with  positive 
electricity,  the  latter  will  be  repelled,  proving  that  the 
flannel  is  charged  with  positive  electricity  ;  while  if  the 
shellac  is  presented  to  the  pith  ball,  it  will  be  attracted, 
showing  that  the  shellac  is  charged  with  negative 
electricity.  Both  electricities  are  present  in  equal 
quantities  ;  for  if  the  rod  be  presented  to  the  electro- 
scope before  removing  the  cap,  no  action  is  observed. 
The  electricity  developed  on  a  body  by  friction 
depends  on  the  rubber  as  well  as  the  body  rubbed. 
Thus  glass  becomes  negatively  electrified  when  rubbed 
with  cat;s  skin,  but  positively  when  rubbed  with  silk. 
In  the  following  list  the  substances  are  arranged  in  such  an  order  that  each 
becomes  positively  electrified  when  rubbed  with  any  of  the  bodies  following, 
but  negatively  when  rubbed  with  any  of  those  which  precede  it  :  — 


Fig  5Q2> 


1.  Cat's  skin.  5.  Glass. 

2.  Flannel.  6.  Cotton. 

3.  Ivory.  7.  Silk. 

4.  Rock  crystal.  8.  The  hand. 


9.  Wood.  13.  Resin. 

10.  Metals.  14.  Sulphur. 

11.  Caoutchouc.  15.  Gutta-percha. 

12.  Sealing-wax.  16.  Gun-cotton. 


The  nature  of  the  electricity  set  free  by  friction  depends  also  on  the 
degree  of  polish,  the  direction  of  the  friction,  and  the  temperature.  If  two 
glass  discs  of  different  degrees  of  polish  are  rubbed  against  each  other,  that 
which  is  most  polished  is  positively,  and  that  which  is  least  polished  is 
negatively  electrified.  If  two  silk  ribbons  of  the  same  kind  are  rubbed  across 
each  other,  that  which  is  transversely  rubbed  is  negatively  and  the  other 
positively  electrified.  If  two  bodies  of  the  same  substance,  of  the  same 
polish,  but  of  different  temperatures,  are  rubbed  together,  that  which  is  most 
heated  is  negatively  electrified.  Generally  speaking,  the  particles  which  are 
most  readily  displaced  are  negatively  electrified. 

Poggendorff  has  observed  that  many  substances  which  have  hitherto  been 
regarded  as  highly  negative,  such  as  gun-paper,  gun-cotton,  and  ebonite,  yield 
positive  electricity  when  rubbed  with  leather  coated  with  amalgam. 

731.  Development  of  electricity  by  pressure  and  cleavage.  — 
Electrical  excitement  may  be  produced  by  other  causes  than  friction.  If  a 
disc  of  wood,  covered  with  oiled  silk,  and  a  metal  disc,  each  provided  with 
an  insulating  handle,  be  pressed  together,  and  then  suddenly  separated,  the 
metal  disc  is  negatively  electrified.  A  crystal  of  Iceland  spar  pressed  be- 
tween the  fingers  becomes  positively  electrified,  and  retains  this  state  for 
some  time.  The  same  property  is  observed  in  several  other  minerals,  even 
though  conductors,  provided  they  be  insulated.  If  cork  and  caoutchouc  be 
pressed  together,  the  first  becomes  positively  and  the  other  negatively 
electrified.  A  disc  of  wood  pressed  on  an  orange  and  separated  carries 
away  a  good  charge  of  electricity  if  the  contact  be  rapidly  interrupted. 
But  if  the  disc  is  slowly  removed  the  quantity  is  smaller,  for  the  two  fluids 
recombine  at  the  moment  of  their  separation.  For  this  reason  there  is  no 
apparent  effect  when  the  two  bodies  pressed  together  are  good  conductors. 

Cleavage  also  is  a  source  of  electricity.     If  a  plate  of  mica  be  rapidly 

EE3 


634  Frictional  Electricity.  [731- 

split  in  the  dark,  a  slight  phosphorescent  light  is  perceived.  Becquerel 
fixed  glass  handles  to  each  side  of  a  plate  of  mica,  and  then  rapidly  sepa- 
rated them.  On  presenting  each  of  the  plates  thus  separated  to  an  electro- 
scope, he  found  that  one  was  negatively  and  the  other  positively  electrified 
If  a  stick  of  sealing-wax  be  broken,  the  ends  exhibit  different  electricities. 

All  badly  conducting  crystalline  substances  exhibit  electrical  indications 
by  cleavage.  The  separated  plates  are  always  in  opposite  electrical  condi- 
tions, provided  they  are  not  good  conductors  :  for  if  they  were,  the  separa- 
tion would  not  be  sufficiently  rapid  to  prevent  the  recombination  of  the  two 
electricities.  To  the  phenomena  here  described  is  due  the  luminous  appear- 
ance seen  in  the  dark  when  sugar  is  broken. 

732.  Pyroelectricity. — Certain  minerals,  when  warmed,  acquire  electri- 
cal properties  ;  a  phenomenon  to  which  the  name  pyroelectricity  is  given. 
It  is  best  studied  in  tourmaline,  in  which  it  was  first  discovered  from  the 
fact  that  this  mineral  has  the  power  of  first  attracting  and  then  repelling  hot 
ashes  when  placed  among  them. 

To  observe  this  phenomenon,  a  crystal  of  tourmaline  is  suspended  hori- 
zontally by  a  silk  thread,  in  a  glass  cylinder  placed  on  a  heated  metal  plate. 
On  subsequently  investigating  the  electric  condition  of  the  ends  by  approach- 
ing to  them  successively  an  electrified  glass  rod,  one  end  will  be  found  to  be 
positively  electrified,  and  the  other  end  negatively  electrified,  and  each  end 
shows  this  polarity  as  long  as  the  temperature  rises.  The  arrangement  of 
the  electricity  is  thus  like  that  of  the  magnetism  in  a  magnet.  The  points 
at  which  the  intensity  of  free  electricity  is  greatest  are"  called  the  poles,  and 
the  line  connecting  them  is  the  electric  axis.  When  a  tourmaline,  while 
thus  electrified,  is  broken  in  the  middle,  each  of  the  pieces  has  its  two 
poles. 

These  polar  properties  depend  on  the  change  of  temperature.  When  a 
tourmaline,  which  has  become  electrical  by  being  warmed,  is  allowed  to  cool 
regularly,  it  first  loses  electricity,  and  then  its  polarity  becomes  reversed  ; 
that  is,  the  end  which  was  positive  now  becomes  negative,  and  that  which 
Avas  negative  becomes  positive,  and  the  position  of  the  poles  now  remains 
unchanged  so  long  as  the  temperature  sinks.  Tourmaline  only  becomes 
pyroelectric  within  certain  limits  of  temperature  ;  these  vary  somewhat  with 
the  length,  but  are  usually  between  10°  and  150°  C.  Below  and  above  these 
temperatures  it  behaves  like  any  other  body,  and  shows  no  polarity. 

The  name  analogous  pole  is  given  to  that  end  of  the  crystal  which  shows 
positive  electricity  when  the  temperature  is  rising,  and  negative  electricity 
when  it  is  sinking  ;  antilogous  pole  to  that  end  which  becomes  negative  by 
being  heated,  and  positive  by  being  cooled. 

The  phenomena  of  pyroelectricity  are  intimately  connected  with  the 
crystalline  form  of  the  mineral  ;  and  are  only  seen  in  those  crystals  whose 
forms  are  hemihedral,  or  which  are  differently  modified  at  the  ends  of  their 
crystallographical  principal  axis. 

Besides  tourmaline  the  following  minerals  are  found  to  be  pyroelectric  : 
boracite,  topaz,  prehnite,  silicate  of  zinc,  scolezite,  axenite.  And  the  follow- 
ing organic  bodies  are  pyroelectric  :  cane-sugar,  Pasteur's  salt  (racemate  of 
sodium  and  ammonium),  tartrate  of  potassium,  &c. 


-734]        Laws  of  Electrical  Attractions  and  Repulsions.          635 


CHAPTER  II. 

QUANTITATIVE  LAWS  OF  ELECTRICAL  ACTION. 

733.  Electrical  quantity.— In  the  experiment  with  the  flannel  cap  ab, 
described  above  (730),  each  time  the  experiment  is  made,  equal  quantities  of 
neutral  fluid  are  decomposed  into  positive  electricity,  which  remains  on  the 
flannel,  and  negative  electricity,  which  remains  on  the  sealing-wax.     The 
flannel,  with  its  charge  of  electricity,  may  be  detached,  and  if  we  work  under 
precisely   uniform   conditions,  equal  quantities  of  electricity  can  thus  be 
separated. 

If  \ve  fill  water  from  a  constant  source  into  a  cask  by  means  of  a  measure, 
the  quantity  added  would  be  directly  proportional  to  the  number  of  such 
measures.  Now,  although  in  the  above  experiment  the  quantities  of  elec- 
tricity produced  each  time  are  equal,  yet  when  the  flannel  cap  is  applied 
each  time  to  an  insulated  conductor  it  does  not  necessarily  follow  that  the 
quantity  of  electricity  imparted  each  time 
is  directly  proportional  to  the  number  of 
such  applications. 

734,  Saws  of  electrical  attractions 
and  repulsions. — The  laws  which  regu- 
late   the    attractions   and    repulsions    of 
electrified  bodies  may  be  thus  stated  : — 

I.  The  repulsions  or  attractions  be~ 
f-i'een   two  electrified  bodies  are  in   the 
inverse  ratio  of  the  squares  of  their  dis- 
tance. 

I 1.  The  distance  remaining  the  same, 
the  force  of  attraction  or  repulsion  between 
t'i'o  electrified  bodies  is  directly  as  the  pro- 
duct of  the  quantities  of  electricity  U'ith 
ichich  they  are  charged. 

These  laws  were  established  by  Cou- 
lomb, by  means  of  the  torsion  balance, 
used  in  determining  the  laws  of  magnetic 
attractions  and  repulsions  (704),  modified 
in  accordance  with  the  requirements  of  the 
case.  The  wire,  on  the  torsion  of  which  Fig.  593. 

the  method  depends,  is  so  fine  that  a  foot 

weighs  only  ^  of  a  grain.  At  its  lower  extremity  there  is  a  fine  shellac  rod, 
nP  (fig-  593)>  at  one  end  of  which  is  a  small  disc  of  copper  foil,  n.  Instead  of 
the  vertical  magnetic  needle,  there  is  a  glass  rod,  *,  terminated  by  a  gilt 


.636  Frictional  Electricity.  [734- 

pith  ball,  ;;z,  which  passes  through  the  aperture  r.  The  scale  oc  is  fixed 
round  the  sides  of  the  vessel,  and  during  the  experiment  the  ball  m  is 
opposite  the  zero  point  o.  The  micrometer  consists  of  a  small  graduated 
disc,  £•,  moveable  independently  of  the  tube,  d,  and  of  a  fixed  index,  «,  which 
shows  by  how  many  degrees  the  disc  is  turned.  In  the  centre  of  the  disc 
there  is  a  small  button  /,  to  which  is  fixed  the  wire  which  supports  np. 

i.  The  micrometer  is  turned  until  the  zero  point  is  opposite  the  index, 
and  the  tube  d  is  turned  until  the  knob  n  is  opposite  zero  of  the  graduated 
circle  :  the  knob  m  is  in  the  same  position,  and  thus  presses  against  n.  The 
knob  m  is  then  removed  and  electrified,  and  replaced  in  the  apparatus, 
through  the  aperture  r.  As  soon  as  the  electrified  knob  m  touches  ;z,  the 
latter  becomes  electrified,  and  is  repelled,  and  after  a  few  oscillations  re- 
mains constant  at  a  distance  at  which  the  force  of  repulsion  is  equal  to  the 
force  of  torsion.  In  a  special  experiment  Coulomb  found  the  angle  of  tor- 
sion between  the  two  to  be  36°  ;  and  as  the  force  of  torsion  is  proportional 
to  the  angle  of  torsion,  this  angle  represents  the  repulsive  force  between  m 
and  n.  In  order  to  reduce  the  angle  to  1 8°  it  was  necessary  to  turn  the  disc 
through  126°.  The  wire  was  twisted  126°  in  the  direction  of  the  arrow  at 
its  upper  extremity,  and  18°  in  the  opposite  direction  at  its  lower  extremity, 
and  hence  there  was  a  total  torsion  of  144°.  On  turning  the  micrometer  in 
the  same  direction,  until  the  angle  of  deviation  was  8^°,  567°  of  torsion  was 
necessary.  Hence  the  whole  torsion  was  575^.  Without  sensible  error 
these  angles  of  deviation  may  be  taken  at  36°,  18°,  and  9°,  and  on  comparing 
them  with  the  corresponding  angles  of  torsion  36°,  144°,  and  576°,  we  see 
that  while  the  first  are  as 

i :  i  :  i 
the  latter  are  as 

i  :4  :  16; 

that  is,  that  for  a  distance  %  as  great  the  angle  of  torsion  is  4  times  as 
great,  and  that  for  a  distance  \  as  great  the  repulsive  force  is  16  times  as  great. 

In  experimenting  with  this  apparatus,  the  air  must  be  thoroughly  dry,  in 
order  to  diminish,  as  far  as  possible,  loss  of  electricity.  This  is-  effected  by 
placing  in  it  a  small  dish  containing  chloride  of  calcium. 

The  experiments  by  which  the  law  of  attraction  is  proved  are  made  in 
much  the  same  manner,  but  the  two  balls  are  charged  with  opposite  electri- 
cities. A  certain  quantity  of  electricity  is  imparted  to  the  moveable  ball,  by 
means  of  an  insulated  pin,  and  the  micrometer  moved  until  there  is  a  certain 
angle  below.  A  charge  of  electricity  of  the  opposite  kind  is  then  imparted 
to  the  fixed  ball.  The  two  balls  tend  to  move  towards  each  other,  but  are  pre- 
vented by  the  torsion  of  the  wire,  and  the  moveable  ball  remains  at  a  distance 
at  which  there  is  equilibrium  between  the  force  of  attraction,  which  draws  the 
balls  together,  and  that  of  torsion,  which  tends  to  separate  them.  The  mi- 
crometer screw  is  then  turned  to  a  greater  extent,  by  which  more  torsion 
and  a  greater  angle  between  the  two  balls  are  produced.  And  it  is  from  the 
relation  which  exists  between  the  angle  of  deflection  on  the  one  hand,  and 
the  angle  which  expresses  the  force  of  torsion  on  the  other,  that  the  law  of 
attraction  has  been  deduced. 

ii.  To  prove  this  second  law  let  a  charge  be  imparted  to  m  •  n  being  in 
contact  with  it  becomes  charged  and  is  repelled  to  a  certain  distance.  The 


-735] 


Distribution  of  Electricity. 


637 


angle  of  deflection  being  noted,  let  the  ball  m  be  touched  by  an  insulated 
but  unelectrified  ball  of  exactly  the  same  size  and  kind  ;  in  this  way  half  its 
charge  is  removed,  and  the  angle  of  deflection  will  now  be  found  to  be  only 
half  its  original  amount.  In  like  manner  if  either  ;;/  or  the  moveable  body 
be  now  again  deprived  of  half  its  electricity,  the  deflection  will  be  a  quarter 
of  what  it  originally  was,  and  so  on. 

The  two  laws  are  included  in  the  formula  F  =  ~  ,  where  F  is  the  force, 

e  and  e  the  quantities  of  electricity  on  any  two  surfaces,  and  d  the  distance 
between  them.  If  e  and  e'  are  of  opposite  electricities  the  action  is  one  of 
attraction,  while  if  they  are  the  same  it  is  a  repulsive  action. 

On  the  centimetre-gramme-second  system  the  unit  quantity  of  electricity 
is  that  amount  which,  acting,  at  a  distance  of  one  centimetre  across  air,  on 
a  quantity  of  electricity  equal  to  itself,  would  repel  it  with  a  force  equal  to 
one  dyne  (709). 

735.  Distribution  of  electricity. — When  an  insulated  sphere  of  con- 
ducting material  is  charged  with  electricity,  the  electricity  passes  to  the 
surface  of  the  sphere,  and  forms  an  extremely  thin  layer.  If,  in  Coulomb's 
balance,  the  fixed  ball  be  replaced  by  another  electrified  sphere,  a  certain 
repulsion  will  be  observed.  If  then  this  sphere  be  touched  with  an  insulated 
sphere  identical  with  the  first,  but  in  the  neutral  state,  the  first  ball  will  be 
found  to  have  lost  half  its  electricity,  and  only  half  the  repulsion  will  be 
observed.  By  repeating  this  experiment  with  spheres  of  various  substances 
solid  and  hollow,  but  all  having  the  same  superficies,  the  result  will  be 
the  same,  excepting  that,  with  imperfectly  conducting  materials,  the  time 
required  for  the  distribution  will  be  greater.  From  this  it  is  concluded  that 
the  distribution  of  electricity  depends  on  the  extent  of  the  surface,  and  not 
on  the  mass,  and,  therefore,  that  electricity  does  not  penetrate  into  the 
interior,  but  is  confined  to  the  surface.  This 
conclusion  is  further  established  by  the  following- 
experiments  : — 

i.  A  thin  hollow  copper  sphere  provided 
with  an  aperture  of  about  an  inch  in  diameter 
(fig.  594),  and  placed  on  an  insulating  support, 
is  charged  in  the  interior  with  electricity.  When 
the  carrier  or  proof  plane  (a  small  disc  of  copper 
foil  at  the  end  of  a  slender  glass  or  shellac  rod) 
is  applied  to  the  interior,  and  is  then  brought 
near  an  electroscope,  no  electrical  indications 
are  produced.  But  if  the  proof  plane  is  applied 
to  the  electroscope  after  having  been  in  contact 
with  the  exterior,  a  considerable  divergence 
ensues. 

The  action  of  the  proof  plane  as  a  measure  of 
the  quantity  of  electricity  is  as  follows  : — When 
it  touches  any  surface  the  proof  plane  becomes 
confounded  with  the  element  touched  ;  it  takes 
in  some  sense  its  place  relatively  to  the  electricity,  or  rather,  it  becomes 
itself  the  element  on  which  the  electricity  is  diffused.  Thus  when  the  proof 


Fig-  594- 


638 


Frictional  Electricity. 


[735- 


plane  is  removed  from  contact  we  have  In  effect  cut  away  from  the  surface, 
an  element  of  the  same  thickness  and  the  same  extent  as  its  own,  and  have 


any  of  the  electricity  which 


595- 

transferred  it  to  the  balance  without  its  losim 

covered  it. 

ii.  A  hollow  globe,  fixed  on  an  insulating  support,  is  provided  with  two 

hemispherical  enve- 
lopes \vhich  fit  closely, 
and  can  be  separated 
by  glass  handles.  The 
interior  is  now  elec- 
trified, and  the  two 
hemispheres  brought 
in  contact.  On  then 
rapidly  removing  them 
(fig-  595)>  the  cover* 
ings  will  be  found  to 
be  electrified,  while  the 
sphere  is  in  its  natural 
condition. 

iii.  The  distribu- 
tion of  electricity  on 
the  surface  may  also 
be  shown  by  means  of 
the  following  appara- 
tus : — It  consists  of  a 
metallic  cylinder  on 
insulated  supports,  on 
which  is  fixed  a  long1 

5g6<  strip  of  tin  foil  which 

can  be  rolled   up   by 

means  of  a  small  insulating  handle  (fig.  596).      A  quadrant  electrometer 

is  fitted  in  metallic  communication  with  the  cylinder.     When  the  sphere 


-736] 


Electric  Density. 


639 


is  rolled  up,  a  charge  is  imparted  to  the  cylinder,  by  which  a  certain 
divergence  is  produced.  On  unrolling  the  tinfoil,  this  divergence  gradually 
diminishes,  and  increases  as  it  is  again  rolled  up.  The  quantity  of  electri- 
city remaining  the  same,  the  electrical  force,  on  each  unit  of  surface,  is 
therefore  less  as  the  surface  is  greater. 

iv.  The  following  ingenious  experiment  by  Faraday  further  illustrates 
this  law  : — A  metal  ring  is  fitted  on  an  insulated  support,  and  a  conical 
gauze  bag,  such  as  is  used  for  catching  butterflies,  is  fitted  to  it  (fig.  597). 

By  means  of  a  silk  thread,  the  bag  can  be 
drawn  inside  out.  After  electrifying  the  bag, 
it  is  seen  by  means  of  a  proof  plane  that  the 
electricity  is  on  the  exterior;  but  if  the  positions 
are  reversed  by  drawing  the  bag  inside  out, 
so  that  the  interior  has  now  become  the  ex- 
terior, the  electricity  will  still  be  found  on  the 
exterior. 

v.  The  same  point  maybe  further  illustrated 
by  an  experiment  due  to  Terquem.  A  bird-cage, 
preferably  of  metal  wire,  is  suspended  by  insu- 
lators, and  contains  either  a  gold-leaf  electro- 
scope or  pieces  of  Dutch  metal,  feathers,  pith 
balls,  &c.  When  the  cage  is  connected  with 
an  electrical  machine,  the  articles  in  the  interior 
are  quite  unaffected,  although  strong  sparks 
may  be  taken  from  the  outside.  Bands  of  paper 


Fig.  597- 


may  be  fixed  to  the  inside  ;  while  those  fixed  to  the  outside  diverge  widely. 
A  bird  in  the  inside  is  quite  unaffected  by  the  charge  or  discharge  of  the 
electricity  of  the  cage. 

The  property  of  electricity,  of  accumulating  on  the  outside  of  bodies, 
is  ascribed  to  the  repulsion  which  the  particles  exert  on  each  other.  Electri- 
citv  tends  constantly  to  pass  to  the  surface  of  bodies,  whence  it  continually 
tends  to  escape,  but  is  prevented  by  the  resistance  of  the  feebly  conducting 
atmosphere. 

To  the  statement  that  electricity  resides  on  the  surface  of  bodies,  two  ex- 
ceptions may  be  noted.  When  two  opposite  electricities  are  discharged 
through  a  wire — a  phenomenon  which,  when  continuous,  forms  an  electrical 
current — the  discharge  is  effected  throughout  the  whole  mass  of  the  conductor. 
Also  a  body  placed  inside  another  may,  if  insulated  from  it,  receive  charges 
of  electricity.  On  this  depends  the  possibility  of  electrical  experiments  in 
ordinary  rooms. 

736.  Electric  density. — On  a  metallic  sphere  the  distribution  of  the 
electricity  will  be  uniform  in  ever}"  part,  simply  from  its  symmetry.  This 
can  be  demonstrated  by  means  of  the  proof  plane  and  the  torsion  balance. 
A  metallic  sphere  placed  on  an  insulating  support  is  electrified,  and 
touched  at  different  parts  of  its  surface  with  the  proof  plane,  which  each 
time  is  applied  to  the  moveable  needle  of  the  torsion  balance.  As  in  all 
cases  the  torsion  observed  is  sensibly  the  same,  it  is  concluded  that  the 
proof  plane  each  time  receives  the  same  quantity  of  electricity.  In  the 
case  of  an  elongated  ellipsoid  (fig.  598)  it  is  found  that  the  distribution 
of  electricity  is  different  at  different  points  of  the  surface.  The  electricity 


640 


Frictional  Electricity. 


[736- 


accumulates  at  the  most  acute  points.     This   is  demonstrated  by  succes- 
sively touching  the  ellipsoid  at  different  parts  with  the  proof  plane,  and 

then  bringing  this 
into  the  torsion 
balance.  By  this 
means  Coulomb 
found  that  the 
greatest  deflection 
was  produced  when 
the  proof  plane  had 
been  in  contact 
with  the  point  a, 
and  the  least  by 
contact  with  the 
middle  space  e. 

The  electric  den- 
.  sity  or  electric 
thickness  is  the 
term  used  to  ex- 
press the  quantity  of  electricity  found  at  any  moment  on  a  given  surface. 
If  S  represents  the  surface  and  Q  the  quantity  of  electricity  on  that  surface, 
then,  assuming  that  the  electricity  is  equally  distributed,  its  electrical  density 

is  equal  to  2|. 

Coulomb  found,  by  quantitative  experiments,  that  in  an  ellipsoid  the 
density  of  the  electricity,  at  the  equator  of  the  ellipsoid,  is  to  that  at  the  ends 
in  the  same  ratio  as  the  length  of  the  minor  to  the  major  axis.  On  an  insu- 
lated cylinder,  terminated  by  two  hemispheres,  the  density  of  the  electrical 
layer  at  the  ends  is  greater  than  in  the  middle.  In  one  case,  the  ratio  of 
the  two  densities  was  found  to  be  as  2-3  :  i.  On  a  circular  disc  the  density 
is  greatest  at  the  edges. 

737.  Force  outside  an  electrified  body. — The  force  F  which  a  sphere, 
charged  with  a  quantity  of  electricity  Q,  exerts  on  a  point  at  a  distance  d 

from  its  centre,  is  ~  ;  this  is  equal  to  £-  if  S  is  the  area  of  the  sphere,  and 
d~  d 

p  the  density  of  electricity  on  the  unit  of  surface.     Now  the  area  of  the 
sphere  is  4?rR2,  and  if  the  distance  d  is  equal  to  the  radius  R  then  the  force 

at  the  surface  is  ^^>-2—  —  47rP- 

This  holds  also  if  the  point  considered  is  at  a  very  small  distance  just 
outside  the  sphere.  Let  a  small  segment  ab  be  cut  in  a  sphere  (fig.  599). 
Then  its  action  on  a  point  p  just  inside  the  sphere  will  be  exactly  neutralised 
by  the  action  of  the  rest  of  the  sphere  acb  on  this  point,  since  there  is  no 
electrical  force  inside  a  sphere  (735)  ;  that  is,  the  action  of  the  two  portions 
is  equal,  but  in  opposite  directions.  Now  for  a  point  p ,  just  outside  the 
sphere,  the  actions  will  also  be  equal,  but  in  the  same  directions.  But  the 
total  action  of  the  whole  sphere  is  4rrp  ;  hence  the  action  of  each  portion  is 
half  of  this  ;  that  is,  2?rp. 


-738]  Potential.  641 

It  may  be  shown  in  like  manner  that  the  whole  force  of  any  closed 
conductor  is  4717). 

On  an  insulated  conductor,  where  the  electricity  is  in  equilibrium,  a 
particle  of  electricity  will  have  no  tendency  to  move  along  the  surface,  for 
otherwise  there  would  be  no  equilibrium.  But  the 
electricity  does  exert  a  pressure  on  the  external  non- 
conducting medium,  which  is  always  directed  outwards, 
and  is  called  the  electrical  tension  or  pressure. 

The  amount  of  this  pressure  is  27rp2  for  the  unit 
area,  p  being  the  electrical  density  at  the  point  con- 
sidered. The  effect  of  this,  for  instance,  on  a  soap- 
bubble,  if  electrified  with  either  kind  of  electricity, 
would  be  to  enlarge  it.  In  any  case  the  electrification 
would  constitute  a  deduction  from  the  amount  of  atmo-  Fig.  599- 

spheric  pressure  which  the  body  experiences  when  unelectrified. 

The  term  electric  density  and  electrical  tension  are  often  confounded. 
The  latter  ought  rather  to  be  restricted,  as  Maxwell  proposed,  to  express  the 
state  of  strain  or  pressure  exerted  upon  a  dielectric  in  the  neighbourhood  of 
an  electrified  body  ;  a  strain  which,  if  continually  increased,  tends  to  disrup- 
tive discharge.  Electric  tension  may  thus  be  compared  to  the  strain  on  a 
rope  which  supports  a  weight  ;  and  the  dielectric  medium  which  can  support 
a  certain  tension  and  no  more  is  said  to  have  a  certain  strength,  in  the  same 
sense  as  a  rope  which  bears  a  certain  weight  without  breaking  is  said  to 
have  a  certain  strength. 

738.  Potential — In  the  experiment  (fig.  598),  instead  of  applying  the 
test  sphere  directly  to  the  large  sphere,  let  the  two  be  placed  at  a  consider- 
able distance  from  each  other,  and  let  them  be  connected  by  a  long  thin  wire, 
and  then,  detaching  the  small  sphere,  let  the  quantity  upon  it  be  measured 
by  the  torsion  balance  ;  the  angle  of  deflection  will  show  that  this  quantity  is 
the  same  whatever  part  of  the  large  sphere  be  touched,  as  must  indeed  be 
the  case,  owing  to  symmetry' ;  but  the  amount  of  this  charge  will  be  mate- 
rially different  from  that  in  which  the  small  sphere  is  placed  in  direct  contact 
with  the  larger  one.  Hence  the  quantity  of  electricity  removed  differs  ac- 
cording to  the  mode  in  which  connection  is  made. 

If  now  this  experiment  be  repeated  with  the  ellipsoid,  it  will  be  found 
that  whatever  point  of  this  is  put  in  distant  connection  with  the  proof  sphere 
by  the  long  wire,  the  charge  which  the  small  sphere  acquires  is  everywhere 
the  same  ;  although,  as  we  have  seen,  the  proof  sphere  would  remove  very 
different  quantities  of  electricity  according  to  the  part  where  it  touches. 

Here,  then,  we  are  dealing  with  experimental  facts  which  our  previous 
notions  are  insufficient  to  explain.  It  is  manifest  that  the  difference  in  the 
results  depends  neither  on  the  total  charge  nor  on  the  density.  We  require 
the  introduction  of  a  new  conception,  which  is  that  of  electrical  potential. 
Introduced  originally  into  electrical  science  by  Green,  out  of  considerations 
arising  from  the  mathematical  treatment  of  the  subject,  the  use  of  the  term 
potential  is  justified  and  recommended  by  the  clearness  with  which  it  brings 
out  the  relations  of  electricity  to  work. 

We  have  already  seen,  that  in  order  to  lift  a  certain  mass  against  the 
attraction  of  gravitation  (60-63)  there  must  be  a  definite  expenditure  of  work, 


642  Frictiondl  Electricity.  [738  - 

and  the  equivalent  of  this  work  is  met  with  in  the  energy  which  the  lifted 
mass  retains,  or  what  is  called  the  potential  energy  of  position. 

Let  us  now  suppose  that  we  have  a  large  insulated  metal  sphere  charged 
with  positive  electricity,  and  that,  at  a  distance  which  is  very  great  in  com- 
parison with  the  size  of  the  sphere,  there  is  a  small  insulated  sphere  charged 
with  the  same  kind  of  electricity.  If  now  we  move  the  small  sphere  to  any 
given  point  nearer  the  larger  one,  we  must  do  a  certain  amount  of  work  upon 
it  to  overcome  the  repulsion  of  the  two  electricities. 

The  work  required  to  be  done  against  electrical  forces,  in  order  to  move 
the  unit  of  positive  electricity  from  an  infinite  distance  to  a  given  point  in 
the  neighbourhood  of  an  electrified  conductor,  is  called  \}\Q  potential  at  this 
point.  If,  in  the  above  case,  the  larger  sphere  were  charged  with  negative 
electricity,  then  instead  of  its  being  needful  to  do  work  in  order  to  bring  a 
unit  of  positive  electricity  towards  it,  work  would  be  done  by  electrical  at- 
traction, and  the  potential  of  the  point  near  the  charged  sphere  would  thus 
be  negative. 

The  potential  at  any  point  may  also  be  said  to  be  the  work  done 
against  electrical  force,  in  moving  unit  charge  of  negative  electricity  from 
that  point. 

The  amount  of  work  required  to  move  the  unit  of  positive  electricity 
against  electrical  force,  from  any  one  position  to  any  other,  is  equal  to  the 
excess  of  the  electrical  potential  of  the  second  position  over  the  electrical 
potential  of  the  first.  This  is,  in  effect,  the  same  as  what  has  been  said 
above,  for  at  an  infinite  distance  the  potential  is  zero. 

We  cannot  speak  of  potential  in  the  abstract,  any  more  than  we  can 
speak  of  any  particular  height,  without  at  least  some  tacit  reference  to  a 
standard  of  level.  Thus,  if  we  say  that  such  and  such  a  place  is  300  feet 
high,  we  usually  imply  that  this  height  is  measured  in  reference  to  the  level 
of  the  sea.  So,  too,  we  refer  the  longitude  of  a  place  to  some  definite 
meridian,  such  as  that  of  Greenwich,  either  expressly  or  by  implication. 

In  like  manner  we  cannot  speak  of  the  potential  of  a  mass  of  electricity 
without,  at  least,  an  implied  reference  to  a  standard  of  potential.  This 
standard  is  usually  the  earth,  which  is  taken  as  being  zero  potential.  If  we 
speak  of  the  potential  at  a  given  point,  the  difference  between  the  potential 
at  this  point  and  the  earth  is  referred  to. 

If  in  the  imaginary  experiment  described  above,  we  move  the  small  sphere 
round  the  large  electrified  one  always  at  the  same  distance,  no  work  is  done 
by  or  against  it  for  the  purpose  of  overcoming  or  of  yielding  to  electrical 
attractions  or  repulsions,  just  as  if  we  move  a  body  at  a  certain  constant  level 
above  the  earth's  surface,  no  work  is  done  upon  it  as  respects  gravitation. 
An  imaginary  surface  drawn  in  the  neighbourhood  of  an  electrified  body, 
such  that  a  given  charge  of  electricity  can  be  moved  from  any  one  point  of 
it  to  any  other,  without  any  work  being  done  either  by  or  against  electrical 
force,  is  said  to  be  an  equipotential  surface.  Such  a  surface  may  be  de- 
scribed as  having  everywhere  the  same  electrical  level ;  and  the  notion  of 
bodies  at  different  electrical  levels,  in  reference  to  a  particular  standard,  is 
the  same  as  that  of  bodies  at  different  potentials. 

As  water  only  flows  from  places  at  a  higher  level  to  places  at  a  lower 
level,  so  also  electricity  only  passes  from  places  at  a  higher  to  places  at  a 


-739]  Electrical  Capacity.  643 

lower  potential.  If  an  electrified  body  is  placed  in  conducting  communica- 
tion with  the  earth,  electricity  will  flow  from  the  body  to  the  earth,  if  the 
body  is  at  a  higher  potential  than  the  earth  ;  and  from  the  earth  to  the  body, 
if  the  body  is  at  a  lower  potential.  If  the  potential  of  a  body  is  higher  than 
that  of  the  earth,  it  is  said  to  have  a  positive  potential  ;  and  if  at  a  lower 
potential,  a  negative  potential.  A  body  charged  with/ra  negative  electricity 
is  one  at  lower  potential  than  the  earth  ;  one  charged  with  free  positive 
electricity  is  at  a  higher  potential. 

739.  Electrical  capacity. — The  capacity  of  any  conductor  may  be 
measured  by  the  quantity  of  electricity  which  it  can  acquire  when  placed 
in  contact  with  a  body  which  charges  it  to  unit  electrical  potential. 

We  may  illustrate  the  relation  between  capacity  and  potential  by  refer- 
ence to  the  analogous  phenomenon  of  heat.  In  the  interchange  of  heat 
between  bodies  of  different  temperatures  the  final  result  is  that  heat  only 
passes  from  bodies  of  higher  to  bodies  of  lower  temperature.  So  also  elec- 
tricity only  passes  from  bodies  of  higher  to  bodies  of  lower  potential. 
Potential  is,  as  regards  electricity,  what  temperattire  is  as  regards  heat,  and 
might  indeed  be  called  electrical  temperature.  We  may  have  a  small 
quantity  of  heat  at  a  very  high  temperature.  Thus  a  short  thin  wire  heated 
to  incandescence  has  a  far  higher  heat  potential  or  temperature  than  a 
bucket  of  warm  water.  But  the  latter  will  have  a  far  larger  quantity.  A 
flash  of  lightning  represents  electricity  at  a  very  high  potential,  but  the 
quantity  is  small. 

The  relation  between  electrical  potential  and  density  may  be  further 
illustrated  by  reference  to  the  head  of  water  in  a  reservoir.  The  pressure 
is  proportional  to  the  depth  ;  the  potential  is  everywhere  the  same.  For 
suppose  we  want  to  introduce  an  additional  pound  of  water  into  the  reservoir, 
the  same  amount  of  work  is  required  whether  the  water  be  forced  in  at  the 
bottom  or  be  poured  in  at  the  top. 

If  a  hole  be  made  very  near  the  top  of  the  reservoir,  a  quantity  of  water 
in  falling  to  the  ground  would  generate  an  amount  of  heat  proportional  to 
the  fall.  If  the  same  quantity  escaped  through  a  hole  near  the  bottom,  it 
would  not  produce  so  much  heat  by  direct  fall ;  but  it  will  possess  a  certain 
velocity,  the  destruction  of  which  will  produce  a  quantity  of  heat,  which, 
added  to  that  produced  by  the  fall,  will  give  exactly  as  much  as  the  other. 

When  the  charge  or  quantity  of  electricity  imparted  to  a  body  increases, 
the  potential  increases  in  the  same  ratio  ;  so  that,  calling  Q  the  quantity  of 
electricity,  C  the  capacity,  and  V  the  potential,  we  have 

Q  =  CV. 

Now  for  a  sphere  whose  radius  is  R  the  potential  V  =  i  from  which  we 

R 

get  C  =  R  ;  that  is,  that  the  capacity  of  a  sphere  is  equal  to  its  radius. 

While  there  is  a  close  analogy  between  heat  and  electricity,  as  regards 
capacity,  there  are  important  differences  ;  thus  the  capacity  of  a  body  for  heat 
is  influenced  by  the  temperature  (457),  while  the  capacity  of  a  body  for 
electricity  does  not  depend  on  the  potential.  Again,  the  calorific  capacity 
depends  solely  on  the  mass  of  a  body,  and  in  bodies  of  the  same  material  and 
shape  is  proportional  to  the  cube  of  homologous  dimensions  ;  the  capacity 


644  Frictional  Electricity.  [739- 

for  electricity  is  directly  proportional  to  such  dimensions.  Calorific  capacity 
is  proportional  to  a  specific  coefficient,  which  varies  with  the  material,  but 
is  independent  of  its  shape,  while  electrical  capacity  varies  with  the  shape  of 
a  body,  but  not  with  its  material,  provided  the  electricity  can  move  freely 
upon  it. 

If  we  have  a  series  of  bodies  at  a  considerable  distance  from  each  other, 
whose  capacities  and  potentials  are  respectively  <:,  c\  c",  £c.,  and  v,  v',  v",  &c., 
then,  if  they  are  all  connected  by  fine  wires  of  no  capacity,  they  all  instantly 
acquire  the  same  potential  V,  which  is  determined  by  the  equation 

cv  +  c'v'  -f  c"v" 


c  +  c'  -t  c'f 

The  analogy  of  this  to  the  equalisation  of  temperature  which  takes  place 
when  bodies  at  different  temperatures  are  mixed  together  is  directly  apparent 
(449).  It  may  be  further  illustrated  by  supposing  a  series  of  tubes  of  different 
diameters,  and  connected  by  very  narrow  tubes,  but  in  which  are  stopcocks 
to  cut  off  communication.  If,  while  in  this  state,  water  be  poured  into  the 
tubes  to  different  heights,  it  will  be  manifest  that  they  will  hold  very  various 
quantities  of  water.  If,  however,  the  stopcocks  are  opened,  the  tubes  will 
still  contain  quantities  of  water  proportional  to  their  capacities,  but  the  level 
or  potential  in  all  will  be  the  same. 

740.  Measurement    of  capacity  and   potential. — We  may  use    Cou- 
lomb's balance  for  the  purpose  of  measuring  the  capacity  C,  or  the  potential 
V,  of  a  body  charged  with  electricity.     For  this  purpose  the  body  in  question 
is  placed,  by  means  of  a  long  fine  wire  of  no  capacity,  in  distant  contact  with 
a  small  neutral  insulated  sphere  of  known  radius  r.     This  small  sphere  is 
then  applied  to  the  torsion  balance,  and  its  charge  g  =  rv'\s  measured.    Now, 
since  the  original  charge  on  the  sphere  is  O  =  CV,  after  contact  with  the 
small  sphere,  which  is  neutral,  the  system  will  have  a  new  potential  or  elec- 
trical level,  v,  such  that  CV  =  (C  +  r)  v.     Restoring  now  the  small  sphere  to 
the  neutral  state,  and  repeating  the  experiment  and  the  measurement,  we  shall 
then  get  a  second  value  rz/',  from  which  we  have  the  equation  Cz/  =  (C  -  r}  z/. 

Combining  and  reducing,  we  get  the  ratio  V  =  %-,  which,  seeing  that  rv  and 

rv'  are  numerical  values,  leads  directly  to  the  desired  result. 

In  like  manner  it  is  easy  to  determine  the  capacity  by  obvious  transform- 
ations of  these  equations. 

It  will  thus  be  seen  that  this  process  of  determining  potential  is  ana- 
logous to  that  of  determining  temperature  by  means  of  a  thermometer  ;  and 
the  proof  sphere  plays  the  part,  as  it  were,  of  an  electrical  thermometer. 

It  may  be  observed  that  in  the  case  of  heat  we  pass  from  the  conception 
of  temperature  to  that  of  quantity  of  heat,  while  with  electricity,  starting  with 
the  fact  of  quantity,  or  charge  of  electricity,  we  arrive  at  the  conception  of 
potential  of  electricity. 

741.  Potential  of  a  sphere. — If  q,  q\  and  ^r'are  any  masses  of  electri- 
city on  the  surface  of  an  insulated  conducting  sphere,  and  d,  d\  and  d"  their 

respective  distances  from  any  point  of  the  interior  of  the  sphere,  then  ?,  £» 


-742]  Loss  of  Electricity.  645 

and  9     are  the  values  of  the  potentials  z/,  z>',  and  v"  which  they  would 
a' 

severally  produce  at  this  point.     Let  the  point  in  question  be  the  centre, 
and  let  O  be  the  sum  of  the  whole  quantities  ;  then  V,  the  potential  of  the 

sphere,  equals  A  R  being  the  radius. 
R 

If  there  be  a  sphere,  or  uniform  spheroidal  shell  of  matter,  which  acts 
according  to  the  inverse  square  of  the  distance,  then  the  total  action  of  this 
sphere  is  the  same  as  if  the  whole  matter  were  concentrated  at  the  centre. 
This  was  first  proved  by  Newton  in  the  case  of  gravitation  ;  but  it  also 
applies  to  electricity,  and  hence,  in  calculating  the  potential  at  any  point  out- 
side a  sphere  possessing  a  uniform  charge,  we  need  only  consider  its  dis- 
tance from  the  centre,  and  for  such  a  case  we  may  write  the  value  of  the 

potential  V  •   ~. 

If  a  charge  of  electricity,  Q,  be  imparted  to  two  insulated  conducting 
spheres  whose  radii  are  respectively  r  and  r\  and  which  are  connected  by 
a  long  fine  wire,  the  capacity  of  which  may  be  neglected,  the  electricity 
will  distribute  itself  over  the  two  spheres,  which  will  possess  the  charges 
q  and  q'  ;  that  is,  <?  +  g'  =  Q-  (i)  The  whole  system  will  be  at  the  same 


potential  V,  such  that  V  =    =     .     (2)  Combining  these  two  equations  and 
reducing,  we  get  for  the  quantities  q  and  q'  on  each  sphere  q  =   -  .  ---  and 

" 


.         .  .      . 

Now,  since  the  diameter  of  any  sphere  with  which  we  can  experiment  is 
infinitely  small  compared  with  that  of  the  earth,  it  follows  that  when  a  sphere 
is  connected  with  the  earth  by  a  fine  wire  the  quantity  of  electricity  which 
it  retains  is  infinitely  small. 

For  the  densities  on  the  two  spheres  we  have  ^»_£-.  and  d'  =  —  ^—  from 

~ 


which  by  equation  (2)  it  is  readily  deduced  that  d  :  d'  =  r'  :  r  ;  that  is,  that 
the  electrical  densities  on  two  spheres  in  distant  connection  are  inversely  as 
the  radii. 

If,  for  instance,  a  fine  wire  be  connected  with  a  charged  insulated  sphere, 
the  distant  pointed  end  of  the  wire  may  be  regarded  as  a  sphere  with  an 
infinitely  small  radius,  and  thus  the  density  upon  it  would  be  infinitely 
great. 

742.  Power  of  points.  —  We  have  just  seen  that  on  a  point  in  connection 
with  a  conductor  charged  with  electricity  the  density  may  be  considered  to 
be  infinitely  great,  but  the  greater  the  density  the  greater  will  be  the  tendency 
of  electricity  to  overcome  the  resistance  of  the  air,  and  escape.  If  the  hand 
be  brought  near  a  point  on  an  electrified  conductor  a  slight  wind  is  felt  ;  and 
if  the  disengagement  of  electricity  takes  place  in  the  dark  a  luminous  brush 
is  seen.  If  an  electrified  conductor  is  to  retain  its  electricity  all  sharp 
points  and  edges  must  be  avoided  ;  on  the  other  hand,  to  facilitate  the  out- 
flow of  electricity  in  apparatus,  and  experiments,  frequent  use  is  made  of  this 
property  of  points. 


646  Frictional  Electricity.  [743- 

743.  toss  of  electricity. — Experience  shows  that  electrified  bodies 
gradually  lose  their  electricity,  even  when  placed  on  insulating  supports. 
This  loss  is  due  to  two  causes  :  firstly,  to  the  imperfection  of  the  insulating 
supports  ;  and,  secondly,  to  the  conductivity  of  the  air. 

i.  All  substances  conduct  electricity  in  some  degree  ;  those  which  are 
termed  insulators  are  simply  very  bad  conductors.  An  electrified  con- 
ductor resting  on  supports  must  therefore,  lose  a  certain  quantity  of  its 
electricity. 

ii.  The  loss  by  the  atmosphere  varies  with  the  electric  density,  with  the 
rapidity  with  which  the  air  is  renewed,  and  with  the  hygrometric  state. 

Dry  air  is  a  very  imperfect  conductor  ;  but  when  it  contains  aqueous 
vapour,  it  conducts  pretty  well,  and  the  more  moisture  it  contains  the  better 
it  conducts.  Coulomb  has  attempted  to  show  '  that  in  a  still  atmosphere, 
and  with  a  constant  hygrometric  state,  the  loss  for  a  very  short  space  of 
time  is  directly  proportional  to  the  tension  : '  a  law  analogous  to  Newton's 
law  of  cooling  (416). 

Coulomb  experimented  with  moist  air.  In  perfectly  dry  gases,  Matteucci 
did  not  find  the  loss  of  electricity  in  accordance  with  Coulomb's  law.  He 
found  that,  within  certain  limits,  the  loss  was  independent  of  the  quantity  of 
electricity,  and  proportional  to  the  time  ;  in  other  words,  that  in  equal  times 
there  was  an  equal  loss  of  electricity. 

He  further  found  that  for  equal  temperatures  and  pressures  the  loss  is 
the  same  in  air,  carbonic  acid,  and  hydrogen,  provided  they  are  perfectly 
dry  :  at  a  high  tension  the  loss  of  negative  electricity  is  greater  than  that 
of  positive  ;  in  dry  gases,  under  a  constant  pressure,  the  loss  increases  with 
the  temperature  ;  and  lastly,  that  in  dry  gases  the  loss  is  independent  of  the 
nature  of  the  electrified  body  ;  that  is,  it  is  the  same  whether  it  is  a  conductor 
or  not.  Warburg  has  found  that  the  loss  in  hydrogen  is  greater  than  in 
carbonic  acid  or  air. 

Coulomb  found  not  only  that  supports  never  insulate  completely,  but 
that  they  are  the  cause  of  an  abundant  loss  of  electricity  in  bodies  strongly 
electrified.  The  loss  diminishes  gradually  ;  it  is  constant  when  the  tension 
is  low,  and  may  be  neglected  by  giving  to  the  supports  an  adequate  length. 
Brown  shellac  or  ebonite  is  the  best  insulator ;  glass  is  a  hygroscopic  sub- 
stance, and  must  be  dried  with  great  care.  It  is  best  covered  with  a  thin 
layer  of  shellac  varnish,  as  has  already  been  stated. 

Sir  W.  Thomson  ascribes  the  greater  part  of  the  loss  of  electricity  to  the 
conducting  layer  of  moisture,  which  covers  the  supports  ;  and  he  finds  that 
in  comparison  with  this  the  loss  by  even  moist  air  is  inconsiderable. 


-744] 


Electricity  by  Influence  or  Induction. 


647 


CHAPTER   III. 

ACTION   OF  ELECTRIFIED   BODIES  ON   BODIES   IN  THE  NATURAL  STATE. 
INDUCED  ELECTRICITY.      ELECTRICAL  MACHINES. 

744.  Electricity  by  influence  or  induction. — An  insulated  conductor, 
charged  with  either  kind  of  electricity,  acts  on  bodies  in  a  neutral  state 
placed  near  it  in  a  manner  analogous  to  that  of  the  action  of  a  magnet  on 
soft  iron  ;  that  is,  it  decomposes  the  neutral  fluid,  attracting  the  opposite 


Fig  600 

and  repelling  the  like  kind  of  electricity.     The  action  thus  exerted  is  said  to 
take  place  by  influence  or  induction. 

The  phenomena  of  induction  may  be  demonstrated  by  means  of  a  brass 
cylinder  placed  on  an  insulating  support,  and  provided  at  its  extremities 
with  t\vo  small  electric  pendulums,  which  consist  of  pith  balls  suspended  by 
linen  threads  (fig.  600).  If  this  apparatus  is  placed  near  an  insulated  con- 
ductor ;;/,  charged  with  either  kind  of  electricity — for  instance,  the  conductor 
of  an  electrical  machine,  which  is  charged  with  positive  electricity — the 
natural  electricity  of  the  cylinder  is  decomposed,  free  electricity  will  be 
developed  at  each  end,  and  both  pendulums  will  diverge.  If,  while  they 
still  diverge,  a  stick  of  sealing-wax,  excited  by  friction  with  flannel,  be  ap- 
proached to  that  end  of  the  cylinder  nearest  the  conductor,  the  correspond- 
ing pith  ball  will  be  repelled,  indicating  that  it  is  charged  with  the  same 
kind  of  electricity  as  the  sealing-wax — that  is.  with  negative  electricity  ;  while 
if  the  excited  sealing-wax  is  brought  near  the  other  ball  it  will  be  attracted, 


648  Frictional  Electricity.  [744— 

showing  that  it  is  charged  with  positive  electricity.  If,  further,  a  glass  rod 
excited  by  friction  with  silk,  and  therefore  charged  with  positive  electricity, 
be  approached  to  the  end  nearest  the  conductor,  the  pendulum  will  be 
attracted  ;  while  if  brought  near  the  other  end,  the  corresponding  pendulum 
will  be  repelled.  If  the  influence  of  the  charged  conductor  be  suppressed, 
either  by  removing  it,  or  placing  it  in  communication  with  the  ground,  the 
separated  electricities  will  recombine,  and  the  pendulums  exhibit  no  diver- 
gence. 

The  cause  of  this  phenomenon  is  obviously  a  decomposition  of  the  neutral 
electricity  of  the  cylinder,  by  the  free  positive  electricity  of  the  conductor  ; 
the  opposite  or  negative  electricity  being  attracted  to  that  end  of  the  cylinder 
nearest  the  conductor,  while  the  similar  electricity  is  repelled  to  the  other 
end.  Between  these  two  extremities,  there  is  a  space  destitute  of  free 
electricity.  This  is  seen  by  arranging  on  the  cylinders  a  series  of  pairs  of 
pith  balls  suspended  by  threads.  The  divergence  is  greatest  at  each 
extremity,  and  there  is  a  line  at  which  there  is  no  divergence  at  all,  which  is 
called  the  neutral  line.  The  two  fluids,  although  equal  in  quantity,  are  not 
distributed  over  the  cylinder  in  a  symmetrical  manner  ;  the  attraction  which 
accumulates  the  negative  electricity  at  one  end  is,  in  consequence  of 
the  greater  nearness,  greater  than  the  repulsion  which  drives  the  positive 
electricity  to  the  other  end,  and  hence  the  neutral  line  is  nearer  one  end  than 
the  other.  Nor  is  the  electricity  induced  at  the  two  ends  of  the  cylinder 
under  the  same  conditions.  That  which  is  repelled  to  the  distant  extremity 
is  free  to  escape  if  a  communication  be  made  with  the  ground  ;  whilst,  on  the 
other  hand,  the  unlike  electricity  which  is  attracted  is  held  bound  or 
captive  by  the  inducing  action  of  the  electrified  body.  Even  if  contact  be 
made  with  the  ground  on  the  face  of  the  cylinder  adjacent  to  the  inducing 
body,  the  electricity  induced  on  that  face  will  not  escape.  The  repelled 
electricity,  however,  on  the  distant  surface  is  not  thus  bound  ;  it  is  free  to 
escape  by  any  conducting  channel,  and  hence  will  immediately  disappear 
wherever  contact  be  made  between  the  ground  and  the  cylinder.  Both  the  pith 
balls  will  collapse,  and  all  signs  of  electricity  on  the  cylinder  depart  with  the 
escape  of  the  repelled  or  free  electricity.  But  now,  if  communication  with 
the  ground  be  broken  and  the  inducing  body  be  discharged  or  removed  to  a 
considerable  distance,  the  attracted  or  bound  electricity  is  itself  set  free,  and 
diffusing  over  the  whole  cylinder  causes  the  pith  balls  again  to  diverge,  but 
now  with  the  opposite  electricity  to  that  of  the  original  inducing  body.  The 
reason  for  the  escape  of  the  repelled  electricity  is  as  follows  : — If  the 
cylinder  be  placed  in  connection  with  the  ground,  by  metallic  contact  with 
the  posterior  extremity,  and  the  charged  conductor  be  still  placed  near 
the  anterior  extremity,  the  conductor  will  exert  its  inductive  action  as  before. 
But  it  is  now  no  longer  the  conductor  alone  which  is  influenced.  It  is  a 
conductor  consisting  of  the  conductor  itself,  the  metallic  wire,  and  the  whole 
earth.  The  neutral  line  will  recede  indefinitely,  and,  since  the  conductor  has 
become  infinite,  the  quantity  of  neutral  fluid  decomposed  will  be  increased. 
Hence,  when  the  posterior  extremity  is  placed  in  contact  with  the  ground, 
the  pendulum  at  the  anterior  extremity  diverges  more  widely.  If  the  con- 
necting rod  be  now  removed,  neither  the  quantity  nor  the  distribution  will 
be  altered ;  and  if  the  conductor  be  removed,  or  be  discharged,  a  charge  of 


745] 


Faraday's  Experiments. 


649 


' 


negative  electricity  will  be  left  on  the  cylinder.  It  will,  in  fact,  remain 
charged  with  electricity,  the  opposite  of  that  of  the  charged  conductor.  Even 
if,  instead  of  connecting  the  posterior  extremity  of  the  cylinder  with  the 
ground,  any  other  part  had  been  so  connected,  the  general  result  would  have 
been  the  same.  All  the  parts  of  the  cylinder  would  be  charged  with  negative 
electricity,  and,  on  interrupting  the  communication  with  the  earth,  would 
remain  so  charged. 

Thus  a  body  can  be  charged  with  electricity  by  induction  as  well  as  by 
conduction.  But,  in  the  latter  case,  the  charging  body  loses  part  of  its 
electricity,  which  remains  unchanged  in  the  former  case.  The  electricity 
imparted  by  conduction  is  of  the  same  kind  as  that  of  the  electrified 
body,  while  that  excited  by  induction  is  of  the  opposite  kind.  To  impart 
electricity  by  conduction,  the  body 
must  be  quite  insulated  ;  while  in  the 
case  of  induction  it  must  be  in  con- 
nection with  the  earth — at  all  events 
momentarily. 

A  body  electrified  by  induction 
acts  in  turn  on  bodies  placed  near  it, 
separating  the  two  fluids  in  a  manner 
shown  by  the  signs  on  the  sphere. 

What  has  here  been  said,  has  re- 
ference to  the  inductive  action  exerted' 
on  good  conductors.  Bad  conductors 
are  not  so  easily  acted  upon  by  in- 
duction, owing  to  the  great  resist- 
ance they  present  to  the  circulation 
of  electricity;  but,  when  once  charged, 
the  electric  state  is  more  permanent. 

This  is  analogous  to  what  is 
met  with  in  magnetism  ;  a  magnet 
instantaneously  magnetises  a  piece  of 
soft  iron,  but  this  is  only  temporary,  Fig.  601. 

and  depends  on  the  continuance  of 

the  action  of  the  magnet ;  a  magnet  magnetises  steel  with  far  greater 
difficulty,  but  this  magnetisation  is  permanent. 

The  fundamental  phenomena  of  induction  may  be  conveniently  investi- 
gated and  demonstrated  by  means  of  the  apparatus  represented  in  figure 
60 1,  which  consists  of  a  narrow  cylindrical  brass  tube  BA  supported  by  an 
insulating  glass  handle  and  held  over  the  excited  cake  of  an  electrophorus 
(752). 

745-  Faraday's  experiments. — The  following  experiments  of  Faraday 
are  excellent  illustrations  of  the  operation  of  induction  : — 

A  carefully  insulated  metal  cylinder,  A,  fig.  602,  is  connected  by  a  wire  with 
an  electroscope  E,  at  some  distance.  On  placing  inside  the  cylinder  an  insu- 
lated brass  ball  C,  charged  with  positive  electricity,  the  leaves  of  the  elec- 
troscope diverge  with  positive  electricity,  and  the  divergence  increases  until 
a  certain  depth  is  attained,  when  there  is  no  further  increase.  The  diverg- 
ence now  remains  constant,  whatever  be  the  position  of  the  ball,  even  when 

F  F 


650 


Frictional  Electricity. 


[745- 


Fig.  602. 


it  touches  the  cylinder.  On  withdrawing  the  ball  it  is  found  to  be  perfectly 
discharged.  Hence  the  charge  on  the  surface  is  equal  to  that  which  the 

ball  had  originally. 

Four  such  cylinders,  fig.  603,  are  placed 
concentrically  within  each  other,  and  are 
insulated  from  each  other  by  discs  of 
shellac,  and  the  outer  one  is  connected 
with  the  electroscope.  On  introducing 
the  charged  ball  into  the  central  cavity  the 
leaves  diverge  just  as  if  the  intermediate 
ones  did  not  exist.  Each  of  these  is 
charged  with  equal  quantities  of  opposite 
electricities,  all  equal  in  value  to  that  of  the 
sphere.  The  internal  charge  of  the  cylin- 
der is  the  same  as  if  all  the  intermediate 
cylinders  were  suppressed,  and  the  charge 
does  not  vary  even  when  the  intermediate 
ones  are  connected  with  each  other  or  are 
touched  by  the  electrified  ball  C. 

If,  while  C  is  in  its  original  condition 
the  internal  cylinder,  4,  is  connected  with  the  ground,  the  leaves  collapse, 
and  the  other  cylinders  are  in  the  neutral  state  ;  the  two  layers  which 

remain,  positive  on  C,  and  nega- 
tive on  the  adjacent  cylinder,  are 
without  action  on  an  external 
point.  If  any  other  cylinder  be 
thus  treated  the  external  ones  are 
reduced  to  the  neutral  state. 

746.   Limit    to   the  action    of 
induction.  —  The  inductive  action 
which  an  electrified  body  exerts 
on  an   adjacent  body  in  decom- 
Fis-  6°3-  posing  its  neutral  fluid  is  limited. 

On  the  surface  of  the  insulated  cylinder,  which  we  have  considered  in  the 
preceding  paragraph,  let  there  be  at  n  any  small  quantity  of  neutral  electri- 
city (fig.  604).  The  positive  electricity  of  the  source  m  first  decomposes 
by  induction  the  neutral  electricity  in  «,  attracting  its  negative  towards  A, 
and  repelling  its  positive  towards  B  ;  but  in  the  degree  in  which  the  extremity 
A  becomes  charged  with  negative  electricity,  and  the  extremity  B  with 
positive  electricity,  there  are  developed  at  A  and  B  two  forces,/"  and  /"", 
which  act  in  the  opposite  direction  to  the  original  force.  For  the  forces  f 
and/  concur  in  driving  towards  Bthe  negative  fluid  of  ;z,  and  towards  A  its 
positive  fluid.  But  as  the  inducing  force  F  which  is  exerted  at  m  is  constant, 
while  the  forces  /and/  are  increasing,  a  time  arrives  at  which  the  force  F 
is  balanced  by  the  forces/  and  f.  All  decomposition  of  the  neutral  con- 
dition then  ceases  \  the  inducing  action  has  attained  its  limit. 

If  the  cylinder  be  removed  from  the  source  of  electricity,  as  the  inducing 
action  decreases,  a  portion  of  the  free  electricities  at  A  and  at  B  recombine 
to  form  the  neutral  fluid.  If,  on  the  other  hand,  they  are  brought  nearer,  as 


* 


-748]  Specific  Inductive  Capacity.  65 1 

the  force  F  now  exceeds  the  forces  f  and/*,  a  new  decomposition  of  the 
neutral  fluid  takes  place,  and  fresh  quantities  of  positive  and  negative  elec- 
tricities are  respectively  accumulated  at  A  and  B. 


Fig.  6c4. 

747.  Faraday's  theory  of  induction. — Hitherto,  the  influence  of  the 
medium  which  separates  the  electrified  from  the  unelectrified  body,  in  the 
case  of  induction,  has  been  neglected.     But  Faraday's  researches  prove  that 
it  is  in  this  medium  that  the  inductive  actions  take  place,  and  that  the  in- 
ductive action  is  not  an  action  at  a  distance,  or  rather  at  no  distance  greater 
than  that  between   any  two  molecules.      Faraday  supposes   that   succes- 
sions of  layers  in  this  medium  become  alternately  positively  and  negatively 
electrified.     This  condition  is  called  dielectric  polarisation. 

The  following  experiment  was  devised  by  Faraday  to  illustrate  this 
polarisation  of  tlic  medium,  as  he  has  called  it  : — He  placed  small  filaments 
of  silk  in  a  vessel  of  turpentine  ;  and,  having  plunged  two  conductors  in  the 
liquid  in  opposite  sides,  he  charged  one  and  placed  the  other  in  connection 
with  the  ground.  The  particles  of  silk  immediately  arranged  themselves 
end  to  end,  and  adhered  closely  together,  forming  a  continuous  chain  between 
the  two  sides.  An  experiment  by  Matteucci  also  supports  Faraday's  theory. 
He  placed  several  thin  plates  of  mica  closely  together,  and  provided  the 
outside  ones  with  metallic  coatings,  like  a  fulminating  pane  (769).  Having 
electrified  the  system,  the  coatings  were  removed  by  insulating  handles,  and 
on  examining  the  plates  of  mica  successively,  each  was  found  charged  with 
positive  electricity  on  one  side,  and  negative  electricity  on  the  other. 

On  the  new  view,  the  action  exerted  by  electrified  bodies  on  bodies  in  the 
neutral  state  is  effected  by  the  polarisation  of  the  alternate  layers  of  air  or 
any  other  medium.  On  the  old  view,  the  air  was  supposed  to  be  quite  pas- 
sive, or  at  most,  in  virtue  of  its  non-conductivity,  to  oppose  a  resistance  to 
the  combination  of  the  two  fluids. 

748.  Specific  inductive  capacity. — Faraday  named  the  property  which 
bodies  possess  of  transmitting  the  electric  influence,  the  inductive  fioiuer. 
All  insulating  bodies  do  not  possess  it  in  the  same  degree.     To  determine 
and  compare  the  inductive  power  Faraday  used  the  apparatus  represented 
in  fig.  605,  and  of  which  606  represents  a  vertical  section.     It  consists  of 
a  brass  sphere  made  up  of  two  halves  P  and  O,  which  fit  accurately  into 
each  other,  like  the  Magdeburg  hemispheres.     In  the  interior  of  this  spherical 
envelope   there  is  a  smaller  brass  sphere  C,  connected  with  a  metal  rod, 
terminating  in  a  ball  B.     The  rod  is  insulated  from  the  envelope  PO  by  a 
thick  layer  of  shellac  A.     The  space  mn  receives  the  substance  whose  in- 
ductive power  is  to  be  determined.     The  foot  of  the  apparatus  is  provided 
with  a  screw  and  stopcock,  so  that  it  can  be  screwed  on  the  air  pump,  and 
the  air  in  mn  either  rarefied  or  exhausted. 


652 


Frictional  Electricity. 


[748- 


T\vo  such  apparatus  perfectly  identical  are  used,  and  at  first  they  only 
contain  air.  The  envelopes  PO  are  connected  with  the  ground,  and  the 
knob  B  of  one  of  them  receives  a  charge  of  electricity.  The  sphere  C  thus 
becomes  charged  like  the  inner  coating  of  a  Leyden  jar  (770).  The  layer  mn 
represents  the  insulator  which  separates  the  two  coatings.  By  touching  B 
with  the  proof  plane,  which  is  then  applied  to  the  torsion  balance,  the  quantity 
of  free  electricity  is  measured.  In  one  experiment  Faraday  observed  a 
torsion  of  250°,  which  represented  the  free  electricity  on  B.  The  knob  B 


Fig.  605. 


Fig.  606 


was  then  placed  in  metallic  connection  with  the  knob  B''  of  the  other  appa- 
ratus, and  the  torsion  was  now  found  to  be  125°,  showing  that  the  electricity 
had  become  equally  distributed  on  the  two  spheres,  as  might  have  been 
anticipated,  since  the  pieces  of  apparatus  were  quite  equal  and  each  contained 
air  in  the  space  mn. 

This  experiment  having  been  made,  the  space  mn  in  the  second  appa- 
ratus was  rilled  with  the  substance  whose  inductive  power  was  to  be  deter- 
mined :  for  example,  shellac.  The  other  apparatus,  in  which  mn  is  filled 
with  air,  having  been  charged,  the  density  of  the  free  electricity  on  C  was 
measured.  Let  it  be  taken  at  290°,  the  number  observed  by  Faraday,  in  a 
special  case.  When  the  knob  B  of  the  first  apparatus  was  connected  with 
the  knob  B'  of  the  second,  the  density  was  not  found  to  be  145°,  as  would 
be  expected.  The  apparatus  containing  air  exhibited  a  density  of  1 14°,  and 
that  with  shellac  of  113°.  Hence  the  former  had  lost  176°,  and  had  retained 
1 14°,  while  the  latter  ought  to  have  exhibited  a  density  of  176°  instead  of  1 13°. 
The  second  apparatus  had  taken  more  than  half  the  charge,  and  hence  a 
larger  quantity  of  electricity  had  been  condensed  by  the  shellac.  Of  the 


-749]  Communication  of  Electricity  at  a  Distance.  653 

total  quantity  of  electricity,  the  shellac  had  taken  176°,  and  the  air  114°; 
hence  the  specific  inductive  capacity  of  air  is  to  that  of  shellac  as  114  :  176  ; 
or  as  i  :  1-55.  That  is,  the  inductive  power  of  shellac  is  more  than  half  as 
great  again  as  air. 

By  the  following  simple  experiment  the  influence  of  the  dielectric  may  be 
shown  : — At  a  fixed  distance  above  a  gold-leaf  electroscope,  let  an  electrified 
sphere  be  placed,  by  which  a  certain  divergence  of  the  leaves  is  produced. 
If,  now,  the  charges  remaining  the  same,  a  disc  of  sulphur  or  of  shellac  be 
interposed,  the  divergence  increases,  showing  that  inductive  action  takes 
place  through  the  sulphur  to  a  greater  extent  than  through  a  layer  of  air  of 
the  same  thickness. 

By  various  methods,  the  following  numbers  have  been  obtained  for  the 
specific  inductive  capacity  of  dielectrics,  as  they  are  called  in  opposition  to 
anelectrics  or  conductors  : — 


Air  . 

Spermaceti 

Resin 

Pitch 

Bees-wax 

Glass 


•oo     Sulphur i '93 

•45     Shellac 1*95 

•76     Paraffine 1-98 

•80  India-rubber     ....  2-80 

•86  Gutta-percha    ....  4*00 

•90     Mica 5'oo 


These  values  are  known  as  the  dielectric  constants. 

Boltzmann  divides  dielectrics  into  two  classes  :  to  one  of  which  belong 
shellac,  paraffine,  sulphur,  and  resin,  which  act  like  perfect  insulators  ;  that 
is,  that  in  using  them  the  maximum  charge  is  attained,  if  not  instantaneously, 
at  all  events  after  a  very  short  time  ;  in  others,  such  as  gutta-percha,  stearine, 
and  glass,  the  charge  increases  appreciably  with  the  time. 

A  very  curious  relation  probably  exists  between  the  dielectric  constant 
and  the  refractive  index  of  certain  substances.  Thus  the  following  numbers 
have  been  found  :  — 


n 

Sulphur        .....  .     2-04  1-96 

Resin    ........     1-54  1-59 

Paraffine      .......     1-53  1-52 

where  n  is  the  refractive  index  (538),  and  \/D  the  square  root  of  the  die- 
lectric constant. 

749.  Communication  of  electricity  at  a  distance.  —  In  the  experiment 
represented  in  figure  586  the  opposite  electricities  of  the  conductor  and  that 
of  the  separated  cylinder  tend  to  unite,  but  are  prevented  by  the  resistance 
of  the  air.  If  the  density  is  increased,  or  if  the  distance  of  the  bodies  be 
diminished,  the  opposed  electricities  at  length  overcome  this  obstacle  ;  they 
rush  together  and  combine,  producing  a  spark,  accompanied  by  a  sharp 
sound.  The  negative  electricity  separated  on  the  cylinder,  being  thus  neu- 
tralised by  the  positive  electricity  of  the  charged  body,  a  charge  of  positive 
electricity  remains  on  the  cylinder.  The  same  phenomenon  is  observed 
when  a  finger  is  presented  to  a  strongly  electrified  conductor.  The  latter 
decomposes  by  induction  the  neutral  electricity  of  the  body,  the  opposite 
electricities  combine  with  the  production  of  a  spark,  while  the  electricity  of 


654  Frictional  Electricity.  [749- 

the  same  kind  as  the  electrified  conductor,  which  is  left  on  the  body,  passes 
off  into  the  ground. 

The  striking  distance  varies  with  the  density,  the  shape  of  the  bodies, 
their  conducting  power,  and  with  the  resistance  and  pressure  of  the  inter- 
posed medium. 

750.  Motion  of  electrified  bodies. — The  various  phenomena  of  attrac- 
tion and  repulsion,  which  are  among  the  most  frequent  manifestations  of 
electrical  action,  may  all  be  explained  by  means  of  the 
M  laws  of  induction.     If  M  (fig.  607)  be  a  fixed  insulated 

O  conductor  charged  with  positive  electricity,  and  N  be 

/i\     a  moveable  insulated  body— for  instance,  an  electrical 
*   \jjr   pendulum — there  are  three  cases  to  be  considered  : — 
i.    The  moveable  body  is  unelectrified  and  is  a  con- 
ductor— In   this    case    M,  acting   inductively   on    N, 
attracts  the  negative  and  repels  the  positive  electricity, 

so  that  the  maxima  of  density  are  respectively  at  the  points  a  and  b.  Now 
a  is  nearer  c  than  it  is  to  b  ;  and,  since  attractions  and  repulsions  are  in- 
versely as  the  square  of  the  distance,  the  attraction  between  a  and  c  is 
greater  than  the  repulsion  between  b  and  c ;  and,  therefore,  N  will  be 
attracted  to  M  by  a  force  equal  to  the  excess  of  the  attractive  over  the 
repulsive  force. 

ii.  The  moveable  body  is  a  conductor  and  is  electtified. — If  the  electricity 
of  the  moveable  body  is  different  from  that  of  the  fixed  body,  there  is  always 
attraction  ;  but  if  they  are  of  the  same  kind,  there  is  at  first  repulsion  and 
afterwards  attraction.  This  anomaly  may  be  thus  explained  :  Besides  its 
charge  of  electricity,  the  moveable  body  contains  neutral  fluid.  This  is 
decomposed  by  the  induction  of  the  positive  fluid  on  M  ;  and  consequently 
the  hemisphere  $  obtains  an  additional  supply  of  positive  electricity,  while  a, 
becomes  charged  with  negative  electricity.  There  is  thus  attraction  and 
repulsion,  as  in  the  foregoing  case.  The  force  of  repulsion  is  at  first  greater, 
because  the  quantity  of  positive  electricity  on  N  is  greater  than  that  of 
negative  ;  but  as  the  distance  a  c  diminishes,  the  attractive  force  increases 
more  rapidly  than  the  repulsive  force,  and  finally  exceeds  it. 

iii.  The  moveable  body  is  a  bad  conductor. — If  N  is  charged,  repulsion  or 
attraction  takes  place,  according  as  the  electricity  is  of  the  same  or  opposite 
kind  to  that  of  the  fixed  body.  If  it  is  in  the  natural  state,  the  body  M  will 
decompose  the  neutral  fluid  of  N,  and  attraction  will  take  place  as  in  the 
first  case,  since  a  powerful  and  permanent  source  of  electricity  can  more  or 
less  decompose  the  neutral  fluid  even  of  bad  conductors. 

751.  Gold-leaf  electroscope.— The  name  electroscope  is  given  to  instru- 
ments for  detecting  the  presence  and  determining  the  kind  of  electricity  in 
any  body.  The  original  pith-ball  pendulum  is  an  electroscope  ;  but,  though 
sometimes  convenient,  it  is  not  sufficiently  delicate.  Many  successive  im- 
provements have  been  made  in  it,  and  have  resulted  in  the  form  now  gene- 
rally used,  which  is  due  to  Bennett. 

Bennetfs,  or  the  gold-leaf,  electroscope. — This  consists  of  a  tubulated  glass 
shade  B  (fig.  608),  standing  on  a  metal  foot,  which  thus  communicates  with 
the  ground.  A  metal  rod  terminating  at  its  upper  extremity  in  a  knob  C, 
and  holding  at  its  lower  end  two  narrow  strips  of  gold  leaf,  n  n,  fits  in  the 


-751] 


Gold-leaf  Electroscope. 


655 


Fig.  608. 


tubulure  of  the  shade,  the  neck  of  which  is   coated    with    an   insulating 
varnish.     The  air  in  the  interior  is  dried  by  quicklime,  or  by  chloride  of 
calcium,  and   on   the   insides   of  the 
shade  there  are  two  strips  of  gold  leaf 
a,  communicating  with  the  ground. 

When  the  knob  is  touched  with  a 
body  charged  with  either  kind  of 
electricity,  the  leaves  diverge ;  usu- 
ally, however,  the  apparatus  is  charged 
by  induction  thus  : — 

If  an  electrified  body — a  stick  of 
sealing-wax,  for  example — be  brought 
near  the  knob,  it  will  decompose  the 
neutral  electricity  of  the  system,  at- 
tracting to  the  knob  the  electricity  of 
the  opposite  kind,  and  retaining  it 
there,  and  repelling  the  electricity  of 
the  same  kind  to  the  gold  leaves, 
which  consequently  diverge.  In  this 
way  the  presence  of  an  electrical 
charge  is  ascertained,  but  not  its  quality. 

To  ascertain  the  kind  of  electricity  the  following  method  is  pursued  : — If 
while  the  instrument  is  under  the  influence  of  the  body  A,  which  we  will 
suppose  has  a  negative  charge,  the  knob  be  touched  by  the  finger,  the 
negative  electricity  decomposed  by  induction  passes  off  into  the  ground,  and 
the  previously  divergent  leaves  will  collapse  ;  there  only  remains  positive 
electricity,  retained  in  the  knob  by  induction  from  A.  If  now  the  finger  be 
first  removed,  and  then  the  electrified  body,  the  positive  electricity  pre- 
viously retained  by  A  will  spread  over  the  system,  and  cause  the  leaves  to 
diverge.  If  now,  while  the  system  is  charged  with  positive  electricity,  a 
positively  electrified  body — as,  for  example,  an  excited  brass  rod — be  ap- 
proached, the  leaves  will  diverge  more  widely  ;  for  the  electricity  of  the  same 
kind  will  be  repelled  to  the  extremities.  If,  on  the  contrary,  an  excited 
shellac  rod  be  presented,  the  leaves  will  tend  to  collapse,  the  electricity 
with  which  they  are  charged  being  attracted  by  the  opposite  electricity. 
Hence  we  may  ascertain  the  kind  of  electricity,  either  by  imparting  to 
the  electroscope  electricity  from  the  body  under  examination,  and  then 
bringing  near  it  a  rod  charged  with  positive  or  negative  electricity  ;  or  the 
electroscope  may  be  charged  with  a  known  kind  of  electricity,  and  the  elec- 
trified body  in  question  brought  near  the  electroscope. 

It  has  been  proposed  to  use  the  gold-leaf  electroscope  as  an  electrometer 
or  measurer  of  electricity,  by  measuring  the  angle  of  divergence  of  the 
leaves  ;  this  is  done  by  placing  behind  them  a  graduated  scale  ;  for  small 
angles  the  quantity  of  electricity  is  nearly  proportional  to  the  sine  of  half  the 
angle  of  divergence.  There  are,  however,  objections  to  such  a  use,  and  the 
electroscope  is  rarely  employed  for  this  purpose. 


656 


Frictional  Electricity. 


[752- 


ELECTRICAL  MACHINES. 

752.  Eiectrophorus. — It  will  now  be  convenient  to  describe  the  various 
electrical  machines,  or  apparatus  for  generating  and  collecting  large  supplies 
of  statical  electricity.  One  of  the  most  simple  and  inexpensive  of  these  is 
the  electrophorus,  which  was  invented  by  Volta.  It  consists  of  a  cake  of 
resin  B  (fig.  610)  say  about  12  inches  diameter,  and  an  inch  thick,  which  is 
placed  on  a  metallic  surface,  or  frequently  fits  in  a  wooden  mould  lined 
with  tinfoil,  which  is  called  the  form.  Besides  this  there  is  a  metal  disc  A 
(fig.  610),  of  a  diameter  somewhat  less  than  that  of  the  cake,  and  provided 
with  an  insulating  glass  handle  ;  this  is  the  cover.  The  mode  of  working  is 


Fig.  609. 


Fig.  610. 


as  follows  : — All  the  parts  of  the  apparatus  having  been  well  warmed,  the 
cake,  which  is  placed  in  the  form,  or  rests  on  a  metal  surface,  is  briskly 
flapped  with  silk,  or,  better,  with  catskin,  by  which  it  becomes  charged  with 
negative  electricity.  The  cover  is  then  placed  on  the  cake.  Owing,  how- 
ever, to  the  minute  rugosities  of  the  surface  of  the  resin,  the  cover  only 
comes  in  contact  with  a  few  points,  and,  from  the  non-conductivity  of  the 
resin,  the  negative  electricity  of  the  cake  does  not  pass  off  to  the  cover. 
On  the  contrary,  it  acts  by  induction  on  the  neutral  electricity  of  the  cover, 
and  decomposes  it,  attracting  the  positive  electricity  to  the  under  surface, 
and  repelling  the  negative  electricity  to  the  upper.  If  the  upper  surface  be 
now  touched  with  the  finger,  the  negative  electricity,  because  repelled  and 
free,  passes  off,  and  the  cover  remains  charged  with  positive  electricity, 
held,  however,  by  the  negative  electricity  of  the  cake  ;  the  two  electricities 
do  not  unite,  in  consequence  of  the  nonconductivity  of  the  cake  (fig.  609). 
If  now  the  cover  be  raised  by  its  insulating  handle,  the  charge  diffuses  itself 
over  the  surface ;  and  if  a  conductor  be  brought  near  it  (fig.  610),  a  smart 
spark  passes. 


-753]  Plate  Electrical  Machine.  657 

The  metallic  form  on  which  the  cake  rests  plays  an  important  part  in  the 
action  of  the  electrophorus,  as  it  increases  the  quantity  of  electricity,  and 
makes  it  more  permanent.  For  the  negative  electricity  of  the  upper  surface 
of  the  resin,  acting  inductively  on  .the  neutral  electricity  of  the  lower,  decom- 
poses it,  retaining  on  the  under  surface  the  positive  electricity,  while  the 
negative  electricity  passes  off  into  the  ground.  The  positive  electricity  thus 
developed  on  the  under  surface  reacts  on  the  negative  electricity  of  the  upper 
surface,  binding  it,  and  causing  it  to  penetrate  into  the  badly  conducting 
mass,  on  the  surface  of  which  fresh  quantities  of  electricity  can  be  excited, 
far  beyond  the  limits  possible  without  the  action  of  the  form.  It  is  for  this 
reason  that  the  electrophorus,  once  charged,  retains  its  state  for  a  consider- 
able time,  and  sparks  can  be  taken  even  after  a  long  interval.  If  the  form 
be  insulated,  the  charge  obtained  from  it  is  far  less  than  if  it  is  on  a  con- 
ducting support.  For  the  negative  electricity  developed  by  induction  on  the 
lower  surface  being  now  unable  to  escape,  the  condensing  action  referred  to 
cannot  take  place,  and  only  a  feeble  charge  can  be  given  to  the  resin.  The 
retention  of  electricity  is  greatly  promoted  by  keeping  the  cake  on  the  form, 
and  placing  the  cover  upon  it,  by  which  the  access  of  air  is  hindered. 
Instead  of  a  cake  of  resin,  a  disc  of  gutta-percha,  or  vulcanised  cloth,  or 
vulcanite  may  be  substituted  ;  and,  of  course,  if  glass,  or  any  material 
which  becomes  positively  electrified  by  friction,  be  used,  the  cover  acquires 
a  negative  charge. 

The  electrophorus  is  a  good  instance  of  the  conversion  of  work  into 
electro-potential  energy  (64).  When  the  cover  is  lifted  from  the  excited  cake 
work  must  be  expended  in  order  to  overcome  the  attraction  of  the  electricity 
in  the  cake  for  the  opposite  electricity  developed  by  induction  on  the  cover  ; 
and  the  equivalent  of  this  work  appears  in  the  form  of  the  electricity  thus 
detached.  Thus,  when  a  Leyden  jar  is  charged  either  by  the  machine  or  by 
the  electrophorus,  the  energy  of  the  charge  is  a  transformation  of  the  work 
of  the  operator. 

753.  Plate  electrical  machine. — The  first  electrical  machine  was  in- 
vented by  Otto  von  Guericke,  the  inventor  also  of  the  air-pump.  It  con- 
sisted of  a  sphere  of  sulphur,  which  was  turned  on  an  axis  by  means  of  the 
hand,  while  the  other,  pressing  against  it,  served  as  a  rubber.  Resin  was 
afterwards  substituted  for  the  sulphur,  which,  in  turn,  Hawksbee  replaced 
by  a  glass  cylinder.  In  all  these  cases  the  hand  served  as  rubber ;  and 
YVinckler,  in  1740,  first  introduced  cushions  of  horse-hair,  covered  with  silk, 
as  rubbers.  At  the  same  time  Bose  collected  electricity,  disengaged  by 
friction,  on  an  insulated  cylinder  of  tin  plate.  Lastly,  Ramsden,  in  1760, 
replaced  the  glass  cylinder  by  a  circular  glass  plate,  which  was  rubbed  by 
cushions.  The  form  which  the  machine  has  now  is  but  a  modification  of 
Ramsden's  original  machine. 

Between  two  wooden  supports  (fig.  611)  a  circular  glass  plate  P  is  sus- 
pended by  an  axis  passing  through  the  centre,  and  which  is  turned  by  means 
of  a  handle  M.  The  plate  revolves  between  two  sets  of  cushions  or  rubbers, 
F,  of  leather  or  of  silk,  one  set  above  the  axis  and  one  below  which,  by 
means  of  screws,  can  be  pressed  as  tightly  against  the  glass  as  may  be 
desired.  The  plate  also  passes  between  two  brass  rods  shaped  like  a  horse- 
shoe, and  provided  with  a  series  of  points  on  the  sides  opposite  the  glass  ; 

FF3 


658  Frictional  Electricity.  (753  - 

these  rods  are  fixed  to  larger  metallic  cylinders  CC,  which  are  called  the 
prime  conductors.  The  latter  are  insulated  by  being  supported  on  glass  feet, 
and  are  connected  with  each  other  by  a  smaller  rod  r. 

The  action  of  the  machine  is  founded  on  the  excitation  of  electricity  by 
friction,  and  on  the  action  of  induction.  By  friction  with  the  rubbers,  the 
glass  becomes  positively  and  the  rubbers  negatively  electrified.  If  now  the 
rubbers  were  insulated,  they  would  receive  a  certain  charge  of  negative 
electricity  which  it  would  be  impossible  to  exceed,  for  the  tendency  of  the 
opposed  electricities  to  reunite  would  be  equal  to  the  power  of  the  friction  to 


Fig.  611. 

decompose  the  neutral  fluid.  But  the  rubbers  communicate  with  the  ground 
by  means  of  a  chain  ;  and,  consequently,  as  fast  as  the  negative  electricity  is 
generated,  it  is  continually  reduced  to  yero  by  contact  with  the  ground.  The 
positive  electricity  of  the  glass  acts  then  by  induction  on  the  conductor, 
attracting  the  negative  electricity.  This  negative  electricity  collects  on  the 
points  opposite  to  the  glass.  Here  its  tendency  to  discharge  becomes  so 
high  that  it  passes  across  the  intervening  space  of  air,  and  neutralises  the 
positive  electricity  on  the  glass.  The  conductors  thus  lose  their  negative 
electricity  and  remain  charged  with  positive  electricity.  The  plate  accord- 


-755]  Maximum  of  Charge.  659 

ingly  gives  up  nothing  to  the  prime  conductors  ;  in  fact,  it  only  abstracts 
from  them  their  negative  electricity. 

If  the  hand  be  brought  near  the  conductor  when  changed,  a  spark  follows, 
which  is  renewed  as  the  machine  is  turned.  In  this  case  the  positive  elec- 
tricity decomposes  the  neutral  electricity  of  the  body,  attracting  its  negative 
electricity,  and  combining  with  it  when  the  two  have  a  sufficient  tension. 
Thus,  with  each  spark,  the  conductor  reverts  to  the  neutral  state,  but  be- 
comes again  electrified  as  the  plate  is  turned. 

754.  Precautions  in  reference   to  the  machine. — The  glass,  of  which 
the  plate  is  made,  must  be  as  little  hygroscopic  as  possible.     Of  late  ebonite 
has  been  frequently  substituted  for  glass  ;  it  has  the  advantage  of  being 
neither   hygroscopic    nor  fragile,    and   of  readily  becoming   electrified   by 
friction.     The  plate  is  usually  from  i  to  \  of  an  inch  in  thickness,  and  from 
20  to  30  inches  in  diameter,  though  these  dimensions  are  not  unfrequently 
exceeded. 

The  rubbers  require  great  care,  both  in  their  construction  and  their  pre- 
servation. They  are  commonly  made  of  leather,  stuffed  with  horse-hair. 
Before  use  they  are  coated  either  with  powdered  aurum  musivum  (sulphuret 
of  tin),  graphite,  or  amalgam.  The  action  of  these  substances  is  not  very 
clearly  understood.  Some  consider  that  it  merely  consists  in  promoting 
friction.  Others,  again,  believe  that  a  chemical  action  is  produced,  and 
assign,  in  support  of  this  view,  the  peculiar  smell  noticed  near  the  rubbers 
when  the  machine  is  worked.  Amalgams,  perhaps,  promote  most  power- 
fully the  disengagement  of  electricity.  KienmayeSs  amalgam  is  the  best 
of  them.  It  is  prepared  as  follows  : — One  part  of  zinc  and  one  part  of  tin 
are  melted  together  and  removed  from  the  fire,  and  two  parts  of  mercury 
stirred  in.  The  mass  is  transferred  to  a  wooden  box  containing  some  chalk, 
and  then  well  shaken.  The  amalgam,  before  it  is  quite  cold,  is  powdered 
in  an  iron  mortar,  and  preserved  in  a  stoppered  glass  vessel.  For  use  a 
little  cacao  butter  or  lard  is  spread  over  the  cushion,  some  of  the  powdered 
amalgam  sprinkled  over  it,  and  the  surface  smoothed  by  a  ball  of  flattened 
leather. 

In  order  to  avoid  a  loss  of  electricity,  two  quadrant-shaped  pieces  of  oiled 
silk  are  fixed  to  the  rubbers,  so  as  to  cover  the  plate  on  both  sides  :  one  at  the 
upper  part  from  a  to  F,  and  the  other  in  the  corresponding  part  of  the  lower 
rubbers.  These  flaps  are  not  represented  in  the  figure.  Yellow  oiled  silk  is 
the  best,  and  there  must  be  perfect  contact  between  the  plate  and  the  cloth. 

Ramsden's  machine,  as  represented  in  fig.  611,  only  gives  positive  elec- 
tricity. But  it  may  be  arranged  so  as  to  give  negative  electricity  by  placing 
it  on  a  table  with  insulating  supports.  By  means  of  a  chain  the  conductor 
is  connected  with  the  ground,  and  the  machine  worked  as  before.  The 
positive  electricity  passes  off  by  the  chain  into  the  ground,  while  the 
negative  electricity  remains  on  the  supports  and  on  the  insulated  table.  On 
bringing  the  finger  near  the  uprights,  a  sharper  spark  than  the  ordinary  one 
is  obtained. 

755.  Maximum  of  charge. — It  is  impossible  to  exceed  a  certain  limit 
of  electrical  charge  with  the  machine,  whatever  precautions  are  taken,  or 
however  rapidly  the  plate  is  turned.     This  limit  is  attained  when  the  loss  of 
electricity  equals  its  production.     The  loss  depends  on  three  causes  :  i.  The 


66o 


Frictional  Electricity. 


[755- 


loss  by  the  atmosphere,  and  the  moisture  it  contains  :  this  is  proportional  to 
the  density,  ii.  The  loss  by  the  supports,  iii.  The  recombination  of  the 
electricities  of  the  rubbers  and  the  glass. 

The  first  two  causes  have  been  already  mentioned.  With  reference  to 
the  latter,  it  must  be  noticed  that  the  electrical  charge  increases  with  the 
rapidity  of  the  rotation,  until  it  reaches  a  point  at  which  it  overcomes  the 
resistance  presented  by  the  non -conductivity  of  the  glass.  At  this  point,  a 
portion  of  the  two  electricities  separated  on  the  rubbers  and  on  the  glass 
recombines,  and  the  charge  remains  constant  It  is,  therefore,  ultimately 
independent  of  the  rapidity  of  rotation. 

756.  Quadrant  electrometer. — The  electrical  charge  is  measured  by 
the  quadrant  or  Henley's  electrometer,  which  is  attached  to  the  conductor. 
This  is  a  small  electric  pendulum,  consisting  of  a 
wooden  rod  </,  to  which  is  attached  an  ivory  or  card- 
board scale  (fig.  612).  In  the  centre  of  this  is  a  small 
whalebone  index,  moveable  on  an  axis,  and  terminating 
in  a  pith  ball.  Being  attached  to  the  conductor,  the 
index  diverges  as  the  machine  is  charged,  ceasing  to 
rise  when  the  limit  is  attained.  When  the  rotation  is 
discontinued  the  index  falls  rapidly  if  the  air  is  moist  • 
but  in  dry  air  it  only  falls  slowly,  showing,  therefore, 
that  the  loss  of  electricity  in  the  latter  case  is  less  than 
in  the  former. 

757-  Cylinder  electrical  machine. — The  construc- 
tion of  the  cylinder  machines,   as  ordinarily  used  in 
England,  is  due  to   Nairne.     They  are  well  adapted 
Fig.  612.  for  obtaining  either  kind  of  electricity.     In   Xairne's 

machine  (fig.  613)  the  cylinder  is  rubbed  by  only  one  cushion  C,  which  is 
made  of  leather  stuffed  with  horse-hair,  and  is  screwed  to  an  insulated  con- 


Fig,  613. 

ductor  A.     On  the  opposite  side  of  the  cylinder  there  is  a  similar  insulated 
conductor  B,  provided  with  a  series  of  points  on  the  sides  next  the  glass. 


-758] 


A  rmstrongs  Hydro-electric  Machine. 


66 1 


To  the  lower  part  of  the  cushion  C  is  attached  a  piece  of  oiled  silk,  which 
extends  over  the  cylinder  to  just  above  the  points.  This  is  not  represented 
in  the  figure.  When  the  cylinder  is  turned,  A  becomes  charged  with  nega- 
tive and  B  with  positive  electricity  by  the  loss  of  its  negative  from  the  points 
P.  The  two  opposite  electricities  will  now  unite  by  a  succession  of  sparks 
across  D  and  E.  If  use  is  to  be  made  of  the  electricity,  either  the  rubber  or 
the  prime  conductor  must  be  connected  with  the  ground.  In  the  former  case 
positive  electricity  is  obtained  ;  in  the  latter,  negative. 

758.  Armstrong's  hydr6-electric  machine. — In  this  machine  electricity 
is  produced  by  the  disengagement  of  aqueous  vapour  through  narrow  orifices. 
The  discovery^  of 
the  machine  was 
occasioned  by  an 
accident.  A  work- 
man having  acci- 
dentally held  one 
hand  in  a  jet  of 
steam,  which  was 
issuing  from  an 
orifice  in  a  steam 
boiler  at  high  pres- 
sure, while  his  other 
hand  grasped  the 
safety  valve,  was 
astonished  at  ex- 
periencing a  smart 
shock.  Sir  W. 
Armstrong  (then 
Mr.  Armstrong,  of 
Newcastle),  whose 
attention  was 

drawn  to  this  phe- 
nomenon, ascer- 
tained that  the  va- 
pour was  charged 
with  positive  elec- 
tricity, and,  by  re- 
peating the  experi- 


Fig.  614. 


ment  with  an  insulated  locomotive,  he  found  that  the  boiler  was  negatively 
charged.  Armstrong  believed  that  the  electricity  was  due  to  a  sudden 
expansion  of  the  vapour  ;  Faraday,  who  afterwards  examined  the  question, 
ascertained  its  true  cause,  which  will  be  best  understood  after  describing 
a  machine  which  Armstrong  devised  for  reproducing  the  phenomenon. 

It  consists  of  a  wrought-iron  boiler  (fig.  614),  with  a  central  fire,  and 
insulated  on  four  legs.  It  is  about  5  feet  long  by  2  feet  in  diameter,  and 
is  provided  at  the  side  with  a  gauge  O,  to  show  the  height  of  the  water  in 
the  boiler.  C  is  the  stopcock,  which  is  opened  when  the  vapour  has  sufficient 
pressure.  Above  this  is  the  box  B,  in  which  are  the  tubes  through  which 
the  vapour  is  disengaged.  On  these  are  fitted  jets  of  a  peculiar  construction, 


662  Frictional  Electricity.  [758- 

which  will  be  understood  from  the  section  of  one  of  them,  M,  represented  on 
a  larger  scale.  They  are  lined  with  hard  wood  in  a  manner  represented  by 
the  diagram.  The  box  B  contains  cold  water.  Thus,  the  vapour,  before 
escaping,  undergoes  partial  condensation,  and  becomes  charged  with  vesicles 
of  water  ;  a  necessary  condition,  for  Faraday  found  that  no  electricity  is  pro- 
duced when  the  vapour  is  perfectly  dry. 

The  development  of  electricity  in  the  machine  was  at  first  attributed  to 
the  condensation  of  the  vapour ;  but  Faraday  found  that  it  is  solely  due  to 
the  friction  of  the  globules  of  water  against  the  jet.  For  if  the  little  cylinders 
which  line  the  jets  are  changed,  the  kind  of  electricity  is  changed  ;  and  if 
ivory  is  substituted,  little  or  no  electricity  is  produced.  The  same  effect  is 
produced  if  any  fatty  matter  is  introduced  into  the  boiler.  In  this  case  the 
linings  are  of  no  use.  It  is  only  in  case  the  water  is  pure  that  electricity  is 
disengaged,  and  the  addition  of  acid  or  saline  solutions,  even  in  minute 
quantity,  prevents  any  disengagement  of  electricity.  If  turpentine  is  added 
to  the  boiler,  the  effect  is  reversed — the  vapour  becomes  negatively,  and  the 
boiler  positively,  electrified. 

With  a  current  of  moist  air  Faraday  obtained  effects  similar  to  those  of 
this  apparatus,  but  with  dry  air  no  effect  is  produced. 

759.  Holtz's  electrical  machine. — Before  the  end  of  last  century  electrical 
machines  were  known  in  this  country  in  which  the  electricity  was  not  deve- 
loped by  friction,  but  by  the  continuous  inductive  action  of  a  body  already 
electrified,  as  the  electrophorus  ;  within  the  last  few  years  such  machines 
have  been  re-invented  and  come  into  use.  The  form  represented  in  fig.  615 
was  invented  by  Holtz,  of  Berlin. 

It  consists  of  two  circular  plates  of  thin  glass  at  a  distance  of  3  mm.  from 
each  other  ;  the  larger  one,  AA,  which  is  2  feet  in  diameter,  is  fixed  by  means 
of  4  wooden  rollers  cz,  resting  on  glass  axes  and  glass  feet.  The  diameter  of 
the  second  plate,  BB,  is  2  inches  less  ;  it  turns  on  a  horizontal  glass  axis, 
which  passes  through  a  hole  in  the  centre  of  the  large  fixed  plate  without 
touching  it.  In  the  plate  A,  on  the  same  diameter,  are  two  large  apertures, 
or  windows,  FF'.  Along  the  lower  edge  of  the  window  F,  on  the  posterior 
face  of  the  plate,  a  band  of  paper  /,  is  glued,  and  on  the  anterior  face  a  sort 
of  tongue  of  thin  cardboard,  ;z,  joined  to/  by  a  thin  strip  of  paper,  and  pro- 
jecting into  the  window.  At  the  upper  edge  of  the  window,  F',  there  are 
corresponding  parts,  p'  and  n'.  The  papers  p  and  p'  constitute  the  armatures. 
The  two  plates,  the  armatures,  and  their  tongues  are  carefully  covered  with 
shellac  varnish,  but  more  especially  the  edges  of  the  tongues. 

In  front  of  the  plate  B,  at  the  height  of  the  armatures,  are  two  brass 
combs,  O  O',  supported  by  two  conductors  of  the  same  metal,  C  C'.  In  the 
front  end  of  these  conductors  are  two  pretty  large  brass  knobs,  through 
which  pass  two  brass  rods  terminated  by  smaller  knobs,  rr',  and  provided 
with  ebonite  handles,  K  K'.  These  rods,  besides  moving  with  gentle  friction 
in  the  knobs,  can  also  be  turned  so  as  to  be  more  or  less  near  and  inclined 
towards  each  other.  The  plate  B  is  turned  by  means  of  a  winch,  M,  and  a 
series  of  pulleys  which  transmit  its  motion  to  the  axis  ;  the  velocity  which 
it  thus  receives  is  12  to  15  turns  in  a  second,  and  the  rotation  should  take 
place  in  the  direction  indicated  by  the  arrows  ;  that  is,  towards  the  points  ol 
the  cardboard  tongues  n  n'. 


-759] 


Holtzs  Electrical  Machine. 


663 


To  work  the  machine,  the  armatures//'  must  be  first  primed',  that  is, 
one  of  the  armatures  is  positively  and  the  other  negatively  electrified.  This 
is  effected  by  means  of  a  plate  of  ebonite,  which  is  excited  by  striking  it 


Fig  615. 

with  catskin  ;  the  two  knobs  rr'  having  been  connected  so  that  the  two 
conductors  C  C  only  form  one,  as  seen  in  fig.  616,  which  shows  by  a  hori- 
zontal section,  through  the  axis  of  rotation,  the  relative  arrangement  of  the 
plates  and  of  the  conductors.  The  electrified  ebonite  is  then  brought  near 

A        7*  T,  71'      A 


r  r- 


Fig.  616. 

one  of  them—/,  for  instance — and  the  plate  B  is  turned.  The  ebonite  is 
charged  with  negative  electricity,  and  this  withdraws  the  positive  electricity 
of  the  armature  and  charges  it  negatively.  This  latter  acting  by  induction 
through  the  plate  B  as  it  turns,  on  the  conductors  OCC'O  (fig.  616),  attracts 
through  the  comb  O  the  positive  electricity  which  collects  on  the  front  face  of 
the  moveable  plate  ;  while  at  the  same  time  negative  electricity,  repelled  on 


664 


Frictional  Electricity. 


[759- 


the  comb  O',  collects,  like  the  former,  on  the  front  face  of  the  plate  B. 
Hence,  the  two  electricities  being  carried  along  by  the  rotation,  at  the  end 
of  half  a  turn  all  the  lower  half  of  the  plate  B,  from  p  to  F'  (fig.  617),  is  posi- 
tively electrified,  and  its  upper  surface  from  p'  to  F  negatively.  But  the  two 
opposite  electricities  above  and  below  the  window  F'  concur  in  decomposing 
the  electricity  of  the  armature  p'n' ;  the  part  p  is  positively  electrified,  while 
negative  electricity  is  liberated  by  the  tongue  ri,  and  is  deposited  on  the 
inner  face  of  the  plate  B,  which  from  its  thinness  almost  completely  neu- 
tralises the  positiye  electricity  on  the  anterior  face. 

The  two  armatures  are  then  primed,  and  the  same  effect  as  at  F'  is 
pro.duced  at  F  on  the  armature  pn  ;  that  is,  that  the  opposite  electricities 
above  and  below  pn,  decomposing  a  new  quantity  of  neutral  electricity, 
the  negative  charge  of  the  part  p  increases,  while  the  positive  electricity  which 
is  liberated  by  the  tongue  n,  neutralises  the  negative  electricity  which  comes 
from  F'  towards  F  ;  and  so  forth  until  the  machine  having  attained  its 
maximum  charge,  there  is  equilibrium  in  all  its  parts.  From  that  point  it 


Fig.  617. 

only  keeps  itself  up,  and  in  perfectly  dry  air  it  may  work  for  a  long  time 
without  its  being  necessary  to  employ  the  ebonite  plate.  If  this  be  removed 
and  the  knobs  rand  r'  are  moved  apart  (fig.  615)  to  a  distance  dependent 
on  the  power  of  the  machine,  on  continuing  to  turn,  a  torrent  of  sparks 
strikes  across  from  one  knob  to  the  other. 

With  plates  of  equal  dimensions  Holtz's  machine  is  far  more  powerful 
than  the  ordinary  electrical  machine  (753).  The  power  is  still  further 
increased  by  suspending  to  the  conductors  CC'  two  condensers,  H  H'  (766), 
which  consist  of  two  glass  tubes  coated  with  tinfoil,  inside  and  out,  to 
within  a  fifth  of  their  height.  Each  of  them  is  closed  by  a  cork  through 
which  passes  a  rod,  communicating  at  one  end  with  the  inner  coating,  and 
suspended  by  one  of  the  conductors  by  a  crook  at  the  other  end.  The  two 
external  coatings  are  connected  by  a  conductor,  G.  They  are,  in  fact,  only 
two  small  Leyden  jars  (770),  one  of  them,  H,  becoming  charged  with  positive 
electricity  on  the  inside  and  negative  on  the  outside  ;  the  other,  H',  with 
negative  electricity  on  the  inside  and  positive  on  the  outside.  Becoming 


-760]  Carres  Dielectrical  Machine.  66$ 

charged  by  the  play  of  the  machine  and  being  discharged  at  the  same  rate 
by  the  knobs  r  r\  they  strengthen  the  spark,  which  may  attain  a  length  of 
6  or  7  inches. 

The  current  of  the  machine  is  utilised  by  placing  in  front  of  the  frame 
two  brass  uprights,  QQ',  with  binding  screws  in  which  are  copper  wires ;  then, 
by  means  of  the  handles  K  K',  the  rods  which  support  the  knobs  r  r  are 
inclined,  so  that  they  are  in  contact  with  the  uprights.  The  current  being 
then  directed  by  the  wires,  a  battery  of  six  jars  can  be  charged  in  a  few 
minutes,  water  can  be  decomposed,  a  galvanometer  deflected,  and  Geissler's 
tubes  illuminated  as  with  the  voltaic  battery. 

Kohlrausch  found  that  a  H  oltz's  machine  with  a  plate  46  inches  in  diameter, 
and  making  5  turns  in  three  seconds,  produced  a  constant  current  capable  of 
decomposing  water  at  the  rate  of  3^  millionths  of  a  milligramme  in  a  second. 
This  is  equal  to  the  effect  produced  by  a  Grove's  cell  in  a  current  of  45,000 
BA  units. 

Rossetti,  who'made  a  series  of  measurements  with  a  H  oltz's  machine,  found 
that  the  strength  of  the  current  is  nearly  proportional  to  the  velocity  of 
the  rotation  ;  it  increases  a  little  more  rapidly  than  the  rotation.  The  ratio 
of  the  velocity  of  rotation  to  the  strength  of  the  current  is  greater  when  the 
hygrometric  state  increases.  The  current  produced  by  a  H  oltz's  machine 
is  quite  comparable  to  that  of  a  voltaic  couple.  Its  electro-motive  force  and 
resistance  are  constant,  provided  the  velocity  of  rotation  and  the  hygrometric 
state  are  constant. 

The  electro-motive  force  is  independent  of  the  velocity  of  rotation  ;  but 
diminishes  as  the  moisture  increases  ;  it  is  nearly  52,000  times  as  great  as 
that  of  a  DanielFs  cell. 

The  internal  resistance  is  independent  of  the  moisture,  but  diminishes 
rapidly  with  increased  velocity  of  rotation.  Thus  with  a  velocity  of  120  turns 
in  a  minute  it  is  represented  by  2,810  millions  of  BA  units,  and  with  a  velocity 
of  450  turns  it  is  646  such  units. 

H  oltz's  machine  is  very  much  affected  by  the  moisture  of  the  air;  but 
Ruhmkorff  found  that  spreading  on  the  table  a  few  drops  of  petroleum,  the 
vapours  which  condense  on  the  machine  protect  it  against  the  moisture  of 
the  atmosphere. 

760.  Carre's  dielectrical  machine. — This  is  a  combination  of  the  old 
form  of  machine  with  that  of  Holtz. 

It  consists  of  two  plates  turning  in  opposite  directions  (fig.  618) :  one,  A,  of 
glass  and  the  other,  B,  of  ebonite.  They  overlap  each  other,  to  about  f  to  £ 
of  their  radii.  The  lower  one  is  slowly  turned  by  means  of  a  handle,  M, 
while  the  upper  one  is  rapidly  rotated  by  an  endless  cord,  which  passes  from 
the  large  over  the  small  wheel. 

The  plate  A,  after  having  been  electrified  positively  between  two  rubbers 
FF',  acts  inductively  through  the  plate  B  on  a  comb  /',  withdrawing  from  it 
negative  electricity,  which  then  passes  to  the  plate  B,  the  conductor  de 
remaining  positively  electrified  ;  but  as  the  plate  B  turns  very  quickly,  the 
negative  electricity,  as  it  collects  on  its  surface,  acts  inductively  on  a  second 
comb  g,  which  it  charges  with  negative  electricity,  reverting  itself  to  the 
neutral  state,  while  the  two  conductors  C  and  D,  which  are  connected  with 
the  comb  gy  become  charged  with  negative  electricity. 


666 


Frictional  Electricity. 


[760- 


These  conductors,  connected  as  they  are  by  two  ties,  m  and  ;z,  rest  on 
two  columns — the  one,  a,  of  glass,  and  the  other,  £,  of  ebonite.  A  chain  in 
connection  with  the  ground  is  suspended  from  a  hook,  O,  which  can  be  raised 
at  pleasure,  but  put  in  connection  with  the  comb  z.  The  rubbers,  FF',  more- 


Fig.  618. 

over,  are  in  connection  with  the  ground  by  means  of  two  bands  of  tinfoil 
along  the  supports. 

Lastly,  at/  (fig.  619)  is  a  sector  of  varnished  paper  cut  in  the  form  of 
a  comb,  and  fastened  to  an  insulating  segment,  P,  of  the  same  shape,  which 
is  used  as  support.  From  the  teeth  of  the  sector/  positive  electricity  flows 
on  the  plate  B  as  it  moves,  and  by  induction  this  sector/  yields  to  the  comb 
^  a  surcharge  of  negative  electricity.  The  rod  d  and  the  knob  e  may  be 
withdrawn  at  will  from  the  conductor  C  (fig.  618),  so  that  sparks  of  different 
lengths  may  be  taken.  At  r  is  a  hook  to  which  can  be  attached  the  Leyden 
jars  which  are  to  be  charged. 

Owing  to  the  direct  action  and  when  the  inducing  plate  is  at  the 
maximum  charge,  Carry's  machine  is  not  very  much  affected  by  moisture, 


-762] 


Experiments  with  the  Electrical  Machine. 


667 


and  it  yields  a  large  supply  of  electricity.  With  plates  whose  dimensions 
are  respectively  38  and  49  centimetres,  it  gives  sparks  of  15  to  18  centi- 
metres, and  more  when  a  condenser  is  

added,  as  in  Holtz's  machine. 

761.  Work  required  for  the  pro- 
duction of  electricity. — In  all  electrical 
machines  electricity  is  only  produced 
by  the  expenditure  of  a  definite  amount 
of  force,  as  will  at  once  be  seen  by  a 
perusal  of  the  preceding  descriptions. 
The  action  of  those  machines,  however, 
which  work  continuously,  is  somewhat 
complex.  Not  only  is  electricity  pro- 
duced, but  heat  also  ;  and  it  has  been 


Fig.  619. 


hitherto  impossible  to  estimate  separately  the  work  required  for  the  heat 
from  that  required  for  the  electricity.  This  is  easily  done  in  theory,  but 
not  in  practice  ;  how  difficult,  for  instance,  it  would  be  to  determine  the 
temperature  of  the  cushion,  or  of  the  plate  of  a  Ramsden's  machine  ! 

In  lifting  the  plate  off  a  charged  electrophorus,  a  certain  expenditure  ot 
force  is  needed,  though  it  be  too  slight  to  be  directly  estimated  (743).  With 
a  Holtz's  machine  it  may  be  readily  shown  by  experiment  that  there  is  a 
definite  expenditure  of  force  in  working  it.  If  such  a  machine  be  turned 
without  having  been  charged,  the  work  required  is  only  that  necessary  to 
overcome  the  passive  resistances.  If,  however,  one  of  the  sectors  be  charged 
and  the  electric  action  comes  into  play,  it  will  be  observed  that  there  must 
be  a  distinct  increase  in  the  force  necessary  to  work  the  machine. 

From  the  relation  between  the  quantity  of  heat  produced  by  the  current 
of  a  Holtz's  machine  working  under  definite  conditions,  and  the  amount  of 
work  expended  in  producing  the  rotation  of  the  plate,  Rossetti  has  made  a 
determination  of  the  mechanical  equivalent  of  heat  which  gave  the  number 
J?397  •  agreeing,  therefore,  very  well  with  the  numbers  obtained  by  other 
methods  (497). 

The  work  required  to  charge  an  unelectrified  conductor  to  a  given  poten- 
tial may  be  deduced  from  the  following  considerations  : — To  impart  to  a  body 
which  is  at  potential  V  a  quantity  of  electricity  O  would  require  an  amount 
of  work  represented  by  QV  (737).  But  at  the  outset  the  body  is  neutra — that 
is,  at  zero  potential ;  and  we  may  conceive  the  electricity  imparted  to  it 
in  a  series  of  n  very  small  charges,  such  that  nq  =  O  ;  and  as  the  potential 
rises  proportionally  to  the  number  of  charges,  it  may  be  assumed  that  the 
work  done  is  equal  to  that  required  to  charge  the  body  at  an  average  poten- 
tial of  4V  ;  hence  the  work  in  question  W7 


EXPERIMENTS    WITH   THE   ELECTRICAL   MACHINE. 

762.  Spark. — One  of  the  most  curious  phenomena  observed  with  the 
electrical  machine  is  the  spark  drawn  from  the  conductor  when  a  finger  is 
presented  to  it.  The  positive  electricity  of  the  conductor,  acting  inductively 
on  the  neutral  electricity  of  the  body,  decomposes  it,  repelling  the  positive 
and  attracting  the  negative.  When  the  attraction  of  the  opposite  electricities 


668 


Frictional  Electricity. 


[762- 


is  sufficiently  great  to  overcome  the  resistance  of  the  air,  they  recombine 
with  a  smart  crack  and  a  spark.  The  spark  is  instantaneous,  and  is  accom- 
panied by  a  sharp  prickly  sensation,  more  especially  with  a  powerful  machine. 
Its  shape  varies.  When  it  strikes  at  a  short  distance,  it  is  rectilinear,  as 
seen  in  fig.  620.  Beyond  two  or  three  inches  in  length,  the  spark  becomes 


Fig.  620. 


Fig.  621. 


Fig.  62 


irregular,  and  has  the  form  of  a  sinuous  curve  with  branches  (fig.  621).  If 
the  discharge  is  very  powerful,  the  spark  takes  a  zig-zag  shape  (fig.  622). 
These  two  latter  appearances  are  seen  in  the  lightning  discharge. 

A  spark  may  be  taken  from  the  human  body  by  the  aid  of  the  insulating 
stool,  which  is  simply  a  low  stool  with  stout  glass  legs.  The  person  standing 
on  this  stool  touches  the  prime  conductor,  and,  as  the  human  body  is  a  com- 
ductor,  the  electricity  is  distributed  over  its  surface  as  over  an  ordinary 
insulated  metallic  conductor.  The  hair  diverges  in  consequence  of  repulsion, 
a  peculiar  sensation  is  felt  on  the  face,  and  if  another  person,  standing  on 
the  ground,  presents  his  hand  to  any  part  of  the  body,  a  smart  crack  with  a 
pricking  sensation  is  produced. 

A  person  standing  on  an  insulated  stool  may  be  positively  electrified  by 
being  struck  with  a  catskin.  If  the  person  holding  the  catskin  stands  on  an 
insulated  stool,  the  striker  becomes  positively  and  the  person  struck  nega- 
tively electrified. 

763.  Electrical  chimes. — The  electrical  chimes  is  a  piece  of  apparatus 
consisting  of  three  bells  suspended  to  a  horizontal  metal  rod  (fig.  623).  Two 
of  them,  A  and  B,  are  in  metallic  connection  with  the  conductor ;  the  middle 
bell  hangs  by  a  silk  thread,  and  is  thus  insulated  from  the  conductor,  but  is 


-764] 


Electrical  Whirl  or  I  'ane. 


connected  with  the  ground  by  means  of  a  chain.  Between  the  bells  are 
small  copper  balls  suspended  by  silk  threads.  When  the  machine  is  worked, 
the  bells  A  and  B,  being  positively 
electrified,  attract  the  copper  balls,  and 
after  contact  repel  them.  Being  now 
positively  electrified,  they  are  in  turn 
attracted  by  the  middle  bell,  C,  which 
is  charged  with  negative  electricity  by 
induction  from  A  to  B.  After  contact 
they  are  again  repelled,  and  this  pro- 
cess is  repeated  as  long  as  the  machine 
is  in  action. 

Fig.  624  represents  an  apparatus 
originally  devised  by  Volta  for  the 
purpose  of  illustrating  what  he  sup- 
posed to  be  the  motion  of  hail  between  two  clouds  oppositely  electrified. 
It  consists  of  a  tubulated  glass  shade,  with  a  metal  base,  on  which  are 
some  pith  balls.  The  tubulure  has  a  metal  cap,  through  which  passes  a 


Fig.  623. 


Fig.  624. 


Fig.  625 


brass  rod,  provided  with  a  metal  disc  or  sphere  at  the  lower  end,  and  at  the 
upper  with  a  ring,  which  touches  the  prime  conductor. 

When  the  machine  is  worked,  the  sphere  becoming  positively  electrified 
attracts  the  light  pith  balls,  which  are  then  immediately  repelled,  and,  having 
lost  their  charge  of  positive  electricity,  are  again  attracted,  again  repelled, 
and  so  on,  as  long  as  the  machine  continues  to  be  worked.  An  amusing 
modification  of  this  experiment  is  frequently  made  by  placing  between  the 
two  plates  small  pith  figures,  somewhat  loaded  at  the  base.  When  the 
machine  is  worked,  the  figures  execute  a  regular  dance. 

764.  Electrical  whirl  or  vane. — The  electrical  whirl  or  vane  consists  of 
5  or  6  wires,  terminating  in  points,  all  bent  in  the  same  direction,  and  fixed 
in  a  central  cap,  which  rotates  on  a  pivot  (fig.  625).  When  the  apparatus 


6/O  Frictional  Electricity.  [764- 

is  placed  on  the  conductor,  and  the  machine  worked,  the  whirl  begins  to 
revolve  in  a  direction  opposite  that  of  the  points.  This  motion  is  not 
analogous  to  that  of  the  hydraulic  tourniquet  (215).  It  is  not  caused  by  a 
flow  of  material  fluid,  but  is  owing  to  a  repulsion  between  the  electricity  of 
the  points  and  that  which  they  impart  to  the  adjacent  air  by  conduction. 
The  electricity,  being  accumulated  on  the  points  in  a  high  state  of  density, 
passes  into  the  air,  and,  imparting  thus  a  charge  of  electricity,  repels  this 
electricity,  while  it  is  itself  repelled.  That  this  is  the  case  is  evident  from 
the  fact  that  on  approaching  the  hand  to  the  whirl  while  in  motion,  a  slight 
draught  is  felt,  due  to  the  movement  of  the  electrified  air,  while  in  vacuo  the 
apparatus  does  not  act  at  all.  This  draught  or  wind  is  known  as  the  elec- 
trical aura. 

If  the  experiment  be  made  in  water,  the  fly  remains  stationary,  for  water 
is  a  good  conductor ;  but  in  olive  oil,  which  is  a  bad  conductor,  the  whirl 
rotates. 

When  the  electricity  thus  escapes  by  a  point,  the  electrified  air  is  repelled 
so  strongly  as  not  only  to  be  perceptible  to  the  hand,  but  also  to  engender  a 
current  strong  enough  to  blow  out  a  candle.  Fig.  626  shows  this  experiment. 


Fig.  626.  Fig,  627. 

The  same  effect  is  produced  by  placing  a  taper  on  the  conductor  and  bring- 
ing near  it  a  pointed  wire  held  in  the  hand  (fig.  627).  The  current  arises  in 
this  case  from  the  flow  of  air  electrified  with  the  contrary  electricity  which 
escapes  by  the  point  under  the  influence  of  the  machine. 

The  electrical  orrery  and  the  electrical  inclined  plane  are  analogous  in 
their  action  to  these  pieces  of  apparatus. 


-765] 


Condensation  of  Electricity. 


671 


CHAPTER   IV. 

CONDENSATION  OF  ELECTRICITY. 

765.  Condensers.  Theory  of  condensers. — A  condenser  is  an  appa- 
ratus for  condensing  a  large  quantity  of  electricity  on  a  comparatively  small 
surface.  The  form  may  vary  considerably,  but  in  all  cases  consists  essentially 
of  two  insulated  conductors,  separated  by  a  non-conductor,  and  the  working 
depends  on  the  action  of  induction. 

Epinus's  condenser  consists  of  two  circular  brass  plates,  A  and  B  (fig.  628), 
with  a  sheet  of  glass,  C,  between  them.  The  plates,  each  provided  with  a 


Fig.  628. 

pith-ball  pendulum,  are  mounted  on  insulated  glass  legs,  and  can  be  moved 
along  a  support  and  fixed  in  any  position.  When  electricity  is  to  be  ac- 
cumulated, the  plates  are  placed  in  contact  with  the  glass,  and  then  one  of 
them,  B  for  instance,  is  connected  with  the  electrical  machine,  and  the  other 
placed  in  connection  with  the  ground,  as  shown  in  fig.  629. 

In  explaining  the  action  of  the  condenser,  it  will  be  convenient  in  each 
case  to  call  that  side  of  the  metal  plate  nearest  the  glass  the  anterior  and 
the  other  the  posterior  side.  And  first  let  A  be  at  such  distance  from  B  as 
to  be  out  of  the  sphere  of  its  action.  The  plate  B,  which  is  then  connected 
with  the  conductor  of  the  electrical  machine,  takes  its  maximum  charge, 


672  Frictional  Electricity.  [765— 

which  is  distributed  equally  on  its  two  faces,  and  the  pendulum  diverges 
widely.  If  the  connection  with  the  machine  be  interrupted,  nothing  would 
be  changed  ;  but  if  the  plate  A  be  slowly  approached,  its  neutral  fluid  being 
decomposed  by  the  influence  of  B,  the  negative  is  accumulated  on  its 
anterior  face,  n  (fig.  630),  and  the  positive  passes  into  the  ground.  But  as 
the  negative  electricity  of  the  plate  A  reacts  in  its  turn  on  the  positive  of 
the  plate  B,  the  latter  fluid  ceases  to  be  equally  distributed  on  both  faces 
and  is  accumulated  on  its  anterior  face,  m.  The  posterior  face,  p,  having 


\6 


Fig.  629 

thus  lost  a  portion  of  its  electricity,  its  density  has  diminished,  and  is  no 
longer  equal  to  that  of  the  machine,  and  the  pendulum,  b,  diverges  less 
widely.  Hence  B  can  receive  a  fresh  quantity  from  the  machine,  which, 
acting  as  just  described,  decomposes  by  induction  a  second  quantity  of 
neutral  fluid  on  the  plate  A.  There  is  then  a  new  accumulation  of  negative 

fluid  on  the  face  ;z,  and  consequently  of 
positive  fluid  on  m.  But  each  time  that 
the  machine  gives  off  electricity  to  the 
plate,  only  a  part  of  this  passes  to  the 
face  ;;?,  the  other  remaining  on  the  face 
p  ;  the  density  here,  therefore,  continues 
to  increase  until  it  equals  that  of  the 
machine.  From  this  moment  equilibrium 
is  established,  and  a  limit  to  the  charge 
is  attained  which  cannot  be  exceeded. 
The  quantity  of  electricity  accumulated 
now  on  the  two  faces  m  and  n  is  very  considerable,  and  yet  the  pendulum 
diverges  just  as  much  as  it  did  when  A  was  absent,  and  no  more ;  in  fact, 
the  density  at/  is  just  what  it  was  then — namely,  that  of  the  machine. 

When  the  condenser  is  charged — that  is,  when  the  opposite  electricities 
are  accumulated  on  the  anterior  faces—  connection  with  the  ground  is  broken 
by  raising  the  wires.  The  plate  A  is  charged  with  negative  electricity,  but 
simply  on  its  anterior  face  (fig.  630),  the  other  side  being  neutral.  The 


Fig.  630. 


-765]  Condensing  Force.  673 

plate  B,  on  the  contrary,  is  electrified  on  both  sides,  but  unequally ;  the 
accumulation  is  only  on  its  anterior  face,  while  on  the  posterior,  /,  the  den- 
sity is  simply  equal  to  that  of  the  machine  at  the  moment  the  connections 
are  interrupted.  In  fact,  the  pendulum  b  diverges,  and  a  remains  vertical. 
But  if  the  two  plates  are  removed,  the  two  pendulums  diverge  (fig.  628) 
which  is  owing  to  the  circumstance  that,  as  the  plates  no  longer  act  on  each 
other,  the  positive  fluid  is  equally  distributed  on  the  two  faces  of  the  plate 
B,  and  the  negative  on  those  of  the  plate  A. 

766.  Slow  discharge  and  instantaneous  discharge. — While  the  plates 
A  and  B  are  in  contact  with  the  glass  (fig.  629),  and  the  connections  inter- 
rupted, the  condenser  may  be  discharged — that  is,  restored  to  the  neutral 
state — in  two  ways  ;  either  by  a  slow  or  by  an  instantaneous  discharge.  To 
discharge  it  slowly,  the  plate  B — that  is,  the  one  containing  an  excess  of 
electricity — is  touched  with  the  finger  ;  a  spark  passes,  all  the  electricity  on 
p  passes  into  the  ground,  the  pendulum  b  falls,  but  a  diverges.  For  B,  hav- 
ing lost  part  of  its  electricity,  only  retains  on  the  face  m  that  held  by  the 
inductive  influence  of  the  negative  on  A.  But  the  quantity  thus  retained  at 
B  is  less  than  that  on  A  ;  this  has  free  electricity,  which  makes  the  pendulum 
a  diverge,  and  if  it  now  be  touched,  a  spark  passes,  the  pendulum  a  sinks 
while  b  rises,  and  so  on  by  continuing  to  touch  alternately  the  two  plates. 
The  discharge  only  takes  place  slowly  :  in  very  dry  air  it  may  require 
several  hours.  If  the  plate  A  were  touched  first,  no  electricity  would  be 
removed,  for  all  it  has  is  retained  by  that  of  the  plate  B.  To  remove  the 
total  quantity  of  electricity  by  the  method  of  alternate  contacts,  an  infinite 
number  of  such  contacts  would  theoretically  be  required. 

An  instantaneous  discharge  may  be  effected  by  means  of  the  discharging 
rod  (fag.  631).  This  consists  of  two  bent  brass  rods,  terminating  in  knobs, 
and  joined  by  a  hinge.  When  provided  with  glass  handles,  as  in  fig.  631, 
it  forms  a  glass  discharging  rod.  In  using  this  appa- 
ratus one  of  the  knobs  is  pressed  against  one  plate  of 
the  condenser,  and  the  other  knob  brought  near  the 
other.  At  a  certain  distance  a  spark  strikes  from  the 
plate  to  the  knob,  caused  by  the  sudden  recomposi- 
tion  of  the  two  opposite  electricities. 

When  the  condenser  is  discharged  by  the  dis- 
charger no  sensation  is  experienced,  even  though  the 
latter  be  held  in  the  hand  ;  of  the  two  conductors,  the 
electricity  chooses  the  better,  and  hence  the  discharge 
is  effected  through  the  metal,  and  not  through  the  body. 
But  if,  while  one  hand  is  in  contact  with  one  plate, 

the  other  touches  the  second,  the  discharge  takes  place  through  the  breast 
and  arms,  and  a  considerable  shock  is  felt ;  and  the  larger  the  surface  of 
the  condenser,  and  the  greater  the  electric  density,  the  more  violent  is 
the  shock. 

767.  Condensing:  force. — The  condensing  force  is  the  relation  between 
the   whole   charge,  which   the  collecting  plate  can  take  while  under  the 
influence  of  the  second  plate,  to  that  which  it  would  take  if  alone  :  in  other 
words,  it  is  the  relation  of  the  capacities  under  the  two  conditions. 

768.  Limit  of  the  charge  of  condensers. — The  quantity  of  electricity 

G  G 


6/4 


Frictional  Electricity. 


[768^ 


which  can  be  accumulated  on  each  plate  is,  c<zteris  paribus,  proportional 
to  the  density  of  the  electricity  on  the  conductor,  and  to  the  surface  of  the 
plates  ;  it  decreases  as  the  insulating  plate  is  thicker,  and  it  differs  with  the 
specific  inductive  capacity  of  the  substance.  Two  causes  limit  the  quantity 
of  electricity  which  can  be  accumulated.  First,  that  the  electric  density  of 
the  collecting  plates  gradually  increases,  and  ultimately  equals  that  of  the 
machine,  which  cannot,  therefore,  impart  any  free  electricity.  The  second 
cause  is  the  imperfect  resistance  which  the  insulating  plate  offers  to  the 
recombination  of  the  two  opposite  electricities  ;  for  when  the  force  which 
impels  the  two  electricities  to  recombine,  exceeds  the  resistance  offered  by 
the  insulating  plate,  it  is  perforated,  and  the  contrary  electricities  unite. 

769.  Fulminating-  pane.     Franklin's  plate. — This  is  a  simple  form  of 
the  condenser,  and  is  more  suitable  for  giving  strong  shocks  and  sparks. 

It  consists  of  a 
glass  plate  fixed  in 
a  wooden  frame 
(fig.  632)  •  on  each 
side  of  the  glass, 
pieces  of  tinfoil  are 
fastened  opposite 
each  other,  leaving 
a  space  free  be- 
tween the  edge  and 
the  frame.  It  is 
well  to  cover  this 
part  of  the  glass 
with  an  insulating 
layer  of  shellac  var- 
nish. One  of  the 
sheets  of  tinfoil  is 
connected  with  a 
ring  on  the  frame 
by  a  strip  of  tinfoil,  so  that  it  can  be  put  in  communication  with  the  ground 
by  means  of  a  chain.  To  charge  the  pane  the  insulated  side  is  connected 
with  the  machine.  As  the  other  side  communicates  with  the  ground,  the 
two  coatings  play  exactly  the  part  of  the  condenser.  On  both  plates  there 
are  accumulated  large  quantities  of  contrary  electricities. 

The  pane  may  be  discharged  by  pressing  one  knob  of  the  discharger 
against  the  lower  surface,  while  the  other  is  brought  near  the  upper  coating. 
A  spark  ensues,  due  to  the  recombination  of  the  two  electricities  ;  but  the 
operator  experiences  no  sensation,  for  the  discharge  takes  place  through  the 
wire.  But  if  the  connection  between  the  two  coatings  be  made  by  touching 
them  with  the  hands  a  violent  shock  is  felt  in  the  hands  and  breast,  for  the 
combination  then  takes  place  through  the  body. 

770.  Ley  den  jar. — The  Leyden  jar,  so  named  from  the  town  of  Leyden, 
where  it  was  invented,  is  essentially  a  modified  condenser  or  fulminating  pane 
rolled  up.     Fig.  631  represents  a  Leyden  jar  of  the  usual  French  shape  in 
the  process    of  being  charged.     It  consists  of  a  glass  jar  of  any  conve- 
nient size,  the  interior  of  which  is  either  coated  with  tinfoil  or  filled  with  thin 


Fig.  632. 


-770] 


Leydeti  Jar. 


leaves  of  copper,  or  with  gold  leaf.  Up  to  a  certain  distance  from  the  neck  the 
outside  is  coated  with  tinfoil.  The  neck  is  provided  with  a  cork,  through 
which  passes  a  brass  rod, 

which  terminates  at  one  ^m±.          A 

end  in  a  knob,  and  com- 
municates with  the  metal 
in  the  interior.  The  me- 
tallic coatings  are  called 
respectively  the  internal 
and  external  coatings. 
Like  the  condenser,  the 
jar  is  charged  by  connect- 
ing one  of  the  coatings 
with  the  ground,  and  the 
other  with  the  source  of 
electricity.  When  it  is  held  in  the  hand  by  the  external  coating,  and  the  knob 
presented  to  the  positive  conductor  of  the  machine,  positive  electricity  is 
accumulated  on  the  inner  and  negative  electricity  on  the  outer  coating. 
The  reverse  is  the  case  if  the  jar  is  held  by  the  knob,  and  the  external  coat- 
ing presented  to  the  machine.  The  positive  charge  acting  inductively  across 
the  dielectric  glass,  decomposes  the  electricity  of  the  outer  coating,  attracting 
the  negative,  and  repelling  the  positive,  which  escapes  by  the  hand  to  the 
ground.  Thus  it  will  be  seen  that  the  action  of  the  jar  is  the  same  as  that 
of  the  condenser,  and  all  that  has  been  said  of  this  applies  to  the  jar,  sub- 
stituting the  two  coatings  for  the  two  plates  A  and  B  of  fig.  629. 


.  633. 


Fig.  634, 


Fig.  635. 


Like  any  other  condenser,  the  Leyden  jar  may  be  discharged  either  slowly 
or  instantaneously.  For  the  latter  purpose  it  is  held  in  the  hand  by  the  out- 
side coating  (fig.  634),  and  the  two  coatings  are  then  connected  by  means  of 
the  simple  discharger.  Care  must  be  taken  to  touch  first  the  external  coating 
with  the  discharger,  otherwise  a  smart  shock  will  be  felt.  To  discharge 
it  slowly  the  jar  is  placed  on  an  insulated  plate,  and  first  the  inner  and 

G  G  2 


676  Frictional  Electricity.  [770- 

then  the  outer  coating  touched,  either  with  the  hand  or  with  a  metallic 
conductor.  A  slight  spark  is  seen  at  each  discharge. 

Fig.  635  represents  a  very  pretty  experiment  for  illustrating  the  slow 
discharge.  The  rod  terminates  in  a  small  bell,  d,  and  the  outside  coating 
is  connected  with  an  upright  metallic  support,  on  which  is  a  similar  bell,  <?. 
Between  the  two  bells  a  light  brass  ball  is  suspended  by  a  silk  thread.  The 
jar  is  then  charged  in  the  usual  manner  and  placed  on  the  support  m.  The 
internal  coating  contains  a  quantity  of  free  electricity  ;  the  pendulum  is 
attracted  and  immediately  repelled,  striking  against  the  second  bell,  to  which 
it  imparts  its  free  electricity.  Being  now  neutralised,  it  is  again  attracted  by 
the  first  bell,  and  so  on  for  some  time,  especially  if  the  air  be  dry,  and  the 
jar  somewhat  large. 

771.  Leyden  jar  with  moveable  coatings.— This  apparatus  (fig.  636)  is 
used  to  demonstrate  that  in  the  Leyden  jar  the  opposite  electricities  are  not 
distributed  on  the  coatings  merely,  but  reside  principally  on  the  opposite 
sides  of  the  glass.  It  consists  of  a  somewhat  conical  glass  vessel,  B,  with 


Fig.  636. 

moveable  coatings  of  zinc  or  tin,  C  and  D.  These  separate  pieces  placed  one 
in  the  other,  as  shown  in  figure  A,  form  a  complete  Leyden  jar.  After  having 
charged  the  jar,  it  is  placed  on  an  insulating  cake  ;  the  internal  coating  is  first 
removed  by  the  hand,  or  better  by  a  glass  rod,  and  then  the  glass  vessel.  The 
coatings  are  found  to  contain  little  or  no  electricity,  and  if  they  are  placed  on 
the  table  they  are  restored  to  the  neutral  state.  Nevertheless,  when  the  jar 
is  put  together  again,  as  represented  in  the  figure  at  A,  a  shock  may  be  taken 
from  it  almost  as  strong  as  if  the  coatings  had  not  been  removed.  It  is 
therefore  concluded  that  the  coatings  merely  play  the  part  of  conductors, 
distributing  the  electricity  over  the  surface  of  the  glass,  which  thus  becomes 
polarised,  and  retains  this  state  even  when  placed  on  the  table,  owing  to  its 
imperfect  conductivity. 

The  experiment  may  be  conveniently  made  by  forming  a  Leyden  jar,  of 
which  the  inside  and  outside  coatings  are  of  mercury,  charging  it ;  then 
having  mixed  the  two  coatings,  the  apparatus  is  put  together  again,  upon 
which  a  discharge  may  be  once  more  taken. 

772.  Xiichtenberg's  figures. — This  experiment  well  illustrates  the  oppo- 
site electrical  conditions  of  the  two  coatings  of  a  Leyden  jar.  Holding  a 
jar  charged  with  positive  electricity  by  the  hand,  a  series  of  lines  are  drawn 
with  the  knob  on  a  cake  of  resin  or  vulcanite  ;  then  having  placed  the  jar 


-773]  Penetration  of  the  Charge.  677 

on  an  insulator,  it  is  held  by  the  knob,  and  another  series  traced  by  means 
of  the  outer  coating.  If  now  a  mixture  of  red-lead  and  flour  of  sulphur  be 
projected  on  the  cake,  the  sulphur  will  attach  itself  to  the  positive  lines,  and 
the  red-lead  to  the  negative  lines  ;  the  reason  being  that  in  mixing  the 
powders  the  sulphur  has  become  negatively  electrified,  and  the  red-lead 
positively.  The  sulphur  will  arrange  itself  in  tufts  with  numerous  diverging 
branches,  while  the  red-lead  will  take  the  form  of  small  circular  spots,  in- 
dicating a  difference  in  the  two  electricities  on  the  surface  of  the  resin. 

773.  Penetration  of  the  charge.  Residual  charge. — Not  only  do  the 
electricities  adhere  to  the  two  surfaces  of  the  insulating  medium  which 
separates  them,  but  they  penetrate  to  a  certain  extent  into  the  interior,  as  is 
shown  by  the  following  experiment : — A  condenser  is  formed  of  a  plate  of 
shellac,  and  moveable  metal  plates.  It  is  then  charged,  retained  in  that 
state  for  some  time,  and  aftenvards  discharged.  On  removing  the  metal 
coatings  and  examining  both  surfaces  of  the  insulator,  they  show  no  signs  of 
electricity.  After  some  time,  however,  each  face  exhibits  the  presence  of 
some  electricity  of  the  same  kind  as  that  of  the  plate  with  which  it  was  in 
contact  while  the  apparatus  was  charged.  This  is  explained,  by  some,  by 
assuming  that  the  electricity  had  slowly  penetrated  from  the  exterior  to  the 
interior  during  the  first  phase  of  the  experiment,  and  had  returned  to  the 
surface  during  the  second. 

A  phenomenon  frequently  observed  in  Leyden  jars  is  of  the  same  nature. 
When  a  jar  has  been  discharged  and  allowed  to  stand  a  short  time,  it  ex- 
hibits a  second  charge,  which  is  called  the  electric  residue.  The  jar  may  be 
again  discharged,  and  a  second  residue  will  be  left,  feebler  than  the  first, 
and  so  on,  for  three  or  four  times.  Indeed,  with  a  delicate  electroscope  a 
long  succession  of  such  residues  may  be  demonstrated.  Time  is  required 
for  the  penetration  of  the  electricities  into  the  mass  ;  and  hence  the  residue 
is  greater  the  longer  the  jar  has  remained  charged.  The  magnitude  of  the 
residue  further  depends'on  the  amount  of  the  charge,  and  also  on  the  degree 
in  which  the  metal  plates  are  in  contact  with  the  insulator.  It  varies  with 
the  nature  of  the  substance,  but  there  is  no  residue  with  either  liquids  or 
gaseous  insulators.  Faraday  found  that  with  paraffine  the  residue  was 
greatest,  then  with  shellac,  while  with  glass  and  sulphur  it  was  least  of  all. 
Kohlrausch  has  found  that  the  residue  is  nearly  proportional  to  the  thickness 
of  the  insulator.  If  successive  small  charges,  alternately  positive  and 
negative,  be  imparted  to  the  jar,  it  is  found  that  the  residual  charges  come  out 
in  the  reverse  order  in  which  the  original  charges  go  in. 

It  is  probable  that  the  dielectric  in  a  charged  Leyden  jar  is  in  a  condition 
resembling  that  of  an  elastic  body  subjected  to  a  mechanical  strain.  An 
elastic  plate  which  has  been  bent  continually  tends  to  revert  to  its  original 
condition  ;  when  the  straining  force  is  removed  it  does  not  completely  regain 
its  original  shape ;  a  certain  length  of  time  is  required  for  this  elastic  after- 
action  to  take  place.  This  is  quite  analogous  to  the  residual  charge  in  the 
Leyden  jar;  an  analogy  which  is  confirmed  by  Hopkinson's  experimental 
observation,  that  the  reappearance  of  the  residual  charge,  like  the  resilience 
of  an  elastic  body,  is  accelerated  by  the  gentle  mechanical  action  of  tapping 
the  jar.  The  same  observer  draws  a  parallel  between  the  phenomena  of  the 
residual  charge  and  those  of  residual  magnetism  (715). 


6/8 


Frictional  Electricity. 


[774- 


774.  Electric  batteries. — The    charge   which   a    Leyden  jar  can  take 
depends  on  the  extent  of  the  coated  surface,  and  for  small  thicknesses  is 
inversely  proportional  to  the  thickness  of  the  insulator.     Hence,  the  larger 
and  thinner  the  jar  the  more  powerful  the  charge.     But  very  large  jars  are 

expensive,  and  li- 
able to  break  ;  and 
when  too  thin,  the 
accumulated  elec- 
tricities are  apt  to 
discharge  them- 
selves through  the 
glass,  especially  if 
it  is  not  quite  ho- 
mogeneous. Ley- 
den  jars  have 
usually  from  \  to  3 
square  feet  of  coated 
surface.  For  more 
powerful  charges 
electric  batteries 
are  used. 

An  electric  bat- 
tery consists   of  a 

-    637-  •  f          T  j 

series     of    Leyden 

jars,  whose  internal  and  external  coatings  are  respectively  connected  with 
each  other  (fig.  637).  They  are  usually  placed  in  a  wooden  box  lined  on  the 
bottom  with  tinfoil.  This  lining  is  connected  with  two  metal  handles  in  the 
sides  of  the  box.  The  inner  coatings  are  connected  with  each  other  by 
metallic  rods,  and  the  battery  is  charged  by  placing  the  inner  coatings  in 
connection  with  the  prime  conductor,  while  the  outer  coatings  are  connected 
with  the  ground  by  means  of  a  chain  fixed  to  the  handles.  A  quadrant 
electrometer  fixed  to  one  jar  indicates  the  charge  of  the  battery.  Although 
there  is  a  large  quantity  of  electricity  accumulated  in  the  apparatus  the 
divergence  is  not  great,  for  it  is  simply  due  to  the  free  electricity  on  the 
inner  coating.  The  larger  and  more  numerous  they  are,  the  longer  is  the 
time  required  to  charge  the  battery,  but  the  effects  are  so  much  the  more 
powerful. 

When  a  battery  is  to  be  discharged,  the  coatings  are  connected  by  means 
of  the  discharging  rod,  the  outside  coating  being  touched  first.  Great  care 
is  required,  for  with  large  batteries  serious  and  even  fatal  accidents  may  occur. 

775.  The  universal  discharger. — This  is  an  almost  indispensable  ap- 
paratus in  experiments  with  the  electric  battery.     On  a  wooden  stand  (fig. 
638)  are  two  glass  legs,  each  provided  with  universal  joints,  in  which  moveable 
brass  rods  are  fitted.     Between  these  legs  is  a  small  ivory  table,  on  which  is 
placed  the  object  under  experiment.     The  two  metal  knobs  being  directed 
towards  the  objects,  one  of  them  is  connected  with  the  outer  coating  of 
the  battery,  and  the  moment  communication  is  made  between  the  outer  and 
the  inner  coating  by  means  of  the  glass  discharging  rod,  a  violent  shock 
passes  through  the  object  on  the  table. 


-776] 


CJiarging  by  Cascade. 


679 


776.  Charging  by  cascade. — A  series  of  Leyden  jars  are  placed  each 
separately  on  insulating  supports.  The  knob  of  the  first  is  in  connection 
with  the  prime  conductor  of  the  machine,  and  its  outer  coating  joined  to  the 
knob  of  the  second,  the  outer  coating  of  the  second  to  the  knob  of  the  third, 
and  so  on  ;  the  outer  coating  of  the  last  communicating  with  the  ground. 
The  inner  coating  of  the  first  receives  a  charge  of  positive  electricity  from 


Fig.  638, 

the  machine,  and  the  corresponding  positive  electricity  set  free  by  induction 
on  its  outer  coating,  instead  of  passing  to  the  ground,  gives  a  positive  charge 
to  the  inner  coating  of  the  second,  which,  acting  in  like  manner,  develops  a 
charge  in  the  third  jar,  and  so  on,  to  the  last,  where  the  positive  electricity 
developed  by  induction  on  the  outer  coating  passes  to  the  ground.  The  jars 
may  be  discharged  either  singly  by  connecting  the  inner  and  outer  coatings 
of  each  jar,  or  simultaneously  by  connecting  the  inner  coating  of  the  first 
with  the  outer  of  the  last.  In  this  way  the  quantity  of  electricity  necessary 
to  charge  one  jar  is  available  for  charging  a  series  of  jars. 

For  from  the  preceding  explanation  it  is  clear,  that  with  a  series  of 
similar  Leyden  jars  charged  by  cascade,  if  we  call  the  charge  of  positive 
electricity  which  the  inside  of  the  first  jar  receives  I,  it  will  develop  by  in- 
duction on  the  outside  a  quantity  m(m<  i)  of  negative  electricity,  and  the 
same  quantity  in  of  positive  electricity  which  will  pass  into  the  inside  of  the 
second  jar  ;  this  in  turn  will  develop  ;;/  x  111  =  1)1*  of  negative  electricity  on 
the  outside  of  that  jar,  and  the  same  quantity  m*  of  positive  electricity  \\ill 


68o  Frictional  Electricity.  [776- 

pass  into  the  inside  of  the  third  jar,  and  so  forth.  Thus  it  will  be  seen  that 
the  quantities  of  positive  electricity  developed  in  a  series  of  n  similar  jars  by 
the  unit  charge  of  positive  electricity  will  be 

i  —  ;/zn 
i  4-  m  +  wr  +  ;;z  +     .     .     .     m       = •> 

and  of  negative  electricity  on  the  corresponding  outsides  of 

m  ( i  -  ;;zn) 
m  +  nr  +  ?/r  +  m  +     .     .     .     mr  =  —  —  • 

I  —  //2 

Thus,  if  there  be  six  jars  and  m  =  0-9,  the  quantity  of  positive  electricity 
developed  by  the  unit  charge  is  4-69. 

777.  Measurement  of  the  cliarg-e  of  a  "battery,  lane  s  electro- 
meter.— When  the  outer  and  inner  coatings  of  a  charged  Leyden  jar 
are  gradually  brought  nearer  each  other,  at  a  certain  distance  a  spontaneous 

discharge  ensues.  The  distance 
is  called  the  striking  distance. 
It  is  inversely  proportional  to 
the  pressure  of  the  air  and 
directly  proportional  to  the  elec- 
tric density  of  that  point  of  the 
inner  coating  at  which  the  dis- 
charge takes  place.  As  the 
density  of  any  point  of  the  inner 
coating,  other  things  remaining 

~ ~  the  same,  is  proportional  to  the 

entire  charge,  the  striking  dis- 
tance is  proportional  to  the  quantity  of  electricity  in  a  jar.  The  measure- 
ment of  the  charge  of  a  battery,  however,  by  means  of  the  striking  distance, 
can  only  take  place  when  the  charge  disappears. 

By  means  of  Lane's  electrometer,  which  depends  on  an  application  of 
this  principle,  the  charge  of  a  jar  or  battery  may  be  measured.  This 
apparatus,  c  (fig.  639),  consists  of  an  ordinary  Leyden  jar,  near  which  there 
is  a  vertical  metallic  support.  At  the  upper  end  is  a  brass  rod,  with  a  knob 
at  one  end,  which  can  be  placed  in  metallic  connection  with  the  outside  of 
the  jar  :  the  rod  being  moveable,  the  knob  can  be  kept  at  a  measured  dis- 
tance from  the  knob  of  the  inner  coating.  Fig.  639  represents  the  operation 
of  measuring  the  charge  of  a  jar  by  means  of  this  apparatus.  The  jar  $, 
whose  charge  is  to  be  measured,  is  placed  on  an  insulated  stool  with  its 
outer  coating  in  metallic  connection  with  the  inner  coating  of  Lane's  jar  c, 
the  outer  coating  of  which  is  in  connection  with  the  ground,  or  still  better 
with  a  system  of  gas  or  water  pipes  ;  a  is  the  conductor  of  the  machine. 
When  the  machine  is  worked,  positive  electricity  passes  into  the  jar  b  ;  a  pro- 
portionate quantity  of  positive  electricity  is  repelled  from  its  outer  coating, 
passes  into  the  inner  coating  of  the  electrometer,  and  there  produces  a 
charge.  When  this  has  reached  a  certain  limit,  it  discharges  itself  between 
the  two  knobs,  and  as  often  as  such  a  discharge  takes  place,  the  same 
quantity  of  positive  electricity  will  have  passed  from  the  machine  into  the 
battery;  hence  its  charge  is  proportional  to  the  number  of  discharges  of  the 
electrometer. 


-779]  Volte!  s  Condensing  Electroscope.  68 1 

Harris's  unit  jar  (fig.  640)  is  an  application  of  the  same  principle,  and  is 
very  convenient  for  measuring  quantities  of  electricity.  It  consists  of  a  small 
Leyden  phial,  4  inches  in  length  and  £ 
of  an  inch  in  diameter,  coated  to  about 
an  inch  from  the  end,  so  as  to  expose 
about  6  inches  of  coated  surface.  It  is 
fixed  horizontally  on  a  long  insulator, 
and  the  charging  rod  connected  at  P 
with  the  conductor  of  the  machine,  while 
the  outer  coating  is  connected  with  the 
jar  or  battery  by  the  rod  /  p.  When  the 
accumulation  of  electricity  in  the  interior 

has  reached  a  certain  height  depending  on  the  distance  of  the  two  balls  ;// 
and  /;,  a  discharge  ensues,  and  marks  a  certain  quantity  of  electricity  received 
as  a  charge  by  the  battery,  in  terms  of  the  small  jar. 

778.  Xiaws  of  electric  charge. — Harris,  by  means  of  experiments  with 
the  unit  jar  suitably  modified,  and  Riess,  by  analogous  arrangements,  have 
found,  by  independent  researches,  that  for  small  distances  the  striking  dis- 
tance is  directly  proportional  to  the  quantity  of  electricity,  and  inversely 
proportional  to  the  extent  of  coated  surface  ;  in  other  words,  it  is  proportional 
to  the  electric  density.     Thus,  taking  the  surface  of  one  jar  as  unity,  if  a 
battery  of  six  Leyden  jars  charged  by  100  turns  of  the  machine  has  a  striking 
distance  of  9  millimetres,  a  battery  of  four  similar  jars  charged  by  120  turns 
will  have  the  striking  distance  of  16-2  millimetres.     For 

'°°:  9=—^.-^=.6-2 
6  4 

The  charge  also  depends  on  the  nature  of  the  glass,  or  other  dielectric,  of 
which  the  jar  is  made  ;  and,  further,  is  stated  by  Wheatstone  to  be  inversely 
proportional  to  the  square  of  the  thickness  of  the  dielectric.  Riess  has  also 
found  that  when  a  battery  or  jar  is  discharged  in  the  striking  distance,  a 
charge  still  remains  ;  for  when  the  coatings  are  brought  nearer,  a  similar  dis- 
charge may  be  taken,  and  so  on.  The  amount  of  this  residual  charge,  when 
the  discharge  takes  place  at  the  greatest  striking  distance,  is  always  in  the 
same  proportion  to  the  entire  charge.  In  Riess's  experiments,  0*846  or  }}  of 
the  total  charge  disappeared,  and  only  ^  remained. 

779.  Volta's  condensing:  electroscope. — The  condensing  electroscope 
invented  by  Volta  is  a  modification  of  the  ordinary  gold-leaf  electroscope 
(751).     The  rod  to  which  the  gold  leaves  are  affixed  terminates  in  a  disc 
instead  of  in  a  knob,  and  there  is  another  disc  of  the  same  size  provided  with 
an  insulating  glass  handle.     The  discs  are  covered  with  a  layer  of  insulating 
shellac  varnish  (fig.  641). 

To  render  very  small  quantities  of  electricity  perceptible  by  this  apparatus, 
one  of  the  plates,  which  thus  becomes  the  collecting  plate,  is  touched  with 
the  body  under  examination.  The  other  plate,  the  condensing  plate,  is  con- 
nected with  the  ground  by  touching  it  with  the  finger.  The  electricity  of 
the  body,  being  diffused  over  the  collecting  plate,  acts  inductively  through 
the  varnish  on  the  neutral  fluid  of  the  other  plate,  attracting  the  opposite 
electricity,  but  repelling  that  of  like  kind.  The  two  electricities  thus  become 

G  G  3 


682 


Frictional  Electricity. 


[779- 


accumulated  on  the  two  plates  just  as  in  a  condenser,  but  there  is  no  diver- 
gence of  the  leaves,  for  the  opposite  electricities  counteract  each  other  The 
finger  is  now  removed,  and  then  the  source  of  electricity,  and  still  there  is  no 
divergence;  but  if  the  upper  plate  be  raised  (fig.  642)  the  neutralisation 
ceases,  and  the  electricity  being  free  to  move  diffuses  itself  over  the  rod  and 
the  leaves,  which  then  diverge  widely.  The  delicacy  of  the  apparatus  is  in- 
creased by  adapting  to  the  foot  of  the  apparatus  two  metallic  rods,  termi- 
nating in  knobs,  for  these  knobs  being  excited  by  induction  from  the  gold 
leaves  react  upon  them. 

A  still  further  degree  of  delicacy  is  attained  if  the  rods  be  replaced  by  two 


Fig.  641. 


Fig.  642. 


Bohnenberger's  dry  piles,  one  of  which  presents  its  positive  and  the  other  its 
negative  pole.  Instead  of  two  gold  leaves  there  is  only  one  ;  the  least  trace 
of  electricity  causes  it  to  oscillate  either  to  one  side  or  to  the  other,  and  at 
the  same  time  shows  the  kind  of  electricity. 

780.  Thomson's  quadrant  electrometer. — Sir  William  Thomson  has 
devised  a  new  and  delicate  form  of  electrometer,  by  which  accurate  measure- 
ments of  the  amount  of  electrical  charge  may  be  made.  The  principle  of 
this  instrument  may  be  understood  from  the  following  description  of  a  form 
of  it  constructed  for  lecture  purposes  by  Messrs.  Elliott. 

A  light  flat  broad  aluminium  needle  (fig.  643)  hangs  by  a  very  fine  wire 
from  the  inner  coating  of  a  charged  Leyden  jar,  the  outer  coating  being  in 
conducting  communication  with  the  earth.  The  whole  apparatus  is  enclosed 
within  a  glass  shade,  and  the  air  is  kept  dry  by  means  of  a  dish  of  sulphuric 


-781] 


Thomson's  Absolute  Electrometer. 


683 


acid  ;  there  is,  therefore,  very  little  loss  of  electricity,  and  the  needle  remains 
at  a  virtually  constant  charge. 

The  needle  is  suspended  over 
four  quadrantal  metal  plates,  in- 
sulated  from  each  other  and  from 
the  ground  by  resting  on  glass 
rods.  The  alternate  quadrants 
are  in  conducting  communication 
with  each  other  by  means  of  wires. 
If  now  all  the  quadrants  are  in  the 
same  electrical  condition,  the  needle 
will  be  at  rest  when  it  is  directly 
over  one  of  the  diametrical  slits. 
But  if  the  two  pairs  of  quadrants 
are  charged  with  opposite  kinds  of 
electricity,  as  when,  for  instance, 
they  are  connected  with  the  two 
poles  of  an  insulated  voltaic  cell  by 
means  of  the  knobs,  then  each  end 
of  the  needle  will  be  repelled  by  the 
pair  of  quadrants  which  are  electri- 
fied like  itself,  and  will  be  attracted 
by  the  other  pair.  It  will  thus  be 
subject  to  the  action  of  a  couple 
tending  to  set  it  obliquely  to  the  slit. 

In  order  to  render  the  slightest  motion  of  the  needle  visible,  a  small 
silver  concave  mirror  with  a  radius  of  about  a  metre  is  fixed  above  it.  The 
light  of  a  petroleum  lamp,  not  represented  in  the  figure,  strikes  against  this, 
and  is  reflected  as  a  spot  on  a  horizontal  scale.  Any  deflection  of  the  needle, 
either  on  one  side  or  the  other,  is  indicated  by  the  motion  of  the  spot  of 
light  on  the  scale  (520). 

781.  Thomson's  absolute  electrometer. — Another  class  of  electro- 
meters, also  invented  by  Sir  W.  Thomson,  have  the  advantage  of  furnishing 
a  direct  measure  of  electrical  constants  in  absolute  measure.  Fig.  644 
represents  the  essential  features  of  a  modified  form  of  the  electrometer, 
which  has  been  devised  by  Professor  Foster  for  class  experiments. 

Two  plane  metal  discs  A  and  B,  about  10  cm.  in  diameter,  are  kept  at  a 
distance  from  each  other,  which  is  small  in  proportion  to  their  diameters, 
but  which  can  be  very  accurately  measured.  Out  of  the  centre  of  the  upper 
one  is  cut  a  disc  c ;  this  is  suspended  by  insulating  threads  from  one  end  of 
the  arm  a  b  of  a  balance,  at  the  other  end  of  which  is  a  counterpoise,  or  a 
scale  pan  p.  At  the  end  of  the  arm  is  a  fork,  across  which  is  stretched  a 
line  wire ;  when  the  disc  is  exactly  in  the  plane  of  the  circular  band  or  ring, 
which  surrounds  it,  and  which  is  called  the  guard  ring,  this  fine  wire  is 
exactly  across  the  interval  between  two  marks  in  the  upright,  and  the  posi- 
tion of  which  can  be  accurately  determined  by  means  of  the  lens  C.  The 
disc  and  the  guard  ring  are  kept  at  a  constant  potential,  being  connected  by 
a  wire  with  a  constant  source  of  electricity,  while  the  other  can  be  kept  at 
any  potential. 


684 


Friciional  Electricity. 


[781- 


Suppose  now  that  the  whole  system  is  at  the  same  potential,  and  that  the 
disc  is  exactly  balanced  so  as  to  be  in  the  plane  of  the  guard  ring.     If  now 

it  be    electrified  to    a  given 
potential,    while     the    other 
plate  is  connected  with   the 
earth,  then  the  body  charged 
with  electricity  of  higher  po- 
tential— that  is,  the  disc — will 
be  urged  towards  the  body 
of  lower  potential,  the  fixed 
plate,  and  in  order  to  retain 
it  exactly  in  the  plane  of  the 
guard  ring  the  force  applied 
at  the  other  end  of  the  lever 
must     be     increased.      This 
may  be  done  by  altering  the 
________  distance  of  the  counterpoise, 

or  by  adding    weights  to    a 

scale  pan,  and  the  additional  force  thus  applied  is  a  measure  of  the  attractive 
force. 

Now  it  can  be  shown  that  the  attractive  force  between  any  two  plates 
electrified  to  different  potentials  is  proportional  to  the  square  of  the  differ- 
ence of  potentials,  provided  the  distance  between  them  is  small  in  comparison 
with  their  area,  and  that  the  portions  of  the  plates  opposite  each  other  are 
at  some  distance  from  the  edge.  These  conditions  are  fulfilled  in  the  above 
case.  If  S  is  the  area  of  the  disc,  of  the  distance  of  the  plates,  V- Va  the 
difference  of  potentials,  and  F  the  force  required  to  balance  a  certain  attrac- 
tion, then 

F_(v-v-)'s 


^O;  this  is  and  V 


Now  as  F  is  expressed  by  a  weight,  and  S  and  ^/are  measures  of  length,  we 
have  a  means  of  expressing  difference  of  potentials  in  absolute  measure  (709). 

It  is  also  clear  that  the  experiments  may  be  modified  by  making  the 
weight  constant,  and  the  distance  variable.  By  means  of  micrometric 
arrangements  the  distance  of  the  plates  may  be  varied  and  measured  with 
very  great  accuracy. 

782.  Potential  of  a  leyden  jar. — Let  us  suppose  A  (fig.  645)  to  represent 
an  insulated  metal  sphere,  and  let  us  consider  it  placed  in  conducting  com- 
munication with  a  source  of,  say,  positive  electricity,  which  is  supposed  to  be 

at  a  constant  potential  V.     Then  its  potential  V  is  "  ,  and  its  charge  q  =  VR, 

R 

R  being  the  radius  of  the  sphere  A, 

Suppose  now  it  be  possible  to  surround  this  sphere  by  an  external  con- 
ducting shell,  B,  which  is  in  connection  with  the  ground  ;  movements  of 
electricity  will  take  place  ;  a  new  equilibrium  will  be  established,  and  there 
will  now  be  two  electrical  layers — one  on  the  sphere  A,  and  the  other  on  the 


-782]  Potential  of  a  Ley  den  Jar.  68  5 

sphere  B.     These  will  have  no  action  on  any  external  point,  which  is  only 
possible  provided  the  charges  are  equal  and  contrary.     If  +  Q  is  the  charge 
on  the  inner  sphere,  then  —  Q  is  that  on  the 
outer. 

The  charge  of  the  original  sphere  is  at 
first  not  altered  by  this  operation,  but  its 
potential  is  less,  its  capacity  being  now 
greater,  and,  as  it  is  in  contact  with  the 
source,  which  is  constant,  it  receives  fresh 
charges  of  electricity  until  it  is  again  at  the 
potential  of  the  source  V. 

Now  let  us  suppose  that  the  insulating 
layer  which  separates  the  inner  from  the 
outer  coating  is  air,  and  that  its  thickness  is 
/  ;  then  the  potential  V  of  the  whole  system  is  Fig.  645. 

made  up  of  two  parts  Q,the  first  due  to  the  elec- 

trical charge  of  the  inner  sphere  V-   +  ^,  and  the  second  due  to  the  charge 


of  theouter  sphere  =-S;  that  is,  V  =  Q  -  1  -  ^=  ,Rl'  or  Q 

ff     R'  —  R 
Now,  the  charge  of  the  insulated  sphere  q  =  VR  ;  hence  i  =  —  —  —  .      But 

Q         K 

R'—  R  is  the  thickness  of  the  insulator,  which,  for  the  sake  of  simplicity,  we 

O      Rr 
will  suppose  is  air,  and,  calling  this  /,  we  have  -£  =  —  ;    that    is,  that    the 

charge  is  inversely  as  the  thickness. 

It  is  to  be  observed  that  the  results  here  obtained  apply  strictly  only  to 
the  supposed  case  in  which  the  inner  conductor  is  completely  surrounded  by 
the  outer  one,  which  is  not  the  case  with  the  ordinary  form  of  a  Leyden 
jar.  It  may,  however,  be  applied  to  them  if  we  compare  homologous  jars  ; 


in  the  above  formula  Q  =  —       ,  if  R  and  R'  are  nearly  equal,  then  Q  = 

Kj  —  K  / 

^  -  ——  —  where  S  is  the  surface  and  /  the  thickness  of  the  insulating  coat- 
47r/        4irt 

c 
ing.      In  this  formula  —  is  a  constant  for  a  Leyden  jar  of  given  dimen- 

47J-/ 

sions,  and  represents  the  capacity  of  the  jar. 

If  instead  of  air  there  be  a  solid  or  liquid  dielectric,  whose  specific  induc- 

tive capacity  is  AC,  the  formula  becomes  Q=    —  =  —  *.    If  the  dielectric  be 

" 


K 


partly  air  and  partly  some  other  material  such  as  glass,  then  if  the  thick- 

VS 
ness  of  this  latter  is  6,  Q  -  —  —  .     The   expression  6  is   sometimes 


written  /',  and  represents  the  thickness  of  the  layer  of  air  equivalent  to  it  in 
specific  inductive  capacity.     It  is  also  called  the  reduced  thickness. 


686  Fractional  Electricity.  [783- 


THE   ELECTRIC   DISCHARGE. 

783.  Effects  of  the  electric  discharge.— The  recombination  of  the  two 
electricities  which  constitutes  the  electrical  discharge  may  be  either  con- 
tinuous or  sudden  :  continuous,  or  of  the  nature  of  a  current,  as  when  the 
two  conductors  of  a  Holtz's  machine  are  joined  by  a  chain  or  a  wire  ;  and 
sudden,  as  when  the  opposite  electricities  accumulate  on  the  surface  of  two 
adjacent  conductors,  till  their  mutual  attraction  is  strong  enough  to  over- 
come the  intervening  resistances,  whatever  they  may  be.  But  the  difference 
between  a  sudden  and  a  continuous  discharge  is  one  of  degree,  and  not  of 
kind,  for  there  is  no  such  thing  as  an  absolute  non-conductor,  and  the  very 
best  conductors,  the  metals,  offer  an  appreciable  resistance  to  the  passage  of 
electricity.  Still  the  difference  at  the  two  extremes  of  the  scale  is  sufficiently 
great  to  give  rise  to  a  wide  range  of  phenomena. 

Riess  has  shown  that  the  discharge  of  a  battery  does  not  consist  in  a 
simple  union  of  the  positive  and  negative  electricity,  but  that  it  consists  of  a 
series  of  successive  partial  discharges.  The  direction  of  the  discharge 
depends  mainly  on  the  length  and_  nature  of  the  circuit.  By  observations  of 
the  image  of  the  spark  in  a  rotating  mirror,  and  of  the  luminous  phenomena 
at  the  positive  and  negative  poles  when  the  discharge  takes  place  in  highly 
rarefied  gases,  as  well  as  by  the  manner  in  which  a  magnet  affects  the  pheno- 
mena of  discharge,  Feddersen  and  Paalzow  have  shown  that  the  discharge 
consists  of  a  series  of  oscillating  currents  alternating  in  opposite  directions. 
As  the  resistance  of  the  circuit  increases,  the  number  of  these  alternating 
discharges  decreases,  but  at  the  same  time  their  duration  is  greater.  With 
very  great  resistance — as,  for  instance,  when  a  wet  thread  is  interposed — the 
alternating  discharge  becomes  a  single  one. 

784.  Work  effected  by  the  discharge  of  a  leyden  jar. — The  work 

CV2      O2 
required  to  charge  a  Leyden  jar  is  W  =  ^QV= =  -^-  ,    and     from    the 

principle  of  the  conservation  of  energy,  this  stored-up  energy  reappears  when 
the  jar  is  discharged.  This  occurs  partly  in  the  form  of  a  spark,  partly  in  the 
heating  effect  of  the  whole  system  of  conductors  through  which  the  discharge 
takes  place.  When  the  armatures  are  connected  by  a  thick  short  wire,  the 
spark  is  strong  and  the  heating  effect  small  :  if,  on  the  contrary,  the  jar  is 
discharged  through  a  long  fine  wire,  this  becomes  more  heated,  but  the  spark 
is  weaker. 

If  a  series  of  identical  jars  are  each  separately  charged  from  the  same 
source,  they  will  each  acquire  the  same  potential,  which  will  not  be  altered  if 
all  the  jars  are  connected  by  their  inner  and  outer  coatings  respectively. 
The  total  charge  will  be  the  same  as  if  the  battery  had  been  charged  directly 
from  the  source,  and  its  energy  will  be  W  =  ^Vnq  =••  ^VQ  ;  that  is,  the  energy 
of  a  battery  of  n  equal  jars  is  the  same  as  that  of  a  single  jar  of  the  same 
thickness  but  of  n  times  the  surface. 

Let  us  consider  two  similar  Leyden  jars  having  respectively  the  capaci- 
ties c  and  c',  and  let  one  of  them  be  charged  to  potential  V  and  let  the  other 


-786]  Luminous  Effects.  687 

remain  uncharged.  Suppose  now  that  the  inner  and  outer  coatings  of  the 
jars  are  respectively  connected  with  each  other.  Then  the  energy  of  the 

charged  jar  alone  is  W- J  9* ,  and  when  it  is  connected  with  the  other  the 
original  charge  will  spread  itself  over  the  two,  so  that  the  energy  of  the 
charge  in  the  two  jars  is  W  =  Q*  Hence  \V  :  W  =  c  +  ^  :  c ;  and  there- 
fore since  c  +  c*  is  always  greater  than  r,  there  must  be  a  loss  of  energy.  In 
point  of  fact,  when  a  charged  jar  is  connected  with  an  uncharged  one,  a  spark 
passes  which  is  the  equivalent  of  this  loss  of  energy. 

It  follows  further  that  whenever  two  jars  at  different  potentials  are  united 
there  is  always  a  loss  of  energy. 

The  phenomena  of  the  discharge  are  conveniently  divided  into  the 
physiological,  luminous,  mechanical,  magnetical,  and  chemical  effects. 

785.  Physiological  effects.— The  physiological  effects   are  those  pro- 
duced on  living  beings,  or  on  those  recently  deprived  of  life.     In  the  first 
case  they  consist  of  a  violent  excitement  which  the  electricity  exerts  on 
the  sensibility  and  contractility  of  the  organic  tissues  through  which  it  passes  ; 
and  in  the  latter,  of  violent  muscular  convulsions  which  resemble  a  return 
to  life. 

The  shock  from  the  electrical  machine  has  been  already  noticed  (770). 
The  shock  taken  from  a  charged  Leyden  jar  by  grasping  the  outer  coating 
with  one  hand  and  touching  the  inner  with  the  other,  is  much  more  violent, 
and  has  a  peculiar  character.  With  a  small  jar  the  shock  is  felt  in  the  elbow; 
with  a  jar  of  about  a  quart  capacity  it  is  felt  across  the  chest,  and  with  jars 
of  still  larger  dimensions  in  the  stomach. 

A  shock  may  be  given  to  a  large  number  of  persons  simultaneously  by 
means  of  the  Leyden  jar.  For  this  purpose  they  must  form  a  chain  by  join- 
ing hands.  If  then  the  first  touches  the  outside  coating  of  a  charged  jar, 
while  the  last  at  the  same  time  touches  the  knob,  all  receive  a  simultaneous 
shock,  the  intensity  of  which  depends  on  the  charge,  and  on  the  number  of 
persons  receiving  it.  Those  in  the  centre  of  the  chain  are  found  to  receive 
a  less  violent  shock  than  those  near  trie  extremities.  The  Abbd  Nollet  dis- 
charged a  Leyden  jar  through  an  entire  regiment  of  1,500  men,  who  all 
received  a  violent  shock  in  the  arms  and  shoulders. 

With  large  Leyden  jars  and  batteries  the  shock  is  sometimes  very  dan- 
gerous. Priestley  killed  rats  with  batteries  of  7  square  feet  coated  surface, 
and  cats  with  a  batter)'  of  about  4^  square  yards  coating. 

786.  Luminous  effects. — The  recombination  of  two  electricities  of  high 
potential  (738)  is  always  accompanied  by  a  disengagement  of  light,  as  is  seen 
when  sparks  are  taken  from  a  machine,  or  when  a  Leyden  jar  is  discharged. 
The  better  the  conductors  on  which  the  electricities  are  accumulated,  the 
more  brilliant  is  the  spark ;  its  colour  varies  not  only  with  the  nature  of  the 
bodies,  but  also  with  the  nature  of  the  surrounding  medium  and  with  the 
pressure.     The  spark  between  two  charcoal  points  is  yellow,  between  two 
balls  of  silvered  copper  it  is  green,  between  knobs  of  wood  or  ivory  it  is 
crimson.     In  atmospheric  air  at  the  ordinary  pressure  the  electric  spark  is 
white  and  brilliant  ;  in  rarefied  air  it  is  reddish  ;  and  in  vacuo  it  is  violet. 
In  oxygen,  as  in  air,  the  spark  is  white  ;  in  hydrogen  it  is  reddish,  and  green 


688 


Frictional  Electricity. 


[786- 


in  the  vapour  of  mercury  ;  in  carbonic  acid  it  is  also  green,  while  in  nitrogen 
it  is  blue  or  purple,  and  accompanied  by  a  peculiar  sound.  Generally 
speaking,  the  higher  the  potential  the  greater  is  the  lustre  of  the  spark. 
It  is  asserted  by  Fusinieri  that  in  the  electric  spark  there  is  always  a 
transfer  of  material  particles  in  a  state  of  extreme  tenuity,  in  which  case 
the  modifications  in  colour  must  be  due  to  the  transport  of  ponderable 
matter. 

When  the  spark  is  viewed  through  a  prism,  the  spectrum  obtained  is  full 
of  dark  lines  (578),  the  number  and  arrangement  of  which  depend  on  the 
material  of  which  the  poles  are  made. 

787.  Spark  and  brush  discharge. — The  shapes  which  luminous  electric 
phenomena  assume  may  be  classed  under  two  heads — the  spark  and  the 
brush.  The  brush  forms  when  the  electricity  leaves  the  conductor  in  a 
continuous  flow  ;  the  spark,  when  the  discharge  is  discontinuous.  The 
formation  of  one  or  the  other  of  these  depends  on  the  nature  of  the  con- 
ductor and  on  the  nature  of  the  conductors  in  its  vicinity  ;  and  small  altera- 
tions in  the  position  of  the  surrounding  conductors  transform  the  one  into 
the  other. 

The  spark  which  at  short  distances  appears  straight,  at  longer  distances 
has  a  zigzag  shape  with  diverging  branches.  Its  length  depends  on  the 
density  at  the  part  of  the  conductor  from  which  it  is  taken  ;  and  to  obtain 
the  longest  sparks  the  electricity  must  be  of  as  high  density  as  possible,  but 
not  so  high  as  to  discharge  spontaneously.  With  long 
sparks  the  luminosity  is  different  in  different  parts  of 
the  spark. 

The  brush  derives  its  name  from  the  radiating 
divergent  arrangement  of  the  light,  and  presents  the 
appearance  of  a  luminous  cone,  whose  apex  touches 
the  conductor.  Its  size  and  colour  differ  with  the 
nature  and  form  of  the  conductor ;  it  is  accompanied 
by  a  peculiar  hissing  noise,  very  different  from  the 
sharp  crack  of  the  spark.  Its  luminosity  is  far  less 
than  that  of  the  spark  ;  for  while  the  latter  can 
easily  be  seen  by  daylight,  the  former  is  only  visible 
in  a  darkened  room.  The  brush  discharge  may  be 
obtained  by  placing  on  the  conductor  a  wire  filed 
round  at  the  end,  or,  with  a  powerful  machine,  by 
placing  a  small  bullet  on  the  conductor.  The  brush 
from  a  negative  conductor  is  less  than  from  a  positive 
conductor  ;  the  cause  of  this  difference  has  not  been 
satisfactorily  made  out,  but  may  originate  in  the  fact? 
which  Faraday  has  observed,  that  negative  electricity 
discharges  into  the  air  at  a  somewhat  lower  density 
than  positive  electricity ;  so  that  a  negatively  charged 
knob  sooner  attains  that  density  at  which  spontaneous 
discharge  takes  place,  than  does  a  positively  charged 
one,  and  therefore  discharges  the  electricity  at  smaller  intervals  and  in  less 
quantities. 

When  electricity,  in  virtue  of  its  high  density,  issues  from  a  conductor, 


Fig.  646. 


-789]  Luminous  Tube,  Square,  and  Bottle.  689 

no  other  conductor  being  near,  the  discharge  takes  place  without  noise,  and 
at  the  places  at  which  it  appears  there  is  a  pale  blue  luminosity  called  the 
electrical  glow,  or,  on  points,  a  star-like  centre  of  light.  It  is  seen  in  the 
dark  by  placing  a  point  on  the  conductor  of  the  machine. 

788.  Electric   egrgr. — The  influence   of  the    pressure   of  the  air  on  the 
electric  light  may  be  studied  by  means  of  the  electric  egg.     This  consists  of 
an  ellipsoidal  glass  vessel  (fig.  646),  with  metal  caps  at  each  end.     The 
lower  cap  is  provided  with  a  stopcock,  so  that  it  can  be  screwed  into  an 
air-pump,  and  also  into  a  heavy  metallic  foot.     The  upper  metal  rod  moves 
up  and  down  in  a  leather  stuffing  box  ;  the  lower  one  is  fixed  to  the  cap. 
A  vacuum  having  been  made,  the  stopcock  is  turned,  and  the  vessel  screwed 
into  its  foot ;  the  upper  part  is  then  connected  with  a  powerful  electrical 
machine,  and  the  lower  one  with  the  ground.     On  working  the  machine,  the 
globe  becomes  filled  with  a  feeble  violet  light  continuous  from  one  end  to 
the  other,  and  resulting  from  the  recomposition  of  the  positive  fluid  of  the 
upper  cap  with  the  negative  of  the  lower.     If  the  air  be  gradually  allowed 
to  enter  by  opening  the  stopcock,  the  light  now  appears  white  and  brilliant, 
and  is  only  seen  as  an  ordinary  intermittent  spark. 

Some  beautiful  effects  of  the  electric  light   are  obtained  by  means  of 
Geissler's  tubes,  which  will  be  noticed  under  Dynamical  Electricity. 

789.  Luminous  tube,  square,  and  bottle. — The  luminous  tube  (fig.  647) 
is  a  glass  tube  about  a  yard  long,  round  which  are  arranged  in  a  spiral  form 


Fig.  647. 

a  series  of  lozenge-shaped  pieces  of  tinfoil,  between  which  are  very  short 
intervals.  There  is  a  brass  cap  with  hooks  at  each  end,  in  which  the  spiral 
terminates.  If  one  end  be  presented  to  a  machine  in  action,  while  the  other 
is  held  in  the  hand,  sparks  appear  simultaneously  at  each  interval,  and  pro- 
duce a  brilliant  luminous  appearance,  especially  in  the  dark. 

The  luminous  pane  (fig.  648)  is  constructed  on  the  same  principle,  and 
consists  of  a  square  of  ordinary  glass,  on  which  is  fastened  a  narrow  strip  of 
tinfoil  folded  parallel  to  itself  for  a  great  number  of  times.  Spaces  are  cut 
out  of  this  strip  so  as  to  represent  any  figure,  a  portico  for  example.  The 
pane  being  fixed  between  two  insulating  supports,  the  upper  extremity  of  the 
strip  is  connected  with  the  electrical  machine,  and  the  lower  part  with  the 
ground.  When  the  machine  is  in  operation,  a  spark  appears  at  each 
interval,  and  reproduces  in  luminous  flashes  the  object  represented  on  the 
glass. 

The  luminous  jar  (fig.  649)  is  a  Leyden  jar  whose  outer  coating  consists 
of  a  layer  of  varnish  strewed  over  with  metallic  powder.  A  strip  of  tin  fitted 


6go 


Frictional  Electricity. 


[789- 


on  the  bottom  is  connected  with  the  ground  by  means  of  a  chain  ;  a  second 
band  at  the  upper  part  of  the  coating  has  a  projecting  part,  and  the  rod  of 

the  bottle  is  curved  so  that  the 
knob  is  about  f  of  an  inch  from 
the  projection.  This  jar  is  sus- 
pended from  the  machine,  and, 
as  rapidly  as  this  is  worked, 
large  and  brilliant  sparks  pass 
between  the  knob  and  the  outer 
coating,  illuminating  the  outside 
of  the  apparatus. 

790.  Heating1  effects. — Be- 
sides being  luminous,  the  electric 
spark  is  a  source  of  intense 
heat.  When  it  passes  through 
inflammable  liquids,  as  ether  or 
alcohol,  it  inflames  them.  An 
arrangement  for  effecting  this  is 
represented  in  fig.  650.  It  is  a 
small  glass  cup  through  the 
bottom  of  which  passes  a  metal 
rod,  terminating  in  a  knob  and 
fixed  to  a  metal  foot.  A  quan- 
tity of  liquid  sufficient  to  cover  the  knob  is  placed  in  the  vessel.  The 
outer  coating  of  the  jar  having  been  connected  with  the  foot  by  means  of  a 
chain,  the  spark  which  passes  when  the  two  knobs  are  brought  near  each 
other  inflames  .the  liquid.  With  ether  the  experiment  succeeds  very  well, 
but  alcohol  requires  to  be  first  warmed. 

Coal  gas  may  also  be  ignited  by  means  of  the  electric  spark.  A  person 
standing  on  an  insulated  stool  places  one  hand  on  the  conductor  of  a 
machine  which  is  then  worked,  while  he  presents  the  other  to  the  jet  of  gas 
issuing  from  a  metallic  burner.  The  spark  which  passes  ignites  the  gas. 
When  a  battery  is  discharged  through  an  iron  or  steel  wire  it  becomes 
heated,  and  even  made  incandescent  or  melted,  if  the  discharge  is  very 
powerful. 

If,  in  discharging  a  jar,  the  discharge  does  no  other  work,  then  the  whole 
of  the  energy  of  the  charge  (784)  appears  in  the  form  of  heat ;  and  if  we 
divide  this  by  Joule's  equivalent  (497),  we  have  the  total  heating  due  to 
any  charge. 

The  laws  of  this  heating  effect  have  been  investigated  independently  by 
Harris  and  by  Riess  by  means  of  the  electric  thermometer.  This  is  essentially 
an  air  thermometer,  across  the  bulb  of  which  is  a  fine  platinum  wire.  When 
a  discharge  is  passed  through  the  wire  it  becomes  heated,  expands  the  air 
in  the  bulb,  and  this  expansion  is  indicated  by  the  motion  of  the  liquid  along 
the  graduated  stem  of  the  thermometer.  In  this  way  it  has  been  found  that 
the  increase  in  temperature  in  the  wire  is  proportional  to  the  square  of  the 
quantity  of  electricity  divided  by  the  surface — a  result  which  follows  from 
the  formula  already  given  (784).  Riess  has  also  found  that  with  the  same 
charge,  but  with  wires  of  different  dimensions,  the  rise  of  temperature  is  in- 


-790] 


Magnetic  Effects. 


691 


verse/}'  as  the  fourth  power  of  the  diameter.     Thus,  compared  with  a  given 
wire  as  unity,  the  rise  of  temperature  in  a  wire  of  double  or   treble  the 

diameter  would  be  j1^  or  /T  as  small  ;  but 
as  the  masses  of  these  wires  are  four  and 
nine  times  as  great,  the  heat  produced  would 
be  respectively  \  and  \  as  great  as  in  a  wire 
of  unit  thickness. 

When  an  electric  discharge  is  sent 
through  gunpowder  placed  on  the  table  of  a 
Henley's  discharger,  it  is  not  ignited,  but  is 
projected  in  all  directions.  But  if  a  wet 
string  be  interposed  in  the  circuit,  a  spark 


Fig.  649. 


Fig.  650. 


passes  which  ignites  the  powder.  This  arises  from  the  retardation  which 
electricity  experiences  in  traversing  a  semi-conductor,  such  as  a  wet  string  ; 
for  the  heating  effect  is  proportional  to  the  duration  of  the  discharge. 

When  a  charge  is  passed  through  sugar,  heavy  spar,  fluor-spar,  and  other 
substances,  they  afterwards  become  phosphorescent  in  the  dark.  Eggs, 
fruit,  £c.,  may  be  made  luminous  in  the  dark  in  this  way. 

When  a  battery  is  discharged  through  a  gold  leaf^  pressed  between  two 
glass  plates  or  between  two  silk  ribbons,  the  gold  is  volatilised  in  a  violet 
powder  which  is  finely  divided  gold.  In  this  way  what  are  called  electric 
Portraits  are  obtained. 

Siemens  has  shown  that  when  a  jar  is  charged  and  discharged  several 
times  in  succession  the  glass  becomes  heated.  Hence  during  the  discharge 
there  must  be  movements  of  the  molecules  of  the  glass,  as  Faraday  sup- 
posed ;  we  have  here,  probably,  something  analogous  to  the  heating  pro- 
duced in  iron  when  it  is  rapidly  magnetised  and  demagnetised. 

Duter  has  found  that  when  a  Leyden  jar  is  discharged,  the  insulating 
plate  undergoes  a  mechanical  expansion  which  he  considers  can  neither  be 
due  to  a  heating  effect  nor  to  electrical  pressure,  but  which  he  ascribes  to  a 
special  electrical  effect.  For  one  and  the  same  dielectric  it  appears  directly 
proportional  to  the  square  of  the  potential  and  inversely  as  the  thickness. 


692 


Frictional  Electricity. 


[791- 


791.  Magnetic    effects. — By    the  discharge    of  a  large  Leyden  jar  or 
battery,  a  steel  wire  may  be  magnetised  if  it  is  laid  at  right  angles  to  a  con- 
ducting wire  through  which  the  discharge  is  effected,  either  in  contact  with 
the  wire  or  at  some  distance.     And  even  with  less  powerful  discharges,  a 
steel  bar  or  needle  may  be  magnetised  by  placing  it  inside  a  tube  on  which 
is  coiled  a  fine  insulated  copper  wire.     On  passing  the  discharge  through 
this  wire  the  steel  becomes  magnetised. 

To  effect  a  deflection  of  the  magnetic  needle  by  the  electric  current  pro- 
duced by  frictional  electricity  is  more  difficult.  It  may  be  accomplished 
by  making  use  of  a  galvanometer  consisting  of  400  or  500  turns  of  fine  silk- 
covered  wire,  which  is  further  insulated  by  being  coated  with  shellac  varnish, 
and  by  separating  the  layers  by  means  of  oiled  silk.  When  the  prime  con- 
ductor of  a  machine  in  action  is  connected  with  one  end  of  the  galvanometer 
wire,  and  the  other  with  the  ground,  a  deflection  of  the  needle  is  produced. 

792.  Mechanical  effects. — The  mechanical  effects  are  the  violent  lacera- 
tions, fractures,  and  sudden  expansions  which  ensue  when  a  powerful  dis- 
charge is  passed  through  a  badly  conducting  substance.     Glass  is  perforated, 

wood  and  stones  are  frac- 
tured, and  gases  and 
liquids  are  violently  dis- 
turbed. The  mechanical 
effects  of  the  electric 
spark  may  be  demon- 
strated by  a  variety  of  ex- 
periments. 

Fig.  651  represents  an 
arrangement  for  peforat- 
ing  a  piece  of  glass  or 
card.  It  consists  of  two 
glass  columns,  with  a 
horizontal  cross-piece,  in 
which  is  a  pointed  con- 
ductor, B.  The  piece  of 
glass,  A,  is  placed  on  an 
insulating  glass  support, 
in  which  is  placed  a 
second  conductor,  ter- 
minating also  in  a  point, 
which  is  connected  with 
the  outside  of  the  battery,  while  the  knob  of  the  inner  coating  is  brought 
near  the  knob  of  B.  When  the  discharge  passes  between  the  two  conductors 
the  glass  is  perforated.  The  experiment  only  succeeds  with  a  single  jar 
when  the  glass  is  very  thin  ;  otherwise  a  battery  must  be  used. 

The  perturbation  and  sudden  expansion  which  the  discharge  produces 
may  be  illustrated  by  means  of  Kinnersley's  thermometer.  This  consists  of 
two  glass  tubes  (fig.  652),  which  fit  into  metallic  caps,  and  communicate  with 
each  other.  At  the  top  of  the  large  tube  is  a  rod  terminating  in  a  knob,  and 
moving  in  a  stuffing-box,  and  at  the  bottom  there  is  a  similar  rod  with  a 
knob.  The  apparatus  contains  water  up  to  the  level  of  the  lower  knob. 


Fig.  651. 


-793] 


Chemical  Effects. 


693 


When  the  electric  shock  passes  between  the  two  knobs,  the  water  is  driven 
out  of  the  larger  tube  and  rises  to  a  slight  extent  in  the  small  one.  The  level 
is  immediately  re-established,  and  therefore  the  phenomenon  is  not  due  to 
an  increase  of  temperature. 

For  the  production  of  mechanical  effects  the  universal  discharger  (fig.  622) 
is  of  great  service.     A  piece  of  wood,  for  instance,  placed  on  the  table 
between  the  two  conductors,  is 
split  when  the  discharge  passes. 

793.  Chemical  effects.  - 
The  chemical  effects  are  the 
decompositions  and  recombina- 
tions effected  by  the  passage  of 
the  electric  discharge.  When 
two  gases  which  act  on  each 
other  are  mixed  in  the  propor- 
tions in  which  they  combine,  a 
single  spark  is  often  sufficient 
to  determine  their  combination  ; 
but  when  either  of  them  is  in 
great  excess,  a  succession  of 
sparks  is  necessary.  Priestley 
found  that  when  a  series  of  elec- 
tric sparks  was  passed  through 
moist  air,  its  volume  dimin- 
ished, and  blue  litmus  intro- 
duced into  the  vessel  was 
reddened.  This,  Cavendish 
discovered,  was  due  to  the  for-  Fis-  652- 

mation  of  nitric  acid. 

Several  compound  gases  are  decomposed  by  the  continued  action  of  the 
electric  spark.  With  olefiant  gas,  sulphuretted  hydrogen,  and  ammonia,  the 
decomposition  is  complete  ;  while  carbonic  acid  is  partially  decomposed 


Fig.  653. 


Fig.  654. 


into  oxygen  and  carbonic  oxide.  The  electric  discharge  also  by  suitable 
means  can  feebly  decompose  water,  oxides,  and  salts  ;  but,  though  the  same 
in  kind,  the  chemical  effects  of  statical  electricity  are  by  no  means  so  powerful 
and  varied  as  those  of  dynamical  electricity.  The  chemical  action  of  the 
spark  is  easily  demonstrated  by  means  of  a  solution  of  iodide  of  potassium. 


Frictional  Electricity. 


[793- 


A  small  lozenge-shaped  piece  of  filtering  paper,  impregnated  with  iodide  of 
potassium,  is  placed  on  a  glass  plate,  and  one  corner  connected  with  the 
ground.  When  a  few  sparks  from  a  conductor  charged  with  positive  elec- 
tricity are  taken  at  the  other  corner,  brown  spots  are  produced  due  to  the 
separation  of  iodine. 

The  electric  pistol  is  a  small  apparatus  which  serves  to  demonstrate  the 
chemical  effects  of  the  spark.  It  consists  of  a  brass  vessel  (fig.  653),  in 
which  is  introduced  a  detonating  mixture  of  two  volumes  of  hydrogen  and 
one  of  oxygen,  and  which  is  then  closed  with  a  cork.  In  a  tubulure  in  the 
side  there  is  a  glass  tube,  in  which  fits  a  metal  rod,  terminated  by  the 
knobs  A  and  B.  The  vessel  is  held  as  represented  in  fig.  654,  and  brought 
near  the  machine.  The  knob  A  becomes  negatively,  and  B  positively,  elec- 
trified by  induction  from  the  machine,  and  a  spark  passes  between  the  con- 
ductor and  A.  Another  spark  passes  at  the  same  time  between  the  knob  B 
and  the  side  ;  this  determines  the  combination  of  the  gases,  which  is  accom- 
panied by  a  great  disengagement  of  heat,  and  the  vapour  of  water  formed 
acquires  such  an  expansive  force,  that  the  cork  is  projected  with  a  report 
like  that  of  a  pistol. 

Among  the  chemical  effects  must  be  enumerated  the  formation  of  ozone, 
which  is  recognised  by  its  peculiar  odour,  and  by  certain  chemical  proper- 
ties. The  odour  is  perceived  when  elec- 
tricity issues  from  a  conductor  into  the 
air  through  a  series  of  points.  It  has 
been  established  that  ozone  is  an  allo- 
tropic  modification  of  oxygen. 

With  these  effects  may  be  associated 
a  certain  class  of  phenomena  observed 
when  gases  are  made  to  act  as  the  dielec- 
tric in  a  charged  Leyden  jar.  An  appa- 
ratus by  which  this  is  effected  is  repre- 
sented in  fig.  655  ;  it  is  a  modification 
of  one  invented  by  Siemens.  It  con- 
sists of  a  glass  cylinder  E,  containing 
weak  sulphuric  acid  ;  a  is  a  glass  tube 
closed  at  the  bottom,  and  also  containing 
sulphuric  acid,  in  an  enlargement  of  which 
at  the  top  the  inner  tube  e  c  fits.  There  is 
a  tube  /by  which  gas  enters,  and  one  dt', 
by  which  it  emerges.  When  the  acids  in 
E  and  e  are  respectively  connected  with 
the  two  combs  of  a  Holtz's  machine,  or 
with  the  two  terminals  of  a  Ruhmkorff  s 
coil,  a  certain  condition  or  strain  is  pro- 
duced in  the  dielectric,  which  is  known  as 
the  silent  discharge  or  the  electric  effluvium, 
What  that  condition  is  cannot  be  definitely  stated  ;  but  it  gives  rise  to  power- 
ful and  characteristic  chemical  actions,  often  differing  from  those  produced 
by  the  spark. 

By  this  apparatus  large  quantities  of  ozone  may  be  produced. 


Fig.  655. 


-794]     Application  of  Electrical  Discharge  to  Firing  Mines.    695 

794.  Application  of  the  electrical  discharge  to  firing  mines. — By  the 

labours  of  Prof.  Abel  in  this  country,  and  of  Baron  von  Ebner  in  Austria,  the 
electrical  discharge  has  been  applied  to  firing  mines  for  military  purposes, 
and  the  methods  have  acquired  a  high  degree  of  perfection.  The  principle 
on  which  the  method  is  based  may  be  understood  from  the  following  state- 
ment : — 

One  end  of  an  insulated  wire  in  which  is  a  small  break  is  placed  in  con- 
tact with  the  outside  of  a  charged  Leyden  jar,  the  other  end  being  placed 
near  the  inner  coating.  If 
now  this  end  be  brought  in 
contact  with  the  inner  coat- 
ing the  jar  is  discharged,  and 
a  spark  strikes  across  the 
break ;  and  if  there  be  here 
some  explosive  compound  it 
is  ignited,  and  this  ignition 
may  of  course  be  communi- 
cated to  any  gunpowder  in 
which  it  is  placed.  If  on 
one  side  of  the  break,  in- 
stead of  having  an  insulated 
wire  direct  back  to  the  outer 
coating  of  the  Leyden  jar, 
an  uncovered  wire  be  led 
into  the  ground,  the  outside 
of  the  jar  being  also  con- 
nected with  the  ground,  the 
result  is  unchanged,  the 
earth  acting  as  a  return  wire. 
Moreover,  if  there  be  several 
breaks,  the  explosion  will 
still  ensue  at  each  of  them, 
provided  the  charge  be  suf- 
ficiently powerful. 

In  the  actual  application  it  is  of  course  necessary  to  have  an  arrange- 
ment for  generating  frictional  electricity  which  shall  be  simple,  portable, 
powerful,  and  capable  of  working  in  any  weather.  Fig.  656  represents  a 
view  of  Von  Ebner's  instrument  as  constructed  by  Messrs.  Elliott,  part  of 
the  case  being  removed  to  show  the  internal  construction. 

It  consists  of  two  circular  plates  of  ebonite,  #,  mounted  on  an  axis  so  that 
they  are  turned  by  a  handle,  £,  between  rubbers,  which  are  so  arranged  as 
to  be  easily  removed  for  the  purposes  of  amalgamation,  &c.  Fastened  to  a 
knob  on  the  base  of  the  apparatus  and  projecting  between  the  plates  is  a 
pointed  brass  rod,  which  acts  as  a  collector  of  the  electricity.  The  condenser 
or  Leyden  jar  arrangement  is  inside  the  case,  part  of  which  has  been  re- 
moved to  show  the  arrangement.  It  consists  of  india-rubber  cloth,  coated 
on  each  side  with  tinfoil,  and  formed  into  a  roll  for  the  purpose  of  greater 
compactness.  By  means  of  a  metal  button  the  knob  is  in  contact  with  one 
tinfoil  coating,  which  thus  receives  the  electricity  of  the  machine,  and  cor- 


Fig.  656. 


Frictional  Electricity. 


[794- 


responds  to  the  inner  coating  of  the  Leyden  jar.  Another  button  connected 
with  the  other  tinfoil  coating,  rests  on  a  brass  band  at  the  base  of  the  appa- 
ratus which  is  in  metallic  contact  with  the  cushions,  the  knob  d,  and  the 
perforated  knob  in  which  slides  a  rod  at  the  front  of  the  apparatus.  These 
are  all  in  connection  with  the  earth.  The  knob  e  is  in  metallic  connection 
with  a  disc  g  provided  with  a  light  arm.  By  means  of  a  flexible  chain  this 
is  so  connected  with  a  trigger  on  the' side  of  the  apparatus,  not  represented 
in  the  figure,  that  when  .the  trigger  is  depressed,  the  arm, 
and  therewith  the  knob  e,  is  brought  into  contact  with 
the  inner  coating  of  the  condenser. 

On  depressing  the  trigger,  after  a  certain  number  of 
turns,  a  spark  passes  between  the  knob  e  and  the  sliding 
rod,  and  the  striking  distance  is  a  measure  of  the  work- 
ing condition  of  the  instrument. 

The  fuse  used  is  known  as  Abel's  electrical  fuse,  and 
has  the  following  construction  : — The  ends  of  two  fine 
copper  wires  (fig.  658)  are  imbedded  in  a  thin  solid  gutta- 
percha  rod,  parallel  to  each  other,  but  at  a  distance  of 
about  1*5  mm.  At  one  end  of  the  gutta-percha  a  small 
cap  of  paper  or  tinfoil,  c  c,  is  fastened,  in  which  is  placed  a 
small  quantity  of  the  priming  composition,  which  consists 
of  an  intimate  mixture  of  subsulphide  of  copper,  sub- 
phosphide  of  copper,  and  chlorate  of  potassium.  The 
paper  is  fastened  down  so  that  the  exposed  ends  of  the 
wires  are  in  close  contact  with  the  powder. 

This  is  the  actual  fuse  ;  for  service  the  capped  end  of 
the  fuse  is  placed  in  a  perforation  in  the  rounded  head 
of  a  wooden  cylinder,  so  as  to  project  slightly  into  the 
cavity  g  of  the  cylinder.  This  cavity  is  filled  with  meal 
powder,  which  is  well  rammed  down,  so  that  the  fuse  is 
firmly  imbedded.  It  is  afterwards  closed  by  a  plug  of 
gutta-percha,  and  the  whole  is  finally  coated  with  black 
varnish. 

The  free  ends  of  the  wire  a  a  are  pressed  into  small 
grooves  in  the  head  of  the  cylinder  (fig.  658),  and  each 
end  is  bent  into  one  of  the  small  channels  with  which  the 
cylinder  is  provided,  and  which  are  at  right  angles  to 
the  central  perforation.  They  are  wedged  in  here  by 
driving  in  small  copper  tubes,  the  ends  of  which  are 
then  filed  flush  with  the  surface  of  the  cylinder.  The 
bared  ends  of  two  insulated  conducting  wires  are  then 
pressed  into  one  of  the  small  copper  tubes  or  eyes,  and 
fixed  there  by  bending  the  wire  round  on  to  the  wood,  as 
shown  at  e. 

The  conducting  wire  used  in  firing  may  be  thin,  but  it  must  be  well  insu- 
lated. One  end,  which  is  bared,  having  been  pressed  into  the  hole  d  of  the 
fuse  (fig.  657),  the  other  is  placed  near  the  exploder.  In  the  other  hole  d'  of 
the  fuse  a  wire  is  placed  which  serves  as  earth  wire,  care  being  taken  that 
there  is  no  connection  between  the  two  wires.  The  fuse  having  been  intro- 


Fig.  657- 


Fig.  658. 


-795]  Duration  of  the  Electric  Spark.  697 

duced  into  the  charge,  the  earth  wire  is  placed  in  good  connection  with  the 
ground.  The  knob/  of  the  exploder  is  also  connected  with  the  earth  by 
leading  uncovered  wire  into  water  or  moist  earth,  and  the  condition  of  the 
machine  tested.  The  end  of  the  insulated  wire  is  then  connected  with  the 
knob  e  and  the  rod  drawn  down  ;  at  the  proper  signal  the  handle  is  turned 
the  requisite  number  of  times,  and  when  the  signal  is  given  the  trigger  is 
depressed,  and  the  explosion  ensues. 

When  a  number  of  charges  are  to  be  fired  they  are  best  placed  in  a  single 
circuit,  care  being  taken  that  the  insulation  is  good. 

795.  Duration  of  the  electric  spark. — Wheatstone  measured  the  dura- 
tion of  the  electric  spark,  by  means  of  the  rotating  mirror  which  he  invented 
for  this  purpose.  At  some  distance  from  this  instrument,  which  can  be  made 
to  rotate  with  a  measured  velocity,  a  Leyden  jar  is  so  arranged  that  the 
spark  of  its  discharge  is  reflected  from  the  mirror.  Now,  from  the  laws  of 
reflection  (520)  the  image  of  the  luminous  point  describes  an  arc  of  double 
the  number  of  degrees  which  the  mirror  describes,  in  the  time  in  which  the 
mirror  passes  from  the  position  in  which  the  image  is  visible  to  that  in  which 
it  ceases  to  be  so.  If  the  duration  of  the  image  were  absolutely  instanta- 
neous the  arc  would  be  reduced  to  a  mere  point.  Knowing  the  number  of 
turns  which  the  mirror  makes  in  a  second,  and  measuring,  by  means  of  a 
divided  circle,  the  number  of  degrees  occupied  by  the  image,  the  duration  of 
the  spark  would  be  determined.  In  one  experiment. Wheatstone  found  that 
this  arc  was  24°.  Now,  in  the  time  in  which  the  mirror  traverses  360° 
the  image  traverses  720°  ;  but  in  the  experiment  the  mirror  made  800  turns 
in  a  second,  and  therefore  the  image  traversed  576,000°  in  this  time  ;  and,  as 
the  arc  was  24°,  the  image  must  have  lasted  the  time  expressed  by  g^oo  or 
__!__  of  a  second.  Thus  the  discharge  is  not  instantaneous,  but  has  a  certain 
duration,  which,  however,  is  excessively  short. 

Feddersen  found  that  when  greater  resistances  were  interposed  in  the 
circuit  through  which  the  discharge  was  effected,  the  duration  of  the 
spark  was  increased.  With  a  tube  of  water  9  mm.  in  length,  the  spark 
lasted  0-0014  second;  and  with  one  of  180  mm.  its  duration  was  0-0183 
second.  The  duration  increased  also  with  the  striking  distance,  and  with 
the  dimensions  of  the  battery. 

To  determine  the  duration  of  the  electric  spark  Lucas  and  Cazin 
used  a  most  accurate  method,  by  which  it  may  be  measured  in  millionths 
of  a  second.  The  method  is  an  application  of  the  vernier.  A  disc  of  mica 
1 5  centimetres  in  diameter  is  blackened  on  one  face,  and  at  the  edge  are 
traced  180  equal  divisions  in  very  fine  transparent  lines.  The  disc  is 
mounted  on  a  horizontal  axis,  and  by  means  of  a  gas  engine  it  may  be  made 
to  turn  with  a  velocity  of  100  to  300  turns 
in  a  second.  A  second  disc  of  silvered 
glass  of  the  same  radius  is  mounted  on 
the  same  axis  as  the  other  and  very  close 
to  it ;  at  its  upper  edge  six  equidistant  ^\  x 
transparent  lines  are  traced,  forming  a  Fjg  6sg 

vernier  with  the  lines  on  the  mica.     For 

this,  the  distance  between  two  consecutive  lines  on  the  two  discs  is  such  that 
rive  divisions  of  the  mica  disc  DC  correspond  to  six  divisions  of  the  glass 

H  H 


698 


Frictional  Electricity. 


[795- 


disc  AB  as  seen  in  fig.  659.  Thus  the  vernier  gives  the  sixths  of  a 
division  of  the  mica  disc  (10).  In  the  apparatus  the  lines  AB  are  not  above 
the  lines  CD,  but  are  at  the  same  distance  from  the  axis,  so  that  the  latter 
coincide  successively  with  the  former. 

The  mica  disc  is  contained  in  a  brass  box  D  (fig.  660),  on  the  hinder  face 
of  which  is  fixed  the  vernier.  In  the  front  face  is  a  glass  window  O,  through 
which  the  coincidence  of  the  two  sets  of  lines  can  be  observed  by  means  of 
a  magnifying  lens  L. 

The  source  of  electricity  is  a  battery  of  2  to  8  jars,  each  having  a  coated 
surface  of  1,243  square  centimetres  and  charged  continuously  by  a  Holtz's 


Fig.  660. 

machine.  The  sparks  strike  between  two  metal  balls  a  and  b,  1 1  millimetres 
in  diameter.  Their  distance  can  be  varied,  and  at  the  same  time  measured, 
by  means  of  a  micrometric  screw,  r.  The  two  opposite  electricities  arrive 
by  wires  m  and  #,  and  the  sparks  strike  at  the  principal  focus  of  a  condensing 
lens  placed  in  the  collimator  C,  so  that  the  rays  which  fall  on  the  vernier  are 
parallel. 

The  motion  is  transmitted  to  the  toothed  wheels  and  to  the  mica  disc  by 
means  of  an  endless  band,  which  can  be  placed  on  any  one  of  three  pulleys 
P,  so  that  the  velocity  may  be  varied.  At  the  end  of  the  axis  of  the  pulleys 
is  a  bent  wire  which  moves  a  counter,  V,  that  marks  on  three  dials  the 
number  of  turns  of  the  disc. 


-796]  Velocity  of  Electricity.  699 

These  details  being  premised,  suppose  the  velocity  of  the  disc  is  400 
turns  in  a  second.  In  each  second  400  x  180  or  72,000  lines  pass  before  the 
observer's  eye  in  each  second  ;  hence  an  interval  of  Y.3^  of  a  second  elapses 
between  two  consecutive  lines.  But  as  the  spark  is  only  seen  when 
one  of  the  lines  of  the  disc  coincides  with  one  of  the  six  lines  of  the  vernier  ; 
and  as  this  gives  sixths  of  a  division  of  the  moveable  disc,  when  the  latter 
has  turned  through  a  sixth  of  a  division,  a  second  coincidence  is  pro- 
duced ;  so  that  the  interval  between  two  successive  coincidences  is 

? — -  =  0-0000023  of  a  second. 

72000x6 

That  being  the  case,  let  the  duration  of  a  spark  be  something  between 
23  and  46  ten-millionths  of  a  second  ;  if  it  strikes  exactly  at  the  moment  of 
a  coincidence,  it  will  last  until  the  next  coincidence  ;  and  owing  to  the  per- 
sistence of  impressions  on  the  retina  (625)  the  observer  will  see  two  luminous 
lines.  But  if  the  spark  strikes  between  two  coincidences  and  has  ceased 
when  the  third  is  produced,  only  one  brilliant  line  is  seen.  Thus,  if  with  the 
above  velocity  sometimes  i  and  sometimes  2  bright  lines  are  seen,  the  dura- 
tion of  the  spark  is  comprised  between  23  and  46  ten-millionths  of  a  second. 

By  experiments  of  this  kind,  with  a  striking  distance  of  5  millimetres 
between  the  balls  a  and  £,  and  varying  the  number  of  the  jars,  MM.  Lucas 
and  Cazin  obtained  the  following  results  : — 

Duration  in 
Number  of  jars  millionths  of 

a  second. 
2  26 

4  41 

6  45 

8  47 

It  will  thus  be  seen  that  the  duration  of  the  spark  increases  with  the 
number  of  jars.  It  also  increases  with  the  striking  distance  ;  but  it  is  inde- 
pendent of  the  diameter  of  the  balls  between  which  the  spark  strikes. 

The  spark  of  electrical  machines  has  so  short  a  duration  that  it  could  not 
be  measured  with  the  chronoscope. 

796.  Velocity  of  electricity. — To  determine  the  velocity  of  electricity 
Wheatstone  constructed  an  apparatus  the  principle  of  which  will  be  under- 
stood from  fig.  66 1  ;  six  insulating  metal  knobs  were 
arranged  in  a  horizontal  line  on  a  piece  of  wood  called 
a  spark  board;  of  these  the  knob  I  was  connected 
with  the  outer,  while  6  could  be  connected  with  the 
inner  coating  of  a  charged  Leyden  jar  ;  the  knob  I 
was  a  tenth  of  an  inch  distant  from  the  knob  2  ; 
while  between  2  and  3  a  quarter  of  a  mile  of  insulated 
wire  was  interposed :  3  was  likewise  a  tenth  of  an 
inch  from  4,  and  there  was  a  quarter  of  a  mile  of 
wire  between  4  and  5  ;  lastly,  5  was  a  tenth  of  an 
inch  from  6,  from  which  a  wire  led  directly  to  the 
outer  coating  of  the  Leyden  jar.  Hence,  when  the 
jar  was  discharged  by  connecting  the  wire  from  6  with  the  inner  coating 
of  the  jar,  sparks  would  pass  between  i  and  2,  between  3  and  4, and  between 
5  and  6.  Thus  the  discharge,  supposing  it  to  proceed  from  the  inner  coat- 

H  H  2 


70O  Frictional  Electricity.  [796- 

ing,  has  to  pass  in  its  course  through  a  quarter  of  a  mile  of  wire  between 
the  first  and  second  spark,  and  through  the  same  distance  between  the 
second  and  third. 

The  spark  board  was  arranged  at  a  distance  of  10  feet  from  the  rotating 
mirror,  and  at  the  same  height,  both  being  horizontal ;  and  the  observer 
looked  down  on  the  mirror.  Thus  the  sparks  were  visible  when  the  mirror 
made  an  angle  of  45°  with  the  horizon. 

Now,  if  the  mirror  were  at  rest  or  had  only  a  small  velocity,  the  images 
of  the  three  sparks  would  be  seen  as  three  dots  j ,  but  when  the  mirror  had 
a  certain  velocity  these  dots  appeared  as  lines,  which  were  longer  as  the 
rotation  was  more  rapid.  The  greatest  length  observed  was  24°,  which, 
with  800  revolutions  in  a  second,  can  be  shown  to  correspond  to  a  duration 
of  24000  °f  a  second.  With  a  slow  rotation  the  lines  present  the  appearance 
.ZZ= ;  they  are  quite  parallel,  and  the  ends  in  the  same  line.  But  with 
greater  velocity,  and  when  the  rotation  took  place  from  left  to  right,  they 

presented  the  appearance  -^^^,  ;  an(j  when  it  turned  from  right  to  left 

the  appearance  ~  ^~,  because  the  image  of  the  centre  spark  was  formed 
after  the  lateral  ones.  Wheatstone  found  that  this  displacement  amounted 
to  half  a  degree  before  or  behind  the  others.  This  arc  corresponds  to  a 

duration  o or  VT^TTKTI  of  a  second  ;  the  space  traversed  in  this 

2  x  720  x  100 

time  being  a  quarter  of  a  mile,  gives  for  the  velocity  of  electricity  288,000 
miles  in  a  second,  which  is  greater  than  that  of  light.  The  velocity  of 
dynamical  electricity  is  far  less  ;  and,  owing  to  induction,  the  transmission 
of  a  current  through  submarine  wires  is  comparatively  slow. 

In  the  above  experiment  the  images  of  the  two  outer  sparks  appear 
simultaneously  in  the  mirror,  from  which  it  follows  that  the  electric  current 
issues  simultaneously  from  the  two  coatings  of  the  Leyden  jar. 

From  certain  theoretical  considerations  based  upon  measurements  of 
constant  electrical  currents  Kirchhoff  concluded  that  the  motion  of  elec- 
tricity in  a  wire  in  which  it  meets  with  no  resistance  is  like  that  of  a  wave 
on  a  stretched  string,  and  has  the  velocity  of  192,924  miles  in  a  second, 
which  is  about  that  of  light  in  vacuo  (507). 

According  to  Walker,  the  velocity  of  electricity  is  18,400  miles,  and  ac- 
cording to  Fizeau  and  Gounelle,  it  is  62,100  miles  in  iron,  and  111,780  in 
copper  wire.  These  measurements,  however,  were  made  with  telegraph  wires, 
which  induce  opposite  electricities  in  the  surrounding  media  ;  there  is  thus 
produced  a  resistance  which  diminishes  the  velocity.  The  velocity  is  less 
in  insulated  wires  in  water  than  in  air.  The  nature  of  the  conductor  appears 
to  have  some  influence  on  the  velocity ;  but  not  the  thickness  of  the  wire, 
nor  the  potential  of  the  electricity. 

For  atmospheric  electricity,  reference  must  be  made  to  the  chapter  on 
Meteorology. 


-797J 


' s  Experiment. 


701 


BOOK   X. 

DYNAMICAL   ELECTRICITY. 


CHAPTER   I. 

VOLTAIC   PILE.      ITS   MODIFICATIONS. 

797.  Galvani'«  experiment  and  theory.— The  fundamental  experiment 
which  led  to  the  discovery  of  dynamical  electricity  is  due  to  Galvani  pro- 
fessor of  anatomy  m  Bologna.  Occupied  with  investigations  on  the  influence 
3f  electricity  on  the  nervous  excitability  of  animals,  and  especially  of  the  frog, 
he  observed  that 
when  the  lumbar 
nerves  of  a  dead 
frog  were  connected 
with  the  crural 
muscles  by  a  me- 
tallic circuit,  the 
1  atter  became 
briskly  contracted. 

To  repeat  this 
celebrated  experi- 
ment, the  legs  of  a 
recently  killed  frog 
are  prepared,  and 
the  lumbar  nerves 
on  each  side  of  the 
vertebral  column 
are  exposed  in  the 
form  of  white 
threads.  A  metal 
conductor,  com- 
posed of  zinc  and 
copper,  is  then  taken  (fig.  662),  and  one  end  introduced  between  the  nerves 
and  the  vertebral  column,  while  the  other  touches  one  of  the  muscles  of  the 
thighs  or  legs  ;  at  each  contact  a  smart  contraction  of  the  muscles  ensues. 

Galvani  had  some  time  before  observed  that  the  electricity  of  machines 
produced  in  dead  frogs  analogous  contractions,  and  he  attributed  the  pheno- 
mena first  described  to  an  electricity  inherent  in  the  animal.  He  assumed 


Fig.  662. 


7O2  Dynamical  Electricity.  [797- 

that  this  electricity,  which  he  called  vital  fluid,  passed  from  the  nerves  to 
the  muscles  by  the  metallic  arc,  and  was  thus  the  cause  of  contraction. 
This  theory  met  with  great  support,  especially  among  physiologists,  but  it 
was  not  without  opponents.  The  most  considerable  of  these  was  Alexander 
Volta,  professor  of  physics  in  Pavia. 

798.  Volta's  fundamental  experiment. — Galvani's  attention  had  been 
exclusively  devoted  to  the  nerves  and  muscles  of  the  frog  ;  Volta's  was 
directed  upon  the   connecting  metal.     Resting  on   the  observation,  which 
Galvani  had  also  made,  that  the  contraction  is  more  energetic  when  the  con- 
necting arc  is  composed  of  two  metals,  than  when  there  is  only  one,  Volta 
attributed  to  the  metals  the  active  part  in  the  phenomenon  of  contraction. 
He  assumed  that  the  disengagement  of  electricity  was  due  to  their  contact, 
and  that  the  animal  parts  only  officiated  as  conductors,  and  at  the  same 
time  as  a  very  sensitive  electroscope. 

By  means  of  the  condensing  electroscope,  which  he  had  then  recently 
invented,  Volta  devised  several  modes  of  showing  the  disengagement  of 
electricity  on  the  contact  of  metals,  of  which  the  following  is  the  easiest  to 
perform  : — 

The  moistened  finger  being  placed  on  the  upper  plate  of  a  condensing 
electroscope  (fig.  640),  the  lower  plate  is  touched  with  a  plate  of  copper,  c, 
soldered  to  a  plate  of  zinc,  2,  which  is  held  on  the  other  hand.  On  breaking 
the  connection  and  lifting  the  upper  plate  (fig.  641),  the  gold  leaves  diverge, 
and,  as  may  be  proved,  with  negative  electricity.  Hence,  when  soldered 
together,  the  copper  is  charged  with  negative  electricity,  and  the  zinc  with 
positive  electricity.  The  electricity  could  not  be  due  either  to  friction  or 
pressure  ;*  for  if  the  condensing  plate,  which  is  of  copper,  is  touched  with 
the  zinc  plate  #,•  the  copper  plate  to  which  it  is  soldered  being  held  in  the 
hand,  no  trace  of  electricity  is  observed. 

A  memorable  controversy  arose  between  Galvani  and  Volta.  The  latter 
was  led  to  give  greater  extension  to  his  contact  theory,  and  propounded  the 
principle  that  when  two  heterogeneous  substances  are  placed  in  contact,  one 
of  them  always  assumes  the  positive  and  the  other  the  negative  electrical 
condition.  In  this  form  Volta's  theory  obtained  the  assent  of  the  principal 
philosophers  of  his  time.  Galvani,  however,  made  a  number  of  highly  in- 
teresting experiments  with  animal  tissues.  In  some  of  these  he  obtained 
indications  of  contraction,  even  though  the  substances  in  contact  were  quite 
homogeneous. 

799.  Disengagement  of  electricity  in  chemical  actions. — The  contact 
theory  which  Volta  had  propounded,  and  by  which  he  explained  the  action 
of  the  pile,  soon  encountered  objectors.     Fabroni,  a  countryman  of  Volta, 
having  observed  that,  in  the  pile,  the  discs  of  zinc  became  oxidised  in  contact 
with  the  acidulated  water,  thought  that  this  oxidation  was  the  principal 
cause   of  the  disengagement  of  electricity.     In    England   Wollaston  soon 
advanced  the  same    opinion,  and  Davy  supported   it   by  many  ingenious 
experiments. 

It  is  true  that  in  the  fundamental  experiment  of  the  contact  theory  (798) 
Volta  obtained  signs  of  electricity.  But  De  la  Rive  showed  that  if  the  zinc 
be  held  in  a  wooden  clamp,  all  signs  of  electricity  disappear,  and  that  the 
same  is  the  case  if  the  zinc  be  placed  in  gases,  such  as  hydrogen  or  nitrogen, 


-799]      Disengagement  of  Electricity  in  Chemical  Action.         703 

which  exert  upon  it  no  chemical  action.  De  la  Rive  accordingly  concluded 
that  in  Volta's  original  experiment  the  disengagement  of  electricity  is  due  to 
the  chemical  actions  which  result  from  the  perspiration  and  from  the  oxygen 
of  the  atmosphere. 

The  development  of  electricity  in  chemical  actions  may  be  demonstrated 
in  the  following  manner  by  means  of  the  condensing  electroscope  (786)  : — A 
disc  of  moistened  paper  is  placed  on  the  upper  plate  of  the  condenser,  and 
on  this  a  zinc  capsule,  in  which  some  very  dilute  sulphuric  acid  is  poured.  A 
platinum  wire,  communicating  with  the  ground,  but  insulated  from  the  sides 
of  the  vessel,  is  immersed  in  the  liquid,  and  at  the  same  time  the  lower  plate 
of  the  condenser  is  also  connected  with  the  ground  by  touching  it  with  the 
moistened  finger.  On  breaking  contact  and  removing  the  upper  plate,  the 
gold  leaves  are  found  to  be  positively  electrified,  proving  that  the  upper 
plate  has  received  a  charge  of  negative  electricity. 

By  a  variety  of  analogous  experiments  it  may  be  shown  that  various 
chemical  actions  are  accompanied  by  a  disturbance  of  the  electrical  equili- 
brium ;  though  of  all  chemical  actions  those  between  metals  and  liquids  are 
the  most  productive  of  electricity.  All  the  various  resultant  effects  are  in 
accordance  with  the  general  rule,  that  when  a  liquid  acts  chemically  on  a 
metal  the  liquid  assumes  the  positive,  and  the  metal  the  negative,  con- 
dition. In  the  above  experiment  the  sulphuric  acid,  by  its  action  on 
zinc,  becomes  positively  electrified,  and  its  electricity  passes  off  through 
the  platinum  wire  into  the  ground,  while  the  negative  electricity  excited 
on  the  zinc  acts  on  the  condenser  just  as  an  excited  rod  of  sealing-wax 
would  do. 

In  many  cases  the  electrical  indications  accompanying  chemical  actions 
are  but  feeble,  and  require  the  use  of  a  very  delicate  electroscope  to  render 
them  apparent.  Thus,  one  of  the  most  energetic  chemical  actions,  that  of 
sulphuric  acid  upon  zinc,  gives  no  more  free  electricity  than  water  alone  does 
with  zinc. 

Opinion — which,  in  this  country  at  least,  had,  mainly  by  the  influence  of 
Faraday's  experiments,  tended  in  favour  of  the  purely  chemical  origin  of 
the  electricity  produced  in  voltaic  action — has  of  late  inclined  more  and  more 
towards  the  contact  theory.  The  following  experiments,  due  to  Sir  W. 
Thomson,  afford  perhaps  the  most  conclusive  arguments  hitherto  adduced 
in  favour  of  the  latter  view  :— 

A  very  light  metal  bar  was  suspended  by  a  fine  wire  so  as  to  be  moveable 
about  an  axis,  perpendicular  to  the  plane  of  a  ring  made  up  of  two  halves, 
one  of  copper  and  the  other  of  zinc.  When  the  two  halves  of  the  ring  were 
in  contact,  or  were  soldered  together,  the  light  bar  turned  from  the  copper 
to  the  zinc  when  it  was  negatively  electrified,  and  from  the  zinc  to  the  copper 
when  it  was  positively  electrified,  thus  showing  that  the  contact  of  the  two 
metals  causes  them  to  assume  different  electrical  conditions,  the  zinc  taking 
the  positive,  and  the  copper  the  negative  electricity. 

When,  however,  the  two  halves,  instead  of  being  in  metallic  contact,  were 
connected  by  a  drop  of  water,  no  change  was  produced  in  the  position  of  the 
bar  by  altering  its  electrification,  provided  it  hung  quite  symmetrically  re- 
lative to  the  two  halves  of  the  ring.  This  result  shows  that,  under  the  cir- 
cumstances mentioned,  no  difference  is  produced  in  the  electrical  condition 


704  Dynamical  Electricity.  [799- 

of  the  two  metals.  Hence  the  conclusion  has  been  drawn  by  Sir  \V.  Thom- 
son and  others,  that  the  movement  of  electricity  in  the  galvanic  circuit  is 
entirely  due  to  the  electrical  difference  produced  at  the  surfaces  of  contact  of 
the  dissimilar  metals.  These  results  have  been  confirmed  by  some  recent 
very  careful  experiments  by  Prof.  Clifton. 

There  are,  however,  other  facts  which  are  not  easily  harmonised  with 
this  view  ;  and  indeed  the  last-mentioned  experiment  can  hardly  be  regarded 
as  proving  that  in  all  cases  two  different  metals  connected  by  an  electrolytic 
(8 1 6)  liquid,  assume  the  same  electrical  condition.  It  may,  therefore,  still 
be  regarded  as  possible,  or  even  probable,  that  the  contact  between  the 
metals  and  the  liquids  of  a  cell  contributes,  at  least  in  some  cases,  to  the 
production  of  the  current. 

An  instructive  discussion  of  this  question,  with  some  additional  experi- 
mental evidence  in  favour  of  the  chemical  theory,  will  be  found  in  a  paper  by 
Dr.  Fleming,  published  in  the  '  Proceedings  of  the  Physical  Society '  (Taylor 
and  Francis). 

800.  Current  electricity. — When  a  plate  of  zinc  and  a  plate  of  copper  are 
partially  immersed  in  dilute  sulphuric  acid,  no  electrical  or  chemical  change 
is  apparent  beyond  perhaps  a  slight  disengagement  of  hydrogen  from  the 
surface  of  the  zinc  plate.     If  now  the  plates  are 
placed  in  direct  contact,  or,  more  conveniently, 
are   connected    by  a   metal    wire,    the   chemical 
action    sets   in,  a  large  quantity  of   hydrogen  is 
disengaged  ;  but  this  hydrogen  is  no  longer  dis- 
engaged at  the    surface   of  the    zinc,  but    at  the 
surface  of  the  copper  plate.     Here  then  we  have 
to  deal  with  something  more  than  mere  chemical 
action,  for  chemical  action  would  be   unable    to 
explain   either   the   increase    in    the  quantity   of 
hydrogen  disengaged  when  the  metals  touch,  or 
Fig.  6637~  tne  fact  tnat  tn^s  hydrogen  is  now  given    off  at 

the  surface  of  the  copper  plate.  At  the  same 
time,  if  the  wire  is  examined  it  will  be  found  to  possess  many  remarkable 
thermal,  magnetic,  and  other  properties  which  will  be  afterwards  described. 
In  order  to  understand  what  here  takes  place,  let  us  suppose  that  we  have 
two  insulated  metal  spheres,  and  that  one  is  charged  with  positive  and  the 
other  with  negative  electricity,  and  that  they  are  momentarily  connected  by 
means  of  a  wire.  Electricity  will  pass  from  a  place  of  higher  to  a  place  of 
lower  potential — that  is,  from  the  positive  along  the  wire  to  the  negative — 
and  the  potentials  become  equal.  This  is,  indeed,  nothing  more  than  an  elec- 
trical discharge  taking  place  through  the  wire  ;  and  during  the  infinitely 
short  time  in  which  this  is  accomplished,  it  can  be  shown  that  the  wire 
exhibits  certain  heating  and  magnetising  effects,  of  which  the  increase  of 
temperature  is  perhaps  the  easiest  to  observe.  If  now  we  can  imagine  some 
agency  by  which  the  different  electrical  conditions  of  the  two  spheres  are 
renewed  as  fast  as  they  are  discharged,  which  is  what  very  nearly  takes 
place  when  the  two  spheres  are  respectively  connected  with  the  two  con- 
ductors rand  rlt  of  a  Holtz's  machine  (figs.  615,  616),  this  equalisation  of 
potentials,  thus  taking  place,  is  virtually  continuous,  and  the  phenomena 
above  mentioned  are  also  continuous. 


-801]  Voltaic  Couple.     Electromotive  Series.  705 

Now  this  is  what  takes  place  when  the  two  metals  are  in  contact  in  a 
liquid  which  acts  upon  them  unequally.  This  is  independent  of  hypothesis 
as  to  the  cause  of  the  phenomena  ;  whether  the  electrical  difference  is  only 
produced  at  the  moment  of  contact  of  the  metals,  or  whether  it  is  due 
to  the  chemical  action,  or  tendency  to  chemical  action,  between  the  metal 
and  the  liquid.  The  rapidly  succeeding  series  of  equalisations  of  potential 
which  takes  place  in  the  wire  being  continuous,  so  long  as  the  chemical 
action  continues,  is  what  is  ordinarily  spoken  of  as  the  electrical  current. 

If  we  represent  by  +e  the  potential  of  the  copper  plate,  and  by  —  e  the 
potential  of  the  zinc,  then  the  electrical  difference — that  is,  the  difference  of 
potentials — is  4  e—  (—<?)  =  ie.  And  this  is  general  ;  the  essential  point  of  any 
such  combination  as  the  above  is,  that  it  maintains,  or  tends  to  maintain,  a 
difference  of  potentials,  which  difference  is  constant.  If,  for  instance,  the 
zinc  plate  be  connected  with  the  earth  which  is  at  zero  potential,  its  potential 
also  becomes  zero  ;  and  since  the  electrical  difference  remains  constant  we 
have  for  the  potential  of  the  copper  plate  +  ie.  Similarly,  if  the  copper  be 
connected  with  the  earth  the  potential  of  the  zinc  plate  is  negative  and  is 

—  2^. 

The  conditions  under  which  a  current  of  electricity  is  formed  in  the  above 
experiment  may  be  further  illustrated  by  reference  to  the  conditions  which 
determine  the  flow  of  water  between  two  reservoirs  containing  water  at 
different  levels.  If  they  are  connected  by  a  pipe,  water  will  flow  from  the 
one  at  a  higher  level  to  the  one  at  a  lower  level  until  the  water  in  the  two  is  at 
the  same  level  in  both,  when  of  course  the  flow  ceases.  If  we  imagine  the 
lower  reservoir  so  large  that  any  water  added  to  it  would  not  affect  its  level — 
if  it  were  the  sea,  for  example — that  would  represent  zero  level,  and  if  the 
higher  reservoir  could  be  kept  at  a  constant  level  there  would  be  a  constant 
flow  in  the  pipe. 

We  must  here  be  careful  not  to  dwell  too  much  on  this  analogy.  It  is  not 
to  be  supposed  that  in  speaking  of  current  of  electricity  we  mean  that  any- 
thing actually  flows — that  there  is  any  actual  transfer  of  matter.  We  say 
'  electricity  flows  '  or  '  a  current  is  produced,'  in  much  the  same  sense  as  that 
in  which  we  say  '  sound  or  light  travels.' 

801.  Voltaic  couple,  electromotive  series. — The  arrangement  just 
described,  consisting  of  two  metals  in  metallic  contact,  and  a  conducting 
liquid  in  which  they  are  placed,  constitutes  a  simple  voltaic  element  or  couple. 
So  long  as  the  metals  are  not  in  contact,  the  couple  is  said  to  be  open,  and 
when  connected  it  is  closed. 

According  to  the  chemical  view,  to  which  we  shall  for  the  present 
provisionally  adhere,  it  is  not  necessary  that,  for  the  production  of  a  current, 
one  of  the  metals  be  unaffected  by  the  liquid,  but  merely  that  the  chemical 
action  upon  the  one  be  greater  than  upon  the  other.  For  then  we  may 
assume  that  the  current  produced  would  be  due  to  the  difference  between 
the  differences  of  potential  which  each  of  the  metals  separately  produces  by 
its  contact  with  the  liquid.  If  the  differences  of  potentials  were  absolutely 
equal — a  condition,  however,  impossible  of  realisation  with  two  distinct 
metals — we  must  assume  that  when  the  metals  are  joined  no  current  would 
be  produced.  The  metal  which  is  most  attacked  is  called  the  positive  or 
generating  plate,  and  that  which  is  least  attacked  the  negative  or  collecting 

H  H  3 


706  Dynamical  Electricity.  [801- 

plate.  The  positive  metal  determines  the  direction  of  the  current,  which 
proceeds  in  the  liquid  from  the  positive  to  the  negative  plate,  and  out  of 
the  liquid  through  the  connecting  wire  from  the  negative  to  the  positive 
plate. 

In  speaking  of  the  direction  of  the  current  the  direction  of  the  positive 
electricity  is  always  understood. 

In  the  fundamental  experiment,  not  only  the  connecting  wire  but  also 
the  liquid  and  the  plates  are  traversed  by  the  electrical  currents — are  the 
scene  of  electrical  actions. 

The  mere  immersion  of  two  different  metals  in  a  liquid  is  not  alone 
sufficient  to  produce  a  current  ;  there  must  be  chemical  action.  When  a 
platinum  and  a  gold  plate  are  connected  with  a  delicate  galvanometer,  and 
immersed  in  pure  nitric  acid,  no  current  is  produced  ;  but  on  adding  a  drop 
of  hydrochloric  acid  a  strong  current  is  excited,  which  proceeds  in  the  liquid 
from  the  gold  to  the  platinum,  because  the  gold  is  attacked  by  the  nitro- 
hydrochloric  acid,  while  the  platinum  is  less  so,  if  at  all. 

As  a  voltaic  current  is  produced  whenever  two  metals  are  placed  in 
metallic  contact  in  a  liquid  which  acts  more  powerfully  upon  one  than  upon 
the  other,  there  is  a  great  choice  in  the  mode  of  producing  such  currents. 
In  reference  to  their  electrical  deportment,  the  metals  have  been  arranged 
in  what  is  called  an  electromotive  series,  in  which  the  most  electropositive  are 
at  one  end,  and  the  most  electronegative  at  the  other.  Hence  when  any  two 
of  these  are  placed  in  contact  in  dilute  acid,  the  current  in  the  connecting 
wire  proceeds  from  the  one  lower  in  the  list  to  the  one  higher.  The  principal 
metals  kre  as  follows  : — 

1.  Zinc  6.  Nickel  n.  Gold 

2.  Cadmium  7.  Bismuth  12.  Platinum 
3-  Tin                              8.  Antimony                   13.  Graphite 

4.  Lead  9.  Copper 

5.  Iron  10.  Silver 

It  will  be  seen  that  the  electrical  deportment  of  any  metal  depends  on 
the  metal  with  which  it  is  associated.  Iron,  for  example,  in  dilute  sulphuric 
acid  is  electronegative  towards  zinc,  but  is  electropositive  towards  copper ; 
copper  in  turn  is  electronegative  towards  iron  and  zinc,  but  is  electropositive 
towards  silver,  platinum,  or  graphite. 

802.  Electromotive  force. — The  force  in  virtue  of  which  continuous 
electrical  effects  are  produced  throughout  a  circuit  consisting  of  two  metals 
in  metallic  contact  in  a  liquid  which  acts  unequally  upon  them,  is  usually 
called  the  electromotive  force.  Electromotive  force  and  difference  of  potentials 
are  commonly  used  in  the  same  sense.  It  is,  however,  more  correct  to  regard 
difference  of  potentials  as  a  particular  case  of  electromotive  force  ;  for  as  we 
shall  afterwards  see,  there  are  cases  in  which  electrical  currents  are  produced 
without  the  occurrence  of  that  particular  condition  which  we  have  called 
difference  of  potentials.  The  electromotive  force  is  greater  in  proportion  to 
the  distance  of  the  two  metals  from  one  another  in  the  series.  That  is  to 
say,  it  is  greater  the  greater  the  difference  between  the  chemical  action  upon 
the  two  metals  immersed.  Thus  the  electromotive  force  between  zinc  and 
platinum  is  greater  than  that  between  zinc  and  iron,  or  between  zinc  and 


-802]  lUcctromoiive  Force.  7°7 

copper.  The  law  established  by  experiment  is,  that  the  electromotive  force 
:  tiny  two  metals  is  equal  to  the  sum  of  the  electromotive  forces  between 
all  the  intervening  metals.  Thus  the  electromotive  force  between  zinc  and 
platinum  is  equal  to  the  sum  of  the  electromotive  forces  between  zinc  and 
iron,  iron  and  copper,  and  copper  and  platinum. 

The  electromotive  force  is  influenced  by  the  condition  of  the  metal  ; 
rolled  zinc,  for  instance,  is  negative  towards  cast  zinc.  It  also  depends  on 
the  degree  of  concentration  of  the  liquid  ;  in  dilute  nitric  acid  zinc  is  positive 
towards  tin,  and  mercury'  positive  towards  lead  ;  while  in  concentrated  nitric 
acid  the  reverse  is  the  case,  mercury  and  zinc  being  respectively  electro- 
negative towards  lead  and  tin. 

The  nature  of  the  liquid  also  influences  the  direction  of  the  current.  If 
two  plates,  one  of  copper  and  one  of  iron,  are  immersed  in  dilute  sulphuric 
acid,  a  current  is  set  up  proceeding  through  the  liquid  from  the  iron  to  the 
copper  ;  but  if  the  plates,  after  being  washed,  are  placed  in  solution  of 
potassium  sulphide,  a  current  is  produced  in  the  opposite  direction  —  the 
copper  is  now  the  positive  metal.  Other  examples  may  be  drawn  from  the 
following  table,  which  shows  the  electric  deportment  of  the  principal  metals 
with  three  different  liquids.  It  is  arranged  like  the  preceding  one  ;  each 
metal  being  electropositive  towards  any  one  lower  in  the  list,  and  electro- 
negative towards  any  one  higher. 


Caustic  potass  Hydrochloric  acid 

Zinc  Zinc  Zinc 

Tin  Cadmium  Copper 

Cadmium  Tin  Cadmium 

Antimony  Lead  Tin 

Lead  Iron  Silver 

Bismuth  Copper  Antimony 

Iron  Bismuth  Lead 

Copper  Nickel  Bismuth 

Nickel  Silver  Nickel 

Silver  Antimony  Iron 

A  voltaic  current  may  also  be  produced  by  means  of  two  liquids  and  one 
metal.  This  may  be  shown  by  the  following  experiment  :  —  In  a  beaker  con- 
taining strong  nitric  acid  is  placed  a  small  porous  cylinder  closed  at  one  end, 
and  containing  strong  solution  of  caustic  potass.  If  now  two  platinum  wires 
connected  with  the  two  ends  of  a  galvanometer  (821)  are  immersed 
respectively  in  the  alkali  and  in  the  acid,  a  voltaic  current  is  produced, 
proceeding  in  the  wire  from  the  nitric  acid  to  the  potass,  which  thus 
correspond  respectively  to  the  negative  and  positive  plates  in  ordinary 
couples. 

A  metal  which  is  acted  upon  by  a  liquid  can  be  protected  from  solution 
by  placing  in  contact  with  it  a  more  electropositive  metal,  and  thus  forming 
a  simple  voltaic  circuit.  This  principle  is  the  basis  of  Davy's  proposal  to 
protect  the  copper  sheathing  of  ships,  which  are  rapidly  acted  upon  by  sea 
water.  If  zinc  or  iron  be  connected  with  the  copper,  these  metals  are  dis- 
solved and  the  copper  protected.  Davy  found  that  a  piece  of  zinc  the  size 
of  a  nail  was  sufficient  to  protect  a  surface  of  forty  or  fifty  square  inches  ; 


;o8 


Dynamical  Electricity. 


[802- 


unfortunately  the  proposal  has  not  been  of  practical  value,  for  the  copper 
must  be  attacked  to  a  certain  extent  to  prevent  the  adherence  of  marine 
plants  and  shellfish. 

803.  Poles  and  electrodes. — If  the  wire  connecting  the  two  terminal 
plates  of  a  voltaic  couple  be  cut,  it  is  clear,  from  what  has  been  said  about  the 
origin  and  direction  of  the  current,  that  positive  electricity  will  tend  to 
accumulate  at  the  end  of  the  wire  attached  to  the  copper  or  negative  plate, 
and  negative  electricity  on  the  wire  attached  to  the  zinc  or  positive  plate. 
These  terminals  have  been  called  the  poles  of  the 
battery.  For  experimental  purposes,  more  especi- 
ally in  the  decomposition  of  salts,  plates  of  platinum 
are  attached  to  the  ends  of  the  wires.  Instead  of  the 
term  poles,  the  word  electrode  (fjXfKTpov  and  6d6s  a 
way)  is  now  commonly  used  ;  for  these  are  the  ways 
through  which  the  respective  electricities  emerge. 
It  is  important  not  to  confound  the  positive  plate 
with  the  positive  pole  or  electrode.  The  positive 
electrode  is  that  connected  with  the  negative  plate, 
while  the  negative  electrode  is  connected  with  the 
positive  plate. 

804.  Voltaic  pile.  Voltaic  battery. — When  a 
series  of  voltaic  elements  or  pairs  are  arranged  so 
that  the  zinc  of  one  element  is  connected  with  the 
copper  of  another,  the  zinc  of  this  with  the  copper 
of  another,  and  so  on,  the  arrangement  is  called  a 
voltaic  battery  ;  and  by  its  means  the  effects  pro- 
duced by  a  single  element  are  capable  of  being  very 
greatly  increased. 

The  earliest  of  these  arrangements  was  devised  by 
Volta  himself.  It  consists  (fig.  664)  of  a  series  of  discs 
piled  one  over  the  other  in  the  following  order  : — At 
the  bottom,  on  a  frame  of  wood,  is  a  disc  of  copper, 
then  a  disc  of  cloth  moistened  by  acidulated  water,  or 
by  brine,  then  a  disc  of  zinc  ;  on  this  a  disc  of  copper, 
and  another  disc  of  moistened  cloth,  to  which  again 
follow  as  many  sets  of  zinc-cloth-copper,  always  in  the 
same  order,  as  may  be  convenient,  the  highest  disc  being  of  zinc.  The 
discs  are  kept  in  vertical  positions  by  glass  rods. 

It  will  be  readily  seen  that  we  have  here  a  series  of  simple  voltaic  couples, 
the  moisture  in  the  cloth  acting  as  the  liquid  in  the  cases  already  mentioned, 
and  that  the  terminal  zinc  is  the  negative  and  the  terminal  copper  the  positive 
pole.  From  the  mode  of  its  arrangement,  and  from  its  discoverer,  the  appa- 
ratus is  known  as  the  voltaic  pile,  a  term  applied  to  all  apparatus  of  this  kind 
for  accumulating  the  effects  of  dynamical  electricity. 

The  distribution  of  electricity  in  the  pile  varies  according  as  it  is  in  con- 
nection with  the  ground  by  one  of  its  extremities,  or  as  it  is  insulated  by 
being  placed  on  a  non-conducting  cake  of  resin  or  glass. 

In  the  former  case,  the  end  in  contact  with  the  ground  is  neutral,  and 
the  rest  of  the  apparatus  contains  only  one  kind  of  electricity  ;  this  is  nega- 


Fig.  664. 


-805] 


W'ol/aslons  Battery. 


709 


tive  if  the  copper  disc,  and  positive  if  the  zinc  disc  is  in  contact  with  the 
ground. 

In  the  insulated  pile  the  electricity  is  not  uniformly  distributed.  By  means 
of  the  proof-plane  and  the  electroscope  it  may  be  demonstrated  that  the 
middle  part  is  in  a  neutral  state,  and  that  one-half  is  charged  with  positive 
and  the  other  with  negative  electricity,  the  potential  increasing  from  the 
middle  to  the  ends.  The  half  terminated  by  a  zinc  disc  is  charged  with  nega- 
tive electricity,  and  that  by  a  copper  with  positive  electricity.  The  pile  is 
thus  similar  to  a  charged  Leyden  jar  ;  with  this  difference,  however,  that 
when  the  jar  has  been  discharged  by  connecting  its  .two  coatings,  the  elec- 
trical effects  cease  ;  while  in  the  case  of  the  pile,  the  cause  which  originally 
brought  about  the  distribution  of  electricity  restores  this  state  of  charge 
after  the  discharge  ;  and  the  continuous  succession  of  charges  and  dis- 
charges forms  the  current.  The  effects  of  the  pile  will  be  discussed  in  other 
places. 

805.  Wollaston'a  battery. — The  original  form  of  the  voltaic  pile  has  a 
great  many  inconveniences,  and  possesses  now  only  an  historical  interest. 
It  has  received  a  great  many  improvements,  the  principal  object  of  which 


Fig.  665. 


has  been  to  facilitate  manipulation,  and  to  produce  greater  electromotive 
force. 

One  of  the  earliest  of  these  modifications  was  the  crown  of  cups,  or 
couronne  des  tasses,  invented  by  Volta  himself ;  an  improved  form  of  this  is 
known  as  Wollastorfs  battery  (fig.  665) ;  it  is  arranged  so  that  when  the 
current  is  not  wanted,  the  action  of  the  battery  can  be  stopped. 

The  plates  Z  are  of  thick  rolled  zinc,  an$i  usually  about  eight  inches  in 
length  by  six  in  breadth.  The  copper  plates,  C,  are  of  thin  sheet,  and  bent 
so  as  to  surround  the  zincs  without  touching  them  :  contact  being  prevented 
.by  small  pieces  of  cork.  To  each  copper  plate  a  narrow  strip  of  copper,  o,  is 


7io  Dynamical  Electricity.  [805- 

soldered,  which  is  bent  twice  at  right  angles  and  is  soldered  to  the  zinc  plate  ; 
and  the  first  zinc,  Z,  is  surrounded  by  the  first  copper  C  ;  these  two  consti- 
tute a  couple,  and  each  couple  is  immersed  in  a  glass  vessel,  containing 
acidulated  water.  The  copper,  C,  is  soldered  to  the  second  zinc  by  the  strip 
<?,  and  this  zinc  is  in  turn  surrounded  by  a  second  copper,  and  so  on. 

Fig.  665  represents  a  pile  of  sixteen  couples  united  in  two  parallel  series 
of  eight  each.  All  these  couples  are  fixed  to  a  cross  frame  of  wood,  by  which 
they  can  be  raised  or  lowered  at  pleasure.  When  the  battery  is  not  wanted, 
the  couples  are  lifted  out  of  the  liquid.  The  water  in  these  vessels  is  usually 
acidulated  with  5\  sulphuric  and  ^  of  nitric  acid. 

Hare's  deflagrator. — This  is  a  simple  voltaic  arrangement,  consisting  of 
two  large  sheets  of  copper  and  zinc  rolled  together  in  a  spiral,  but  preserved 
from  direct  contact  by  bands  of  leather  or  horsehair.  The  whole  is  immersed 
in  a  vessel  containing  acidulated  water,  and  the  two  plates  are  connected 
outside  the  liquid  by  a  conducting  wire. 

806.  Enfeeblement  of  the  current  in  batteries.  Secondary  currents. 
The  various  batteries  already  described — Volta's,  Wollaston's,  and  Hare's, 
which  consist  essentially  of  two  metals  and  one  liquid— labour  under  the 
objection  that  the  currents  produced  rapidly  diminish  in  strength. 

This  is  principally  due  to  three  causes  :  the  first  is  the  decrease  in  the 
chemical  action  owing  to  the  neutralisation  of  the  sulphuric  acid  by  its  com- 
bination with  the  zinc.  This  is  a  necessary  action,  for  upon  it  depends  the 
current  ;  it  therefore  occurs  in  all  batteries,  and  is  without  remedy  except  by 
replacement  of  acid  and  zinc.  The  second  is  due  to  what  is  called  local 
action  ;  that  is,  the  production  of  small  closed  circuits  in  the  active  metal, 
owing  to  the  impurities  it  contains.  These  local  currents  rapidly  wear  away 
the  active  plate,  without  contributing  anything  to  the  continuance  of  the 
general  current.  They  are  remedied  by  amalgamating  the  zinc  with  mercury 
by  which  chemical  action  is  prevented  until  the  circuit  is  closed,  as  will  be 
more  fully  explained  (816).  The  third  arises  from  the  production  of  an 
inverse  electromotive  force,  which  tends  to  produce  a  current  in  a  contrary 
direction  to  the  principal  current,  and  therefore  to  destroy  it  either  totally 
or  partially.  In  the  fundamental  experiment  (fig.  663),  when  the  circuit  is 
closed,  zinc  sulphate  is  formed,  which  dissolves  in  the  liquid,  and  at  the 
same  time  a  layer  of  hydrogen  gas  is  gradually  formed  on  the  surface  of  the 
copper  plate.  This  diminishes  the  activity  of  the  combination  in  more  than 
one  way.  In  the  first  place,  it  interferes  with  the  contact  between  the  metal 
and  the  liquid  ;  in  the  second  place,  in  proportion  as  the  copper  becomes 
coated  with  hydrogen,  we  have  virtually  a  plate  of  hydrogen  instead  of  a 
plate  of  copper  opposed  to  the  zinc,  and  in  addition,  the  hydrogen,  by  react- 
ing on  the  zinc  sulphate,  which  accumulates  in  the  liquid,  gradually  causes 
a  deposition  of  zinc  on  the  surface  of  the  copper ;  hence,  instead  of  having 
two  different  metals  unequally  attacked,  the  two  metals  become  gradually 
less  different,  and,  consequently,  the  total  effect  and  the  current  become 
weaker  and  weaker. 

The  polarisation  of  the  plate  (as  this  phenomenon  is  termed)  may  be 
destroyed  by  breaking  the  circuit  and  exposing  the  copper  plate  to  the  air  ; 
the  deposited  hydrogen  is  thus  more  or  less  completely  got  rid  of,  and  on 
again  closing  the  circuit  the  current  has  nearly  its  original  strength.  The 


-808]  Constant  Currents.  711 

same  result  is  obtained  when  the  current  of  another  battery  is  transmitted 
through  the  battery  in  a  direction  opposite  to  that  of  the  first. 

When  platinum  electrodes  are  used 
to  decompose  water,  a  similar  pheno- 
menon is  produced,  calledfio/arisativn 
of  the  electrodes,  which  may  be  illus- 
trated by  an  arrangement  represented 
in  fig.  666,  in  which  B  is  a  constant 
element,  V  a  voltameter  (845),  G  a 
galvanometer  (821),  and  H  a  mercury 
cup.  The  wire  L  being  disconnected 
from  H,  a  current  is  produced  in  the 
voltameter,  the  direction  of  which  is 
from  P  to  P' ;  if  now  the  wire  F  be 

detached  from  H,  and  L  be  connected  therewith,  a  current  is  produced 
in  the  voltameter,  the  direction  of  which  is  from  P  to  P' ;  if  now  the  wire  F 
be  detached  from  H,  and  L  be  connected  therewith,  a  current  is  produced 
through  the  galvanometer  the  direction  of  which  is  from  P'  to  P  ;  that  is,  the 
opposite  of  that  which  the  element  had  previously  produced.  Becquerel  and 
Faraday  have  shown  that  this  polarisation  of  the  metals  results  from  the 
deposits  caused  by  the  passage  of  the  current. 

CONSTANT  CURRENTS. 

807.  Constant  currents. — With  few  exceptions,  batteries  composed  of 
elements  with  a  single  liquid  have  almost  gone  out  of  use,  in  consequence 
of  the  rapid  enfeeblemenc  of  the  current  produced.     They  have  been  replaced 
by  batteries  with  two  liquids,  which  are  called  constant  batteries  because 
their  action  continues  without  material  alteration  for  a  considerable  period 
of  time.     The  essential  point  to  be  attended  to  in  securing  a  constant  current 
is  to  prevent  the  polarisation  of  the  inactive  metal  ;  in  other  words,  to  hinder 
any  permanent  deposition  of  hydrogen  on  its  surface.     This  is  effected  by 
placing  the  inactive  metal  in  a  liquid  upon  which  the  deposited  hydrogen 
can  act  chemically. 

808.  Daniell's  battery. — This  was  the  first  form  of  the  constant  battery, 
and  was  invented  by  Daniell  in  the  year  1836.     As  regards  the  constancy 
of  its  action,  it  is  perhaps  still  the  best  of  all  constant  batteries.     Fig.  667 
represents   a  single  element.     A  glass  or  porcelain   vessel,  V,  contains  a 
saturated   solution    of  copper    sulphate,    in  which  is    immersed    a   copper 
cylinder,  G,  open  at  both  ends,  and  perforated  by  holes.     At  the  upper  part 
of  this  cylinder  there  is  an  annular  shelf,  G,  also  perforated  by  small  holes, 
and  below  the  level  of  the  solution  ;  this  is  intended  to  support  crystals  of 
copper  sulphate  to  replace  that  decomposed  as  the   electrical  action  pro- 
ceeds.    Inside  the  cylinder  is  a  thin  porous  vessel,  P,  of  unglazed  earthen- 
ware.    This   contains  either  water  or  solution  of  common    salt  or  dilute 
sulphuric  acid,  in  which  is  placed  the  cylinder  of  amalgamated  zinc,  Z.    Two 
thin  strips  of  copper,  p  and  n,  fixed  by  binding  screws  to  the  copper  and  to 
the  zinc,  serve  for  connecting  the  elements  in  series. 

When  a  Daniell's  element  is  closed,   the  hydrogen  resulting  from  the 
action  of  the  dilute  acid  on  the  zinc  is  liberated  on  the  surface  of  the  copper 


712 


Dynamical  Electricity. 


[808- 


plate,  but  meets  there  the  copper  sulphate,  which  is  reduced,  forming  sul- 
phuric acid  and  metallic  copper,  which  is  deposited  on  the  surface  of  the 

copper  plate.  In  this  way  copper  sulphate  in 
solution  is  taken  up  ;  and  if  it  were  all  con- 
sumed, hydrogen  would  be  deposited  on  the 
copper,  and  the  current  would  lose  its  con- 
stancy. This  is  prevented  by  the  crystals  of 
copper  sulphate  which  keep  the  solution  satur- 
ated. The  sulphuric  acid  produced  by  the 
decomposition  of  the  sulphate  permeates  the 
porous  cylinder,  and  tends  to  replace  the  acid 
used  up  by  its  action  on  the  zinc  ;  and  as  the 
quantity  of  sulphuric  acid  formed  in  the  solu- 
tion of  copper  sulphate  is  regular,  and  propor- 
tional to  the  acid  used  in  dissolving  the  zinc, 
the  action  of  this  acid  on  the  zinc  is  regular 
also,  and  thus  a  constant  current  is  produced. 
In  order  to  join  together  several  of  these 


Fig.  667. 


elements  to  form  a  battery,  the  zinc  of  one  is  connected  either  by  a  copper 
wire  or  strip  with  the  copper  of  the  next,  and  so  on,  from  one  element  to 
another,  as  shown  in  fig.  671,  for  another  kind  of  battery. 

Instead  of  a  porous  earthenware  vessel  a  bag  of  sailcloth  may  be  used 
for  the  diaphragm  separating  the  two  liquids.  The  effect  is  at  first  more 
powerful,  but  the  two  solutions  mix  more  rapidly,  which  weakens  the  current. 
The  object  of  the  diaphragm  is  to  allow  the  current  to  pass,  but  to  prevent 
as  much  as  possible  the  mixture  of  the  two  liquids. 

The  current  produced  by  a  Daniell's  battery  is  constant  for  some  hours  ; 
its  action  is  stronger  when  it  is  placed  in  hot  water. 

809.  Grove's  battery. — In  this  battery  the  copper  sulphate  solution  is 
replaced  by  nitric  acid,  and  the  copper  by  platinum,  by  which  greater  electro- 
motive force  is  obtained.  Fig.  668 
represents  one  of  the  forms  of  a 
couple  of  this  battery.  It  consists 
of  a  glass  vessel,  A,  partially  filled 
with  dilute  sulphuric  acid  (i  :  8)  ; 
of  a  cylinder  of  zinc,  Z,  open  at  both 
ends ;  of  a  vessel  V,  made  of  porous 
earthenware,  and  containing  ordi- 
nary nitric  acid  ;  of  a  plate  of 
platinum,  P  (fig.  669),  bent  in  the 
form  of  an  S>  and  fixed  to  a  cover, 
c,  which  rests  on  the  porous  vessel. 
The  platinum  is  connected  with  a 
binding  screw,  b,  and  there  is  a 
similar  binding  screw  on  the  zinc. 
In  this  battery  the  hydrogen,  which 
would  be  disengaged  on  the  platinum  meeting  the  nitric  acid,  decomposes 
it,  forming  hyponitrous  acid,  which  dissolves,  or  is  disengaged  as  nitrous 
fumes.  Grove's  battery  is  the  most  convenient  and  one  of  the  most  powerful 


Fig.  668. 


Fig.  669. 


-810] 


Ilnnscn's  Battery. 


713 


of  the  two-fluid  batteries.  It  is,  however,  expensive,  owing  to  the  high  price 
of  platinum  ;  besides  which  the  platinum  is  liable,  after  some  time,  to 
become  brittle  and  break  very  easily.  But  as  the  platinum  is  not  consumed, 
it  retains  most  of  its  value,  and  when  the  plates  which  have  been  used  in  a 
battery  are  heated  to  redness,  they  regain  their  elasticity. 

8 10.  Bunsen's   battery. —  Kunserfs,    also   known    as    the   zinc  carbon 
battery,  was   invented  in   1843;   it    is  m  effect  a  Grove's  battery,   where 


the  plate  of  platinum  is  replaced  by  a  cylinder  of  carbon.  This  is  made 
either  of  the  graphitoidal  carbon  deposited  in  gas  retorts,  or  by  calcin- 
ing in  an  iron  mould  an  intimate  mixture  of  coke  and  bituminous  coal,  finely 
powdered  and  strongly  compressed.  Both  these  modifications  of  carbon  are 
good  conductors.  Each  element  consists  of  the  following  parts  :  i.  a  vessel, 
F  (fig.  670),  either  of  stoneware  or  of  glass,  containing  dilute  sulphuric  acid; 
2.  a  hollow  cylinder,  Z,  of  amalgamated  zinc  ;  3.  a  porous  vessel,  V,  in  which 
is  ordinary  nitric  acid ;  4.  a  rod  of  carbon,  C,  prepared  in  the  above 
manner.  In  the  vessel  F  the  zinc  is  first  placed,  and  in  it  the  carbon  C  in 
the  porous  vessel  V  as  seen  in  P.  To  the  carbon  is  fixed  a  binding  screw, 
;//,  to  which  a  copper  wire  is  attached,  forming  the  positive  pole.  The  zinc 
is  provided  with  a  similar  binding  screw,  //,  and  wire,  which  is  thus  a  negative 
pole. 

The  elements  are  arranged  to  form  a  battery  (fig.  671)  by  connecting  each 
carbon  to  the  zinc  of  the  following  one  by  means  of  the  clamps  mn,  and  a 
strip  of  copper,  c,  represented  in  the  top  of  the  figure.  The  copper  is  pressed 
at  one  end  between  the  carbon  and  the  clamp,  and  at  the  other  it  is  soldered 
to  the  clamp  n,  which  is  fitted  on  the  zinc  of  the  following  element,  and  so 
forth.  The  clamp  of  the  first  carbon  and  that  of  the  last  zinc  are  alone  pro- 
vided with  binding  screws,  to  which  are  attached  the  wires. 

The  chemical  action  of  Bunsen's  battery  is  the  same  as  that  of  Grove's, 
and  being  equally  powerful,  while  less  costly,  is  almost  universally  used  on 
the  Continent.  But  though  its  first  cost  is  less  than  that  of  Grove's  batter)-, 
it  is  more  expensive  to  work,  and  is  not  so  convenient  to  manipulate. 

Callaris  battery  is  a  modified  form  of  Grove's.  Instead  of  zinc  and  plati- 
num, zinc  and  platinised  lead  are  used,  and  instead  of  pure  nitric  acid  Callan 


714  Dynamical  Electricity.  [810- 

used  a  mixture  of  sulphuric  acid,  nitric  acid,  and  saturated  solution  of  nitre. 
The  battery  is  said  to  be  equal  in  its  action  to  Grove's,  and  is  much  cheaper. 

Callan  has  also  constructed  a  battery  in  which  zinc  in  dilute  sulphuric 
acid  forms  the  positive  plate,  and  cast  iron  in  strong  nitric  acid  the  negative. 
Under  these  circumstances  the  iron  becomes  passive  :  it  is  strongly  electro- 
negative, and  does  not  dissolve.  If,  however,  the  nitric  acid  becomes  too 
weak,  the  iron  is  dissolved  with  simultaneous  disengagement  of  nitrous 
fumes. 

After  being  in  use  some  time,  all  the  batteries  in  which  the  polarisation  is 
prevented  by  nitric  acid  disengage  nitrous  fumes  in  large  quantities,  and  this 
is  a  serious  objection  to  their  use,  especially  in  closed  rooms.  To  prevent 
this,  nitric  acid  is  frequently  replaced  by  chromic  acid,  or,  better,  by  a  mixture 
of  4  parts  potassium  bichromate,  4  parts  sulphuric  acid,  and  18  water.  The 
liberated  hydrogen  reduces  the  chromic  acid  to  the  state  of  oxide  of  chromium, 


Fig.  671. 

which  remains  dissolved  iii  sulphuric  acid.  With  the  same  view,  sesqui- 
chloride  of  iron  is  sometimes  substituted  for  nitric  acid  ;  it  becomes  re- 
duced to  protochloride.  But  the  action  of  the  elements  thus  modified  is 
considerably  less  than  when  nitric  acid  is  used,  owing  to  the  increased  re- 
sistance. 

8 1 1.  Smee's  battery. — In  this  battery  the  polarisation  of  the  negative 
plate  is  prevented  by  mechanical  means.  Each  element  consists  of  a  sheet  of 
platinum  placed  between  two  vertical  plates  of  zinc,  as  in  Grove's  battery; 
but  as  there  is  only  a  single  liquid,  dilute  sulphuric  acid,  the  elements  have 
much  the  form  of  those  in  Wollaston's  battery.  The  adherence  of  hydrogen 
to  the  negative  plate  is  prevented  by  covering  the  platinum  with  a  deposit  of 
finely  divided  platinum.  In  this  manner  the  surface  is  roughened,  which 
facilitates  the  disengagement  of  hydrogen  to  a  remarkable  extent,  and  conse- 
quently diminishes  the  resistance  of  a  couple.  Instead  of  platinum,  silver 
covered  with  a  deposit  of  finely  divided  platinum  is  frequently  substituted,  as 
being  cheaper. 

Walkers  battery. — This  resembles  Smee's  battery,  but  the  electronegative 


-812] 


Recent  Batteries. 


715 


plate  is  either  gas  grapnite  or  platinised  graphite  ;  it  is  excited  by  dilute 
sulphuric  acid.  This  battery  is  used  in  all  the  stations  of  the  South-Eastern 
Railway  ;  it  has  considerable  electromotive  force,  is  convenient  and  econo- 
mical in  manipulation,  and  large-sized  elements  can  be  constructed  at  a 
cheap  rate. 

812.  Recent  batteriec.—  The  mercury  sulphate  battery  (fig.  672)  de- 
vised by  Marie"  Davy,  is  essentially  a  zinc-carbon  element,  but  of  smaller 
dimensions  than  those  elements  usually  are.  In  the  outer  vessel,  V,  ordi- 
nary water  or  brine  is  placed,  and  in  the  porous  vessel  mercury  sulphate. 
This  salt  is  agitated  with  about  three  times  its  volume  of  water,  in  which  it  is 
difficultly  soluble,  and  the  liquid  poured  off  from  the  pasty  mass.  The  carbon 


Fig.  672. 


Fig.  673. 


Fig.  674. 


being  placed  in  the  porous  vessel,  the  spaces  are  filled  with  the  residue,  and 
then  the  decanted  liquid  poured  into  it. 

Chemical  action  takes  place  only  when  the  cell  is  closed.  The  zinc  then 
decomposes  the  water,  liberating  hydrogen,  which,  traversing  the  porous 
vessel,  reduces  the  mercury  sulphate,  forming  metallic  mercury,  which  collects 
at  the  bottom  of  the  vessel,  while  the  sulphuric  acid  formed  at  the  same  time 
traverses  the  diaphragm  to  act  on  the  zinc  and  thus  increases  the  action. 

The  mercury  which  is  deposited  may  be  used  to  prepare  a  quantity  of 
sulphate  equal  to  that  which  has  been  consumed.  A  small  quantity  of  the 
solution  of  mercury  sulphate  may  also  pass  through  the  diaphragm  ;  but 
this  is  rather  advantageous,  as  its  effect  is  to  amalgamate  the  zinc. 

The  electromotive  force  of  this  element  is  about  a  quarter  greater  than  that 
of  DanielFs  element,  but  it  has  greater  resistance ;  it  is  rapidly  exhausted 
when  continuously  worked,  though  it  appears  well  suited  for  discontinuous 
work,  as  with  the  telegraph,  and  with  alarums. 

Gravity  batteries. — The  use  of  porous  vessels  is  liable  to  many  objections, 
more  especially  in  the  case  of  DanielPs  battery,  in  which  they  gradually 
become  encrusted  with  copper,  which  destroys  them.  A  kind  of  battery  has 
been  devised  in  which  the  porous  vessel  is  entirely  dispensed  with,  and  the 
separation  of  the  liquids  is  effected  by  the  difference  of  density.  Such 
batteries  are  called  gravity  batteries.  Fig.  673  represents  a  form  devised 
by  Callaud.  V  is  a  glass  or  earthenware  vessel  in  which  is  a  copper  plate 
soldered  to  a  wire  insulated  by  gutta  percha.  On  the  plate  is  a  layer  of 


716  Dynamical  Electricity.  [812- 

crystals  of  copper  sulphate,  C  ;  the  whole  is  then  filled  with  water,  and  the 
zinc  cylinder,  Z,  is  immersed  in  it.  The  lower  part  of  the  liquid  becomes 
saturated  with  copper  sulphate  ;  the  action  of  the  battery  is  that  of  a  Daniell, 
and  the  zinc  sulphate  which  gradually  forms,  floats  on  the  solution  of  copper 
sulphate  owing  to  its  lower  density.  This  battery  rs  easily  manipulated,  the 
consumption  of  copper  sulphate  is  economical,  and  when  not  agitated  it 
works  constantly  for  some  time,  provided  care  be  taken  to  replace  the  water 
lost  by  evaporation. 

Meidinger's  element,  which  is  much  used  in  Germany,  is  essentially  a 
gravity  battery  of  special  construction  with  zinc  in  solution  of  magnesic 
sulphate,  and  copper  in  solution  of  copper  sulphate. 

Minotttfs  battery. — This  may  be  described  as  a  Daniell's  element,  in 
which  the  porous  vessel  is  replaced  by  a  layer  of  sawdust  or  of  sand.  At 
the  bottom  of  an  earthenware  vessel  (fig.  674)  is  placed  a  layer  of  coarsely- 
powdered  copper  sulphate  a,  and  on  this  a  copper  plate  provided  with  an 
insulated  copper  wire  i.  On  this  there  is  a  layer  of  sand  or  of  sawdust  be, 
and  then  the  whole  is  filled  with  water,  in  which  rests  a  zinc  cylinder  Z. 
The  action  is  just  that  of  a  Daniell ;  the  sawdust  prevents  the  mixture  of 
the  liquids,  but  it  also  offers  great  resistance,  which  increases  with  its  thick- 
ness. From  its  simplicity  and  economy,  and  the  facility  with  which  it  is 
constructed,  this  battery  merits  increased  attention. 

De  la  Rue  and  Mailer's  element  consists  of  a  glass  tube  about  6  inches 
long  by  075  inch  in  diameter,  closed  by  a  vulcanised  india-rubber  stopper 
through  which  passes  a  zinc  rod  18  inches  in  diameter  and  5  inches  long. 
A  flattened  silver  wire  also  passes  through  the  stopper  to  the  bottom  of  the 
tube,  in  which  is  placed  about  half  an  ounce  of  silver  chloride,  the  greater 
part  of  the  cell  being  filled  with  solution  of  sal-ammoniac.  The  hydrogen 
evolved  at  the  negative  plate  reduces  the  chloride  to  metallic  silver,  which 
is  thereby  recovered.  Since  there  is  only  one  liquid,  and  the  solid  electro- 
lyte is  not  acted  upon  when  the  circuit  is  open,  the  element  is  easily  worked 
and  requires  little  attention.  It  is  very  compact,  1,000  elements  occupying 
a  space  of  less  than  a  cubic  yard  ;  De  la  Rue  and  Miiller  have  used  as 
many  as  14,400  such  cells  in  investigations  on  the  stratification  of  the  electric 
light.  A  battery  of  8,040  of  these  cells  gave  a  spark  |  of  an  inch  in  length 
in  air  under  the  ordinary  atmospheric  pressure  ;  while^under  a  pressure  of 
a  quarter  of  an  atmosphere  the  striking  distance  was  I  \  inch. 

The  electromotive  force  of  a  silver  chloride  cell  is  1*03  of  a  volt,  and  that 
of  one  made  with  silver  bromide  is  0-908  ;  hence  a  series  of  4  cells,  three  of 
the  silver  chloride  cells  with  one  of  bromide,  give  an  average  electromotive 
force  of  i  volt -(8 1 4). 

Mr.  Latimer  Clark  has  devised  an  element  which  consists  of  pure  mer- 
cury as  a  negative  plate  covered  with  a  paste,  obtained  by  boiling  sul- 
phate of  mercury  in  a  saturated  solution  of  zinc  sulphate.  The  positive 
metal  is  a  plate  of  zinc  resting  on  this  paste  of  sulphate.  Insulated  wires, 
leading  to  the  mercury  and  the  zinc  respectively,  form  the  connections. 
This  battery  is  not  well  adapted  for  continuous  work,  but  it  furnishes 
a  standard  of  electromotive  force,  which  is  constant  and  can  be  relied 
upon. 

813.  Leclanche's  element. — This  consists  (fig.  675)  of  a  rod  of  carbon, 
C,  placed  in  a  porous  pot,  which  is  then  very  tightly  packed  with  a  mixture 


-814] 


Electromotive  Force  of  Different  Elements. 


717. 


of  pyrolusite  (peroxide  of  manganese)  and  gas  graphite  M.  This  is  covered 
over  with  a  layer  of  pitch.  At  the  top  of  the  carbon  is  soldered  a  mass 
of  lead,  L,  to  which  is  affixed  a  binding 
screw.  The  positive  plate  is  a  rod  of  zinc 
Z,  in  which  is  fixed  a  copper  wire,  «.  The 
exciting  liquid  consists  of  a  strong  solution 
of  sal-ammoniac,  contained  in  a  glass 
vessel  G,  which  is  not  more  than  one-third 
full.  The  electromotive  force  of  the  ele- 
ment is  said  to  be  about  one-third  greater 
than  that  of  a  DanielFs  element ;  its  in- 
ternal resistance  varies  of  course  with  the 
size,  but  is  stated  to  be  from  two  to  three 
times  that  of  an  ohm.  The  battery  is  not 
adapted  for  continuous  work,  as  in  heavy 
telegraphic  circuits,  or  in  electroplating, 
since  it  soon  becomes  polarised  ;  it  has, 
however,  the  valuable  property  of  quickly 
regaining  its  original  strength  when  left  at 
rest,  and  is  extremely  well  adapted  for 
discontinuous  work. 

A  rod  of  carbon  4^xi;x35-  inches 
should  have  a  maximum  resistance  of  I 
ohm ;  but  good  plates  made  from  the 
carbon  of  gas  retorts  do  not  average 
more  than  0-5,  and  in  some  cases  o-i  unit.  If  the  resistance  =  an  ohm,  the 
conducting  power  of  carbon  is  about  0^003  that  of  mercury. 

A  drawback  to  the  use  of  carbon  is  that,  from  its  porosity,  the  exciting 
liquid  rises,  and  forms,  at  the  junction  with  the  binding  screw,  a  local  cur- 
rent which  injures  or  destroys  contact.  This  may  be  remedied  to  a  very 
great  extent  by  soaking  the  plates  before  use  in  hot  melted  paraffine,  which 
penetrates  into  the  pores,  expelling  the  air.  On  cooling  it  solidifies  and 
prevents  the  capillary  action  mentioned  above.  By  carefully  scraping  the 
paraffine  from  the  outside,  a  surface  is  exposed  which  is  as  good  a  conductor 
as  if  the  pores  were  filled  with  air.  Measurements  have  shown  that  the 
resistance  of  a  rod  thus  prepared  is  not  altered. 

814.  Electromotive  force  of  different  elements. — The  following  numbers 
represent  the  electromotive  force  of  some  of  the  elements  most  frequently 
used,  compared  with  that  of  an  ordinary  Daniell's  cell  charged  as  above 
described  ;  they  are  the  means  of  many  careful  determinations  : — 

Daniell's  element  set  up  with  water 

„  „  „       pure  zinc  and  pure  water,  with  pure 

copper  and  pure  saturated  solution 
of  copper  sulphate 

„       zinc   in   saturated   solution   of  am- 
monium chloride  . 


Fig.  675. 


I -00 


I'02 


Leclanchd's 


Marie  Davy's,, 
Bunsen's        „ 

»  55 

Grove;s  „ 


carbon  in  nitric  acid 
carbon  in  chromic  acid 
platinum  in  nitric  acid 


•32 
•4i 
77 
•87 


7 1 8  Dynamical  Electricity.  [814- 

The  greatest  electromotive  force  as  yet  observed  is  by  Beetz  in  a  couple 
consisting  of  potassium  amalgam  in  caustic  potash,  combined  with  pyro- 
lusite  in  a  solution  of  potassium  permanganate.  It  is  three  times  as  much 
as  that  of  a  DanielPs  element. 

The  standard  of  electromotive  force  on  C.  G.  S.  system  is  the  Volt. 
This  is  equal  to  1,000,000,000  or  io8  absolute  electromagnetic  units  ;  the 
latter  way  of  expressing  it  is  convenient,  as  avoiding  the  use  of  long  numbers. 
The  volt  is  rather  less  than  the  electromotive  force  of  a  Daniell's  cell,  the 
mean  value  of  which  may  be  taken  at  1-12  volt.  The  unit  of  current,  which 
is  usually  called  a  Weber*  is  the  current  due  to  an  electromotive  force  of  i 
volt  working  through  a  resistance  of  i  ohm. 

815.  Comparison  of  the  voltaic  battery  with  a  frictional  electrical 
machine. — Except  in  the  case  of  batteries  consisting  of  a  very  large  number 
of  couples,  the  difference  of  potentials  between  the  terminals  is  far  weaker 
than  in  frictional  electrical  machines,  and  is  insufficient  to  give  any  visible 
spark.  With  De  la  Rue  and  Muller's  great  battery  the  striking  distance 
between  two  terminals  was  found  to  increase  with  the  potential,  but  for  high 
potentials  rather  more  rapidly  than  in  direct  ratio.  Thus  while  the  striking 
distance  was  0-012  in.  with  the  potential  due  to  1,200  of  their  cells,  it  was 
0-049  m-  witn  4>8oo  cells,  and  0-133  in.  with  11,000  cells. 

In  the  case  of  a  small  battery  or  of  a  single  cell,  very  delicate  tests  are 
required  to  detect  any  signs  of  free  electrification.  But  by  means  of  a  deli- 
cate condensing  electroscope,  and  by  extremely  careful  insulation,  it  can  be 
shown  that  one  pole  possesses  a  positive  and  the  other  a  negative  charge. 
For  this  purpose  one  of  the  plates  of  the  electroscope  is  connected  with 
one  pole,  and  the  other  with  the  other  pole  or  with  the  ground.  The 
electroscope  thus  becomes  charged,  and  on  breaking  the  communication 
electroscopic  indications  are  observed. 

On  the  other  hand  the  strength  of  current  which  a  voltaic  element  can 
produce  in  a  good  conductor  is  much  greater  than  that  which  can  be  pro- 
duced by  a  machine.  Faraday  immersed  two  wires — one  of  zinc,  and  the 
other  of  platinum,  each  T\  of  an  inch  in  diameter — in  acidulated  water  for  -3- 
of  a  second.  The  effect  thus  produced  on  a  magnetic  needle  in  this  short 
time  was  greater  than  that  produced  by  23  turns  of  the  large  electrical 
machine  of  the  Royal  Institution. 

Nystrom  has  ascertained  by  quantitative  measurements  that  the  potential 
of  the  charge  of  the  cover  of  an  ordinary  electrophorus  is  not  less  than  50,000 
times  as  great  as  the  potential  of  a  Meidinger's  cell  (812)  ;  that  is,  that  not 
less  than  50,000  of  those  elements  would  be  required  to  produce  the  same 
potential  as  the  electrophorus.  In  practice,  a  far  greater  number  would  be 
needed,  owing  to  the  difficulty  of  getting  good  insulation. 

8 1 6.  Amalgamated  zinc,  local  currents. — Perfectly  pure  distilled 
zinc  is  not  attacked  by  dilute  sulphuric  acid,  but  becomes  so  when  immersed 
in  that  liquid  in  contact  with  a  plate  of  copper  or  of  platinum.  Ordinary 
commercial  zinc,  on  the  contrary,  is  rapidly  dissolved  by  dilute  acid.  This, 
doubtless,  arises  from  the  impurity  of  the  zinc,  which  always  contains  traces 
either  of  iron  or  lead.  Being  electronegative  towards  zinc,  they  tend  to 
produce  local  electrical  currents,  which  accelerate  the  chemical  action  with- 
out increasing  the  quantity  of  electricity  in  the  connecting  wire. 


-818]  Dry  Piles.  719 

Zinc,  when  amalgamated,  acquires  the  properties  of  perfectly  pure  zinc 
and  is  unaltered  by  dilute  acid,  so  long  as  it  is  not  in  contact  with  a  copper 
or  platinum  plate  immersed  in  the  same  liquid.  To  amalgamate  a  zinc  plate, 
it  is  first  immersed  in  dilute  sulphuric  or  hydrochloric  acid  so  as  to  obtain  a 
clean  surface,  and  then  a  drop  of  mercury  is  placed  on  the  plate  and  spread 
over  it  with  a  brush.  The  amalgamation  takes  place  immediately,  and  the 
plate  has  the  brilliant  aspect  of  mercury.  Zinc  as  well  as  other  metals  are 
readily  amalgamated  by  dipping  them  in  an  amalgam  of  one  part  sodium 
and  200  parts  of  mercury.  Zinc  plates  may  also  be  amalgamated  by  dipping 
them  in  a  solution  of  mercury  prepared  by  dissolving  one  pound  of  mercury 
in  rive  pounds  of  aqua  regia  (one  part  of  nitric  to  three  of  hydrochloric  acid), 
and  then  adding  five  parts  more  of  hydrochloric  acid. 

The  amalgamation  of  the  zinc  removes  from  its  surface  all  the  impurities, 
especially  the  iron.  The  mercury  effects  a  solution  of  pure  zinc,  which  covers 
the  surface  of  the  plate,  as  with  a  liquid  layer.  The  process  was  first  applied 
to  electrical  batteries  by  Kemp.  Amalgamated  zinc  is  not  attacked  so  long 
as  the  circuit  is  not  closed — that  is,  when  there  is  no  current  ;  when  closed 
the  current  is  more  regular,  and  at  the  same  time  stronger,  for  the  same 
quantity  of  metal  dissolved. 

817.  Dry  piles. —  In  dry  piles  the  liquid  is  replaced  by  a  solid  hygrometric 
substance,  such  as  paper  or  leather.     They  are  of  various  kinds  :  in  Zamboni's, 
which  is  most  extensively  used,  the  electromotors  are  tin  or  silver,  and  bin- 
oxide  of  manganese.     To  construct  one  of  these  a  piece  of  paper  silvered  or 
tinned  on  one  side  is  taken  ;  the  other  side  of  the  paper  is  coated  with  finely- 
powdered  binoxide  of  manganese  by  slightly  moistening  it,  and  rubbing  the 
powder  on  with  a  cork.     Having  placed  together  seven  or  eight  of  these 
sheets,  they  are  cut  by  means  of  a  punch  into  discs  an  inch  in  diameter. 
These  discs  are  then  arranged  in  the  same  order,  so  that  the  tin  or  silver  of 
each  disc  is  in  contact  with  the  manganese  of  the  next.    Having  piled  up  1,200 
or  i, 800  couples,  they  are  placed  in  a  glass  tube,  which  is  provided  with  a 
brass  cap  at  each  end.     In  each  cap  there  is  a  rod  and  knob,  by  which  the 
leaves  can  be  pressed  together,  so  as  to  produce  better  contact.     The  knob 
in  contact  with  the  manganese  corresponds  to  the  positive  pole,  while  that 
at  the  other  end,  which  is  in  contact  with  the  silver  or  tin,  is  the  negative 
pole. 

Dry  piles  are  remarkable  for  the  permanence  of  their  action,  which 
may  continue  for  several  years.  Their  action  depends  greatly  on  the  tem- 
perature and  on  the  hygrometric  state  of  the  air.  It  is  stronger  in  summer 
than  in  winter,  and  the  action  of  a  strong  heat  revives  it  when  it  appears 
extinct.  A  Zamboni's  pile  of  2,000  couples  gives  neither  shock  nor  spark, 
but  can  charge  a  Leyden  jar  and  other  condensers.  A  certain  time  is,  how- 
ever, necessary,  for  electricity  only  moves  slowly  in  the  interior. 

8 1 8.  Bohnenberger's   electroscope. — Bohnenberger  has  constructed  a 
dry  pile  electroscope  of  great  delicacy.     It  is  a  condensing  electroscope 
(fig.  641),  from  the  rod  of  which  is  suspended  a  single  gold  leaf.     This  is  at 
an  equal  distance  from  the  opposite  poles  of  two  dry  piles  placed  vertically, 
inside  the  bell  jar,  on  the  plate  of  the  apparatus.     As  soon  as  the  gold  leaf 
possesses  any  free  electricity  it  is  attracted  by  one  of  the  poles  and  repelled 
by  the  other,  and  its  electricity  is  obviously  contrary  to  that  of  the  pole 
towards  which  it  moves. 


720  Dynamical  Electricity.  [819- . 


CHAPTER   II. 

DETECTION   AND   MEASUREMENT  OF  VOLTAIC  CURRENTS. 

819.  Detection  and  measurement  of  voltaic  currents. — The  remark- 
able phenomena  of  the  voltaic  battery  may  be  classed  under  the  heads  phy- 
siological, chemical,  mechanical,  and  physical  effects  ;  and  these  latter  may 
be  again  subdivided  into  the  thermal,  luminous,  and  magnetic  effects.     For 
ascertaining  the  existence  and  measuring  the  strength  of  voltaic  currents, 
the  magnetic  effects  are  more  suitable  than  any  of  the  others,  and,  accord- 
ingly, the  fundamental  magnetic  phenomena  will  be  described  here,  and  the 
description  of  the  rest  postponed  to  a  special  chapter  on  electro-magnetism. 

820.  Oersted's    experiment. — Oersted  published   in    1819    a   discovery 
which  connected  magnetism  and  electricity  in  a  most  intimate  manner,  and 
became,  in  the  hands  of  Ampere  and  of  Faraday,  the  source  of  a  new  branch 
of  physics.     The  fact  discovered  by  Oersted  is  the  directive  action  which  a 
fixed  current  exerts  at  a  distance  on  a  magnetic  needle. 

To  make  this  experiment  a  copper  wire  is  suspended  horizontally  in  the 

direction  of  the  magnetic  meridian  over 
a  moveable  magnetic  needle,  as  repre- 
sented in  fig.  676.  So  long  as  the  wire 
is  not  traversed  by  a  current  the  needle 
remains  parallel  to  it ;  but  as  soon  as 
the  ends  of  the  wire  are  respectively 
connected  with  the  poles  of  a  battery 
or  of  a  single  element,  the  needle  is  de- 
flected, and  tends  to  take  a  position 
which  is  the  more  nearly  at  right  angles 
to  the  magnetic  meridian  in  proportion 
as  the  current  is  stronger. 

In  reference  to  the  direction  in  which  the  poles  are  deflected,  there  are 
several  cases  which  may,  however,  be  referred  to  a  single  principle.  Re- 
membering our  assumption  as  to  the  direction  of  the  current  in  the  con- 
necting wire  (803)  the  preceding  experiment  presents  the  following  four 
cases  : — 

i.  If  the  current  passes  above  the  needle,  and  goes  from  south  to  north, 
the  north  pole  of  the  magnet  is  deflected  towards  the  west ;  this  arrangement 
is  represented  in  the  above  figure. 

ii.  If  the  current  passes  below  the  needle,  also  from  south  to  north,  the 
north  pole  is  deflected  towards  the  east. 

iii.  When  the  current  passes  above  the  needle,  but  from  north  to  south, 
the  north  pole  is  deflected  towards  the  east. 


-821] 


Galvanometer  or  Multiplier. 


721 


iv.  Lastly,  the  deflection  is  towards  the  west  when  the  current  goes  from 
north  to  south  below  the  needle. 

Ampere  has  given  the  following  memoiiatechtiica  by  which  all  the  various 
directions  of  the  needle  under  the  influence  of  a  current  may  be  remembered. 
If  we  imagine  an  observer  placed  in  the  connecting  wire  in  such  a  manner 
that  the  current  entering  by  his  feet  issues  by  his  head,  and  that  his  face  is 
always  turned  towards  the  needle,  we  shall  see  that  in  the  above  four  posi- 
tions the  north  pole  is  always  deflected  towards  the  left  of  the  observer.  By 
thus  personifying  the  current,  the  different  cases  may  be  comprised  in  this 
general  principle  :  ///  the  directive  action  of  currents  on  magnets,  the  north 
pole  is  always  deflected  towards  the  left  of  the  current. 

821.  Galvanometer  or  multiplier. — The  name  galvanometer,  or  some- 
times multiplier  or  rheometer,  is  given  to  a  very  delicate  apparatus  by  which 
the  existence,  direction,  and  intensity  of  currents  may  be  determined.  It 
was  invented  by  Schweigger  in  Germany  a  short  time  after  Oersted's  dis- 
covery. 

In  order  to  understand  its  principle,  let  us  suppose  a  magnetic  needle 
suspended  by  a  filament  of  silk  (fig.  677),  and  surrounded  in  the  plane  of 


7  p 

Fig.  677. 


Fig.  678. 


the  magnetic  meridian  by  a  copper  wire,  mnopq,  forming  a  complete  circuit 
round  the  needle  in  the  direction  of  its  length.  When  this  wire  is  traversed 
by  a  current,  it  follows,  from  what  has  been  said  in  the  previous  paragraph, 
that  in  every  part  of  the  circuit  an  observer  lying  in  the  wire  in  the  direction 
of  the  arrows,  and  looking  at  the  needle  ab,  would  have  his  left  always  turned 
towards  the  same  point  of  the  horizon,  and  consequently,  that  the  action  of 
the  current  in  every  part  would  tend  to  turn  the  north  pole  in  the  same 
direction  ;  that  is  to  say,  that  the  actions  of  the  four  branches  of  the  circuit 
concur  to  give  the  north  pole  the  same  direction.  By  coiling  the  copper 
wire  in  the  direction  of  the  needle,  as  represented  in  the  figure,  the  action 
of  the  current  has  been  multiplied.  If,  instead  of  a  single  one,  there  are 
several  circuits,  provided  they  are  insulated,  the  action  becomes  still  more 
multiplied,  and  the  deflection  of  the  needle  increases.  Nevertheless,  the 
action  of  the  current  cannot  be  multiplied  indefinitely  by  increasing  the 
number  of  windings,  for,  as  we  shall  presently  see,  the  intensity  of  a  current 
diminishes  as  the  length  of  the  circuit  is  increased. 

As  the  directive  action  of  the  earth  continually  tends  to  keep  the  needle 
in  the  magnetic  meridian,  and  thus  opposes  the  action  of  the  current,  the 

I  i 


722 


Dynamical  Electricity. 


[821- 


eftect  of  the  latter  is  increased  by  using  an  astatic  system  of  two  needles, 
as  shown  in  fig.  678.  The  action  of  the  earth  on  the  needle  is  then  very 
feeble,  and,  further,  the  actions  of  the  current  on  the  two  needles  become 
accumulated.  In  fact,  the  action  of  the  circuit,  from  the  direction  of  the 
current  indicated  by  the  arrows,  tends  to  deflect  the  north  pole  of  the  lower 
needle  towards  the  west.  The  upper  needle  a'b',  is  subjected  to  the  action 
of  two  contrary  currents  no  and  qp,  but  as  the  first  is  nearer,  its  action  pre- 
ponderates. Now  this  current  passing  below  the  needle,  evidently  tends 
to  turn  the  pole  a'  towards  the  east,  and,  consequently,  the  pole  b'  towards 
the  west ;  that  is  to  say,  in  the  same  direction  as  the  pole  a  of  the  other 
needle. 

From  these  principles  it  will  be  easy  to  understand  the  action  of  the 
multiplier.     The  apparatus  represented  in  fig.  679  consists  of  a  thick  brass 

plate,  D,  resting  on  levelling 
screws  ;  on  this  is  a  rotating 
plate,  P,  of  the  same  metal,  to 
which  is  fixed  a  copper  frame, 
the  breadth  of  which  is  almost 
equal  to  the  length  of  the 
needles.  On  this  is  coiled  a 
great  number  of  turns  of  wire 
covered  with  silk.  The  two 
ends  terminate  in  binding 
screws,  /  and  o.  Above  the 
frame  is  a  graduated  'circle,  C, 
with  a  central  slit  parallel  to 
the  direction  in  which  the  wire 
is  coiled.  The  zero  corresponds 
to  the  position  of  this  slit,  and 
there  are  two  graduations  on 
the  scale,  the  one  on  the  right 
and  the  other  on  the  left  of 
zero,  but  they  only  extend  to 
90°.  By  means  of  a  very  fine 
filament  of  silk,  an  astatic  sys- 
tem is  suspended  ;  it  consists 
of  two  needles,  ab  and  a'b',  one 
above  the  scale,  and  the  other 
within  the  circuit  itself.  These 
Fig.  679.  needles,  which  are  joined  to- 

gether by  a  copper  wire,  like 

those  in  fig.  577  and  fig.  678  and  cannot  move  separately,  must  not  have 
exactly  the  same  magnetic  intensity  ;  for  if  they  are  exactly  equal,  every 
current,  strong  or  weak,  would  always  put  them  at  right  angles  with  itself. 

In  using  this  instrument  the  diameter,  to  which  corresponds  the  zero  of 
the  graduation,  is  brought  into  the  magnetic  meridian  by  turning  the  plate 
P  until  the  end  of  the  needle  ab  corresponds  to  zero.  The  instrument  is 
fixed  in  this  position  by  means  of  the  screw  clamp  T. 

The  length  and  diameter  of  the  wire  vary  with  the  purpose  for  which  the 


-822]  Sir  W.  Thomsons  Marine  Galvanometer.  723 

galvanometer  is  intended.  For  one  which  is  to  be  used  in  observing  the 
currents  due  to  chemical  actions,  a  wire  about  |  millimetre  in  diameter,  and 
making  about  800  turns,  is  well  adapted.  Those  for  thermo-electric  currents, 
which  have  low  intensity,  require  a  thicker  and  shorter  wire  ;  for  example, 
thirty  turns  of  a  wire  f  millimetre  in  diameter.  For  very  delicate  experi- 
ments, as  in  physiological  investigations,  galvanometers  with  as  many  as 
30,000  turns  have  been  used. 

By  means  of  a  delicate  galvanometer  consisting  of  2,000  or  3,000  turns 
of  fine  wire,  the  coils  of  which  are  carefully  insulated  by  means  of  silk  and 
shellac,  currents  of  high  potential,  as  those  of  the  electrical  machine  (791) 
may  be  shown.  One  end  of  the  galvanometer  is  connected  with  the  con- 
ductor, and  the  other  with  the  ground,  and  on  working  the  machine  the  needle 
is  deflected,  affording  thus  an  illustration  of  the  identity  of  statical  with 
dynamical  electricity. 

The  deflection  of  the  needle  increases  with  the  strength  of  the  current  ; 
the  relation  between  the  two  is,  however,  so  complex,  that  it  cannot  well 
be  deduced  from  theoretical  considerations,  but  requires  to  be  determined 
experimentally  for  each  instrument.  And  in  the  majority  of  cases  the  in- 
strument is  used  as  a  galvanoscope  or  rheoscope — that  is,  to  ascertain  rather 
the  presence  and  direction  of  currents — than  as  a  galvanometer  or  rheometer 
in  the  strict  sense  ;  that  is,  as  a  measurer  of  their  intensity.  The  term 
galvanometer  is,  however,  commonly  used. 

The  differential  galvanometer  consists  of  a  needle,  as  in  an  ordinary 
galvanometer,  but  round  the  frame  of  which  are  coiled  two  wires  of  the  same 
kind  and  dimensions,  carefully  insulated  from  each  other,  and  provided  with 
suitable  binding  screws,  so  that  separate  currents  can  be  passed  through 
each  of  them.  If  the  currents  are  of  the  same  strength  but  in  different  direc- 
tions, no  deflection  is  produced  ;  where  the  needle  is  deflected  one  of  the 
currents  differs  from  the  other.  Hence  the  apparatus  is  used  to  ascertain 
a  difference  in  strength  of  two  currents,  and  to  this  it  owes  its  name. 

822.  Sir  W.  Thomson's  marine  galvanometer. —  In  laying  submarine 
cables  the  want  was  felt  of  a  galvanometer  sufficiently  sensitive  to  test  insula- 
tion, which  at  the  same  time  was  not  affected  by  the  pitching  and  rolling  of 
the  ship.  For  this  purpose,  Sir  W.  Thomson  invented  his  marine  galvano- 
meter. B  (fig.  680)  represents  a  coil  of  many  thousand  turns  of  the  finest  copper 
wire,  carefully  insulated  throughout,  terminating  in  the  binding  screws  EE.  In 
the  centre  of  this  coil  is  a  slide,  which  carries  the  magnet,  the  arrangement  of 
which  is  represented  on  a  larger  scale  in  D.  The  magnet  itself  is  made  of  a 
piece  of  fine  watch-spring  about  f  of  an  inch  in  length,  and  does  not  weigh 
more  than  a  grain  ;  it  is  attached  to  a  small  and  very  slightly  concave  mirror 
of  very  thin  silvered  glass.  A  single  fibre  of  silk  is  stretched  across  the  slide, 
and  the  mirror  and  magnet  are  attached  to  it  in  such  a  manner  that  the 
fibre  exactly  passes  through  the  centre  of  gravity  in  every  position.  As  the 
mirror  and  magnet  weigh  only  a  few  grains,  they  retain  their  position  rela- 
tively to  the  instrument,  however  the  ship  may  pitch  and  roll.  The  slide  fits  in 
a  groove  in  the  coil,  and  the  whole  is  enclosed  within  a  wrought-iron  case 
with  an  aperture  in  front,  and  a  wrought-iron  lid  on  the  top.  The  object  of 
this  is  to  counteract  the  influence  of  the  terrestrial  magnetism  when  the  ship 
changes  its  course. 

I  I  2 


724 


Dynamical  Electricity. 


[822- 


Underneath  the  coil  is  a  large  curved  steel  magnet  N,  which  compensates 
the  earth's  directive  action  upon  the  magnet  D  ;  and  in  the  side  of  the  case, 
and  on  a  level  with  D,  a  pair  of  magnets,  C,  are  placed  with  opposite  poles 
together.  By  a  screw,  suitably  adjusted,  the  poles  of  the  magnets  may  be 
brought  together  ;  in  which  case  they  quite  neutralise  each  other,  and  thus 
exert  no  action  on  the  suspended  magnet,  or  they  may  be  slid  apart  from 
each  other  in  such  a  manner  that  the  action  of  either  pole  on  D  prepon- 
derates to  any  desired  extent.  This  small  magnet  is  thus  capable  of  very 
delicate  adjustment.  The  large  magnet  N,  and  the  pair  of  magnets,  C,  are 
analogous  to  the  coarse  and  fine  adjustment  of  a  microscope. 

At  a  distance  of  about  three  feet,  there  is  a  scale  with  the  zero  in  the 
centre  and  the  graduation  extending  on  each  side.  Underneath  this  zero 


Fig.  680. 

point  is  a  narrow  slit,  through  which  passes  the  light  of  a  paraffine  lamp,  and 
which,  traversing  the  window,  is  reflected  from  the  curved  mirror  against  the 
graduated  scale.  By  means  of  the  adjusting  magnets  the  image  of  the  slit  is 
made  to  fall  on  the  centre  of  the  graduation. 

This  being  the  case,  if  any  arrangement  for  producing  a  current,  however 
weak,  be  connected  with  the  terminals,  the  spot  of  light  is  deflected  either  to 
one  side  or  the  other,  according  to  the  direction  of  the  current  ;  the  stronger 
the  current  the  greater  the  deflection  of  the  spot  •  and  if  the  current  remains 
of  constant  strength  for  any  length  of  time,  the  spot  is  stationary  in  a  cor- 
responding position. 

The  movement,  on  a  screen,  of  a  spot  of  light  reflected  from  a  body,  is  the 
most  delicate  and  convenient  means  of  observing  motions  which  of  them- 
selves are  too  small  for  direct  measurement  or  observation.  Hence  this 
principle  is  frequently  applied  in  experimental  investigations  and  in  lecture 
illustrations  (522).  It  is  used  in  observing  the  motion  of  oscillating  bodies, 
in  measuring  the  variations  of  magnetism,  in  determining  the  expansion  of 
solids,  &c. 

It  will  be  seen  from  the  article  on  the  Electric  Telegraph,  how  alternate 


-  823]         Tangent  Compass,  or  Tangent  Galvanometer.  72$ 

deflections    of  the  spot   of  light   may  be    utilised  in    forming   a   code    of 

signals. 

823.  Tangent  compass,  or  tangent  galvanometer  —  When  a  magneti 
needle  is  suspended  in  the  centre  of  a  voltaic  current  in  the  plane  of  the 
magnetic  meridian,  it  can  be  proved  that  the  intensity  of  a  current  is  directly 
proportional  to  the  tangent  of  the 
angle  of  deflection,  provided  the 
dimensions  of  the  needle  are  suffi- 
ciently small  as  compared  with  the 
diameter  of  the  circuit.  An  instru- 
ment based  on  this  principle  is 
called  the  tangent  galvanometer  or 
tangent  compass.  It  consists  of  a 
copper  ring,  12  inches  in  diameter, 
and  about  an  inch  in  breadth, 
mounted  vertically  on  a  stand  ;  the 
lower  half  of  the  ring  is  generally 
fitted  in  a  semicircular  frame  of 
wood  to  keep  it  steady.  In  the 
centre  of  the  ring  is  suspended  a 
delicate  magnetic  needle,  whose 
length  must  not  exceed  ±  or  TO  OI" 
the  diameter  of  the  circle.  Under-  Fig 

neath  the  needle  there  is  a  graduated 

circle.  The  ends  of  the  ring  are  prolonged  in  copper  wires,  fitted  with 
mercury  cups,  ab,  by  which  it  can  be  connected  with  a  battery  or  element. 
The  circle  is  placed  in  the  plane  of  the  magnetic  meridian,  and  the  deflection 
of  the  needle  is  directly  read  off  on  the  circle,  and  its  corresponding  value 
obtained  from  a  table  of  tangents. 

On  account  of  its  small  resistance,  the  tangent  galvanometer  is  well 
adapted  for  currents  of  low  potential,  but  in  which  a  considerable  quantity 
of  electricity  is  set  in  motion. 

To  prove  that  the  intensities  of  various  currents  are  proportional  to  the 
tangents  of  the  corresponding  angles  of  deflection,  let  NS,  fig.  682,  represent 
the  wire  of  the  galvanometer  and  ns  the  needle,  and  let  $  be  the  angle  of 
deflection  produced  when  a  current  C  is  passed.  Two  forces  now  act  upon 
the  needle  —  the  force  of  the  earth's  magnetism,  which  we  will  denote  by  H, 
which  tends  to  place  the  needle  in  the  magnetic  meridian,  and  the  strength 
of  the  current  C,  which  strives  to  place  it  at  right  angles  to  the  magnetic 
meridian.  Let  the  magnitudes  of  these  forces  be  represented  by  the  corre- 
sponding lines  an  and  bn.  Now  the  whole  intensities  of  these  forces  do  not 
act  so  as  to  turn  the  point  of  the  needle  round,  but  only  those  components 
which  are  at  right  angles  to  the  needle.  Resolving  them,  we  have  ng  and  nf 
as  the  forces  acting  in  opposite  directions  on  the  needle  ;  and  since  the 
needle  is  at  rest  these  forces  must  be  equal. 

The  angle  nag  is  equal  to  the  angle  0,  and  therefore  ng-=an  sin  <£  ;  and 
in  like  manner  the  angle  bnf'is  equal  to  <£  and  nf=bn  cos  <£  ;  and  therefore 


since  nf=ng,  bn  cos 
C  =  H  tan  <. 


sin  <£,  or  bn   =  an        —     =  an   tan  <£  ;  that  is, 


726 


Dynamical  Electricity. 


[824- 


g 

Fig.  682. 


If  any  other  current  be  passed  through  the  galvanometer  we  shall  have 
similarly  C'  =  H  tan  <£' ;  and  since  the  earth's  magnetism  does  not  appreciably 
alter  in  one  and  the  same  place  C  :  C'  =  tan  <£  :  tan  <£'. 

In  this  reasoning  it  has  been  assumed  that  the  action  of  the  current  on 
the  needle  is  the  same  whatever  be  the  angle  by  which  it  is  deflected.  This 
is  only  the  case  when  the  dimensions  of  the  needle  are 
small  compared  with  the  diameter  of  the  ring  •  it  should 
not  be  more  than  |  or  ^  the  diameter.  In  order  to 
measure  with  accuracy  the  deflection  a  light  index  is 
placed  at  right  angles  to  the  needle. 

Wiedemanrts  tangent  galvanometer  consists  of  a 
short  thick  copper  tube,  in  which  is  suspended,  instead 
of  a  needle,  a  small  but  thick  magnetised  sheet  iron 
mirror,  the  position  of  which  can  be  observed  by  a 
telescope  and  scale  (522).  On  each  side  of  the  copper 
tube,  and  sliding  in  grooves,  are  coils  of  wire  which  can 
be  pushed  over  the  tube.  By  this  lateral  arrangement 
of  the  current  in  reference  to  the  magnetic  needle,  the 
error  of  the  tangent  galvanometer  is  diminished  ;  for 
when  the  needle  is  deflected,  one  end  moves  away  from 
the  current,  while  the  other  approaches  it. 

According  to  Gaugain,  the  tangent  of  the  angle  of  deflection  is  most 
nearly  proportional  to  the  strength  of  the  current  when  the  centre  of  the 

needle  is  at  a  distance  of  one 
quarter  the  diameter  of  the  ring 
from  the  centre  of  the  ring. 

824.  Sine  galvanometer. — 
This  is  another  form  of  galvano- 
meter for  measuring  powerful 
currents.  Round  the  circular 
frame,  M  (fig.  683),  several  turns 
of  stout  insulated  copper  wire 
are  coiled,  the  two  ends  of 
which,  z,  terminate  in  the  bind- 
ing screws  at  E.  On  a  table  in 
the  centre  of  the  ring  there  is  a 
magnetic  needle,  m  ;  a  second 
light  needle,  «,  fixed  to  the  first, 
serves  as  pointer  along  the 
graduated  circle,  N.  Two 
copper  wires,  <2,  b,  from  the 
sources  of  electricity  to  be 
F  measured,  are  connected  with 
E.  The  circles  M  and  N  are 
supported  on  a  foot  O,  which 
can  move  about  a  vertical  axis 
Fig.  683.  passing  through  the  centre  of  a 

fixed  horizontal  circle  H. 

The  circle  M  being  then  placed  in  the  magnetic  meridian,  and  therefore 
in  the  same  plane  as  the  needle,  the  current  is  allowed  to  pass.     The  needles, 


-825] 


Sine  Galvanometer < 


727 


being  deflected,  the  circuit  M  is  turned  until  it  coincides  with  the  vertical 
plane  passing  through  the  magnetic  needle  ;«.  The  directive  action  of  the 
current  is  now  exerted  perpendicularly  to  the  direction  of  the  magnetic  needle, 
and  it  may  be  shown  that  the  strength  of  the  current  is  proportional  to  the 
sine  of  the  angle  of  deflection  :  this  angle  is  measured  on  the  circle  H  by 
means  of  a  vernier  on  the  piece  C.  This  piece,  C,  fixed  to  the  foot  O,  turns 
it  by  means  of  a  knob,  A.  The  angle  of  deflection,  and  hence  its  sine,  being 
known,  the  intensity  of  the  current  may  be  thus 
deduced  :  let  mm'  be  the  direction  of  the  mag- 
netic meridian,  d  the  angle  of  deflection,  C  the 
strength  of  the  current,  and  H  the  directive  action 
of  the  earth.  If  the  direction  and  intensity  of  this 
latter  force  be  represented  by  ak,  it  may  be  replaced 
by  two  components,  ah  and  ac  (fig.  684.)  Now,  as 
the  first  has  no  directive  action  on  the  needle,  the 
component  ac  must  alone  counterpoise  the  force  C, 
that  is,  C  —  ae.  But  in  the  triangle,  ack,  ac  =  ak  cos 
cak,  from  which  ac  =  H  sin  d,  for  the  angle  cak  is  the 
complement  of  the  angle  d,  and  ak  is  equal  to  H  ; 
hence,  lastly,  C  =  H  sin  d,  which  was  to  be  proved.  In 
like  manner  for  any  other  current  C'  which  produces 
a  deflection  d,  we  shall  have  C'  =  H  sin  d',  whence  C  :  C'  =  sin  d :  sin  tf. 

825.  Ohm's  iaw.—  For  a  knowledge  of  the  conditions  which  regulate  the 
action  of  the  voltaic  current,  science  is  indebted  to  the  late  G.  S.  Ohm. 
His  results  were  at  first  deduced  from  theoretical  considerations  ;  but  by 
his  own  researches,  as  well  as  by  those  of  Fechner,  Pouillet,  Daniell,  De  la 
Rive,  Wheatstone,  and  others,  they  have  received  the  fullest  confirmation, 
and  their  great  theoretical  and  practical  importance  has  been  fully  established. 

i.  The  force  or  cause  by  which  electricity  is  set  in  motion  in  the  voltaic 
circuit  is  called  the  electromotive  force.  The  quantity  of  electricity  which  in 
any  unit  of  time  flows  through  a  section  of  the  circuit  is  called  the  intensity 
or,  perhaps  better,  the  strength  of  the  current.  Ohm  found  that  this  strength 
is  the  same  in  all  parts  of  one  and  the  same  circuit,  however  heterogeneous 
they  were  ;  one  and  the  same  magnetic  needle  is  deflected  to  the  same 
extent  over  whatever  part  of  the  circuit  it  is  suspended  ;  and  the  same 
voltameter,  wherever  interposed  in  the  circuit,  indicates  the  same  disengage- 
ment of  gas  ;  he  also  found  that  the  strength  is  proportional  to  the  electro- 
motive force. 

It  has  further  been  found  that  when  the  same  current  is  passed  respec- 
tively through  a  short  and  through  a  long  wire  of  the  same  material,  its 
action  on  the  magnetic  needle  is  less  in  the  latter  case  than  in  the  former. 
Ohm  accordingly  supposed  that  in  the  latter  case  there  was  a  greater  resist- 
ance to  the  passage  of  the  current  than  in  the  former  ;  and  he  proved  that 
'  the  resistance  is  inversely  proportional  to  the  strength  of  the  current? 

On  these  principle*  Ohm  founded  the  celebrated  law  which  bears  his 
name,  that  the  strength  of  the  current  is  equal  to  the  electromotive  force 
divided  by  the  resistance. 

This  is  expressed  by  the  simple  formula 

C-  K 
L~' 


728  Dynamical  Electricity.  [825- 

where  C  is  the  strength  of  the  current,  E  the  electromotive  force,  and  R  the 
resistance. 

ii.  The  resistance  of  a  conductor  depends  on  three  elements  ;  its  conduc- 
tivity, which  is  a  constant,  determined  for  each  conductor  ;  its  section  ;  and 
its  length.  The  resistance  is  obviously  inversely  proportional  to  the  conduc- 
tivity ;  that  is,  the  less  the  conducting  power  the  greater  the  resistance.  It 
has  been  proved  that  the  resistance  is  inversely  as  the  section  and  directly 
as  the  length  of  a  conductor.  If  then  AC  is  the  conductivity,  o>the  section,  and  X 
the  length  of  a  conductor,  we  have,  that  is,  the  strength  of  a  current  is  inversely 


t>       X         ,  ~      E        « 
R  =  —  and  C  =  —  =  —  —  . 

KM  XX 

KO> 

proportional  to  the  length  of  the  conductor  and  directly  proportional  to  its 
section  and  conductivity. 

iii.  In  a  voltaic  batteiy  composed  of  different  elements,  the  strength  of 
the  current  is  equal  to  the  sum  of  the  electromotive  forces  of  all  the  elements 
divided  by  the  sum  of  the  resistances.  Usually,  however,  a  battery  is  com- 
posed of  elements  of  the  same  kind,  each  having,  in  intention  at  least,  the 
same  electromotive  force  and  the  same  resistance, 

In  an  ordinary  element  there  are  essentially  two  resistances  to  be  con- 
sidered :  i.  That  offered  by  the  liquid  conductor  between  the  two  plates, 
which  is  frequently  called  the  internal  or  essential  resistance  ;  and  2.  That 
offered  by  the  interpolar  conductor  which  connects  the  two  places  outside  the 
liquid  ;  this  conductor  may  consist  either  wholly  of  metal,  or  may  be  partly  of 
metal  and  partly  of  liquids  to  be  decomposed  :  it  is  the  externals  non-essential 
resistance.  Calling  the  former  R  and  the  latter  r,  Ohm's  formula  becomes 

C-     1  U 
R  +  r 

iv.  If  any  number,  72,  of  similar  elements  are  joined  together,  there  is  n 
times  the  electromotive  force,  but  at  the  same  time  n  times  the  internal 

resistance,  and  the  formula  becomes  -^  —  .     If  the  resistance  in  the  inter- 

nR  +  r 

polar,  r,  is  very  small  —  which  is  the  case,  for  instance,  when  it  is  a  short, 
thick  copper  wire  —  it  may  be  neglected  in  comparison  with  the  internal  re- 
sistance, and  then  we  have 

r  —   ;/^  —  ^ 
=   nR~  ~R' 

that  is,  a  battery  consisting  of  several  elements  produces  in  this  case  no 
greater  effect  than  a  single  element. 

v.  If,  however,  the  external  resistance  is  very  great,  as  when  the  current 
has  to  produce  the  electric  light,  or  to  work  a  long  telegraphic  circuit,  ad- 
vantage is  gained  by  using  a  large  number  of  elements  ;  for  then  we  have 
the  formula 


if  r  is  very  great  as  compared  with  ;/R,  the  latter  may  be  neglected,  and  the 
expression  becomes 

r  —   n^ 


-825] 


Ohm's  Law. 


729 


that  is,  that  the  strength,  within  certain  limits,  is  proportional  to  the  number 
of  elements. 

In  a  thermo-electric  pile,  which  consists  of  very  short  metallic  conductors, 
the  internal  resistance  R  is  so  small  that  it  may  be  neglected,  and  the 
strength  is  inversely  as  the  length  of  the  connecting  wire. 

vi.  If  the  plates  of  an  element  be  made  m  times  as  large,  there  is  no 
increase  in  the  electromotive  force,  for  this  depends  on  the  nature  of  the 
metals  and  of  the  liquid  (802),  but  the  resistance  is  m  times  as  small,  for  the 
section  is  ///  times  larger  ;  the  expression  becomes  then 

C  -  —  —   =    wE 

R  +  r    R  +  mr 


Hence,  an  increase  in  the  size  of  the  plate — or,  what  is  the  same  thing,  a 
decrease  in  the  internal  resistance — does  not  increase  the  strength  to  an  in- 


Fig.  685. 


T 


Fig.  688. 

definite  extent ;  for  ultimately  the  resistance  of  the  element  R  vanishes  in 
comparison  with  the  resistance  r,  and  the  strength  continually  approximates 

to  the  value  C  =       . 
r 

vii.  Ohm's  law  enables  us  to  arrange  a  battery  so  as  to  obtain  the  greatest 
effect  in  any  given  case.  For  instance,  with  a  battery  of  six  elements  there 
are  the  following  four  ways  of  arranging  them  :  I.  In  a  single  series  (fig. 

i  i  3 


73°  Dynamical  Electricity.  [825- 

685),  in  which  the  zinc  Z  of  one  element  is  united  with  the  copper  C  of  the 
second,  the  zinc  of  this  with  the  copper  of  the  third,  and  so  on  •  2.  Arranged 
in  a  system  of  three  double  elements,  each  element  being  formed  by  joining 
two  of  the  former  (fig.  686)  ;  3.  In  a  system  of  two  elements,  each  of  which 
consists  of  three  of  the  original  elements  joined,  so  as  to  form  one  of  triple 
the  surface  (fig.  687)  ;  lastly,  of  one  large  element,  all  the  zincs  and  all  the 
coppers  being  joined,  so  as  to  form  a  pair  of  six  times  the  surface  (fig.  688). 

With  a  series  of  twelve  elements  there  may  be  six  different  combinations, 
and  so  on  for  a  larger  number. 

Now,  let  us  suppose  that  in  the  particular  case  of  a  battery  of  six  elements 
the  internal  resistance  R  of  each  element  is  3,  and  the  external  resistance 
r=  12.  Then,  in  the  first  case,  where  there  are  six  elements,  arranged  in 
series,  we  have  the  value, 

C=     6E     _      6E       _6E  (n 

6R  +  r    6x3  +  12       30 

If  they  were  united  so  as  to  form  three  elements,  each  of  double  the 
surface,  as  in  the  second  case  (fig.  686),  the  electromotive  force  would  then 
be  the  electromotive  force  in  each  element  ;  there  would  also  be  a  resistance 
R  in  each  element,  but  this  would  only  be  half  as  great,  for  the  section  of 
the  plate  is  now  double  ;  hence  the  strength  in  this  case  would  be 

C'  =     3E     _.  3E     _6E.  ,. 

3R+r     9  +  12     33  ' 

2  2 

accordingly  this  change  would  lessen  the  strength. 

If,  with  the  same  elements,  the  resistance  in  the  connecting  wire  were 
only  r=2,  we  should  have  the  values  in  the  two  cases  respectively  — 

6  x  E    =  6E 
' 


_ 
3R  +  ^      9  +  4       13 

The  result  in  the  latter  case  is,  therefore,  more  favourable.  If  the  re- 
sistance r  were  9,  the  strength  would  be  the  same  in  both  cases.  Hence, 
then,  by  altering  the  size  of  the  plates  or  their  arrangement,  favourable 
or  unfavourable  results  are  obtained  according  to  the  relation  between  R 
and  r. 

826.  Arrangement  of  multiple  battery  for  maximum  current.  —  It  can 
be  shown  that  in  any  given  combination  the  maximum  effect  is  obtained  when 
the  total  resistance  in  the  elements  is  equal  to  the  resistance  of  the  interpolar. 
For  let  N  be  the  total  number  of  cells  available  for  a  given  combination,  and 
let  n  be  the  number  of  cells  arranged  tandem,  or  in  series  ;  that  is,  when 
the  zinc  of  one  is  connected  with  the  copper  of  the  next,  and  so  on  ;  then 

N 

there  will  be  —  elements  arranged  abreast.     If  e  be  the  electromotive  force, 
n 

and  r  the  resistance  of  one  cell,  while  /  is  the  external  resistance,  then  the 
strength  of  the  current  will  be 


-826]  Arrangement  of  Multiple  ^Battery  for  Maximum  Current  731 
C=  nr    "  = //V+ XV 


If  this  combination  be  such  that  the  total  internal  resistance-  r  is 
to  the  external  resistance  /,  we  have 
C=  ne 

~  ~2l' 

For  suppose  that  the  whole  number  of  cells  is  arranged  so  as  to  form 
another  combination  of  cells  tandem,  let  n'  be  this  number,  which  shall  be 
equal  to  n  ±  v  \  then  we  have 


_ 
tfir+vr*      2 

or  since  ,V-N/- 


Xow  the  value  of  C  —  Cl  is  always  positive  ;  for  reducing  to  a  common 
denominator — 

r  _  2  X&  (n  +  rv)  +  v-rne  .    r  2N/<? 


common  denominator.  common  denominator. 

Hence  the  best  effect  is  obtained  when  n  =  A  / — . 

If  in  a  given  case  we  have  8  elements,  each  offering  a  resistance  15,  and 
an  interpolar  with  the  resistance  40,  we  get  n  =  4-3.  But  this  is  an  im- 
possible arrangement,  for  it  is  not  a  whole  number,  and  the  nearest  whole 
number  must  be  taken.  This  is  4;  and  it  will  be  found,  on  making  a  calcula- 
tion analogous  to  that  above,  that  when  arranged  so  as  to  form  4  elements 
each  of  double  surface,  the  greatest  effect  is  obtained. 


732  Dynamical  Electricity.  [827- 


CHAPTER   III. 

EFFECTS   OF  THE   CURRENT. 

827.  Physiological  actions. — Under  this  name  are  included  the  effects 
produced  by  a  battery-current  on  living  organisms  or  tissues. 

When  the  electrodes  of  a  strong  battery  are  held  in  the  two  hands  a  violent 
shock  is  felt,  especially  if  the  hands  are  moistened  with  acidulated  water, 
which  increases  the  conductivity.  The  violence  of  the  shock  increases  with 
the  number  of  elements  used,  and  with  a  large  number — as  200  Bunsen's 
cells — is  even  dangerous. 

The  power  of  contracting  upon  the  application  of  a  voltaic  current  seems 
to  be  a  very  general  property  of  protoplasm — the  physical  basis  of  both 
animal  and  vegetable  life  ;  if,  for  example,  a  current  of  moderate  strength  be 
passed  through  such  a  simple  form  of  protoplasm  as  an  Amoeba,  it  imme- 
diately withdraws  its  processes,  ceases  its  changes  of  form,  and  contracts  into 
a  rounded  ball— soon,  however,  resuming  its  activity,  upon  the  cessation  of 
the  current.  Essentially  similar  effects  of  the  current  have  been  observed 
in  the  protoplasm  of  young  vegetable  cells. 

If  a  frog's  fresh  muscle  (which  will  retain  its  vitality  for  a  considerable 
time  after  removal  from  the  body  of  the  animal)  be  introduced  into  a  galvanic 
circuit,  no  apparent  effect  will  be  observed  during  the  steady  passage  of 
the  current,  but  every  opening  or  closure  of  the  circuit  will  cause  a  mus- 
cular contraction,  as  will  also  any  sudden  and  considerable  alteration  in  its 
intensity.  By  very  rapidly  interrupting  the  current,  the  muscle  can  be  thrown 
into  a  state  of  uninterrupted  contraction,  or  physiological  tetanus,  each  new 
contraction  occurring  before  the  previous  one  has  passed  off.  Other  things 
being  equal,  the  amount  of  shortening  exhibited  by  the  muscle  increases,  up 
to  a  certain  limit,  with  the  intensity  of  the  current.  These  phenomena 
entirely  disappear  with  the  life  of  the  muscle  ;  hence  the  experiments  are 
somewhat  more  difficult  with  warm-blooded  animals,  the  vitality  of  whose 
muscles,  after  exposure  or  removal  from  the  body,  is  maintained  with  more 
difficulty  ;  but  the  results  of  careful  experiment  are  exactly  the  same  here  as 
in  the  case  of  the  frog. 

The  influence  of  an  electric  current  upon  living  nerves  is  very  remark- 
able ;  as  a  general  rule,  it  may  be  stated  that  its  effect  is  to  throw  the  nerve 
into  a  state  of  activity,  whatever  its  special  function  may  be  ;  thus,  if  the 
nerve  be  one  going  to  a  muscle,  the  latter  will  be  caused  to  contract  ;  if  it 
be  one  of  common  sensation,  pain  will  be  produced  ;  if  one  of  special  sense, 
the  sensation  of  a  flash  of  light,  or  of  a  taste,  £c.,  will  be  produced,  accord- 
ing to  the  nerve  irritated.  These  effects  do  not  manifest  themselves  during 
the  even  passage  of  the  current,  but  only  when  the  circuit  is  either  opened  or 


-828]  Eleclrotonus.  733 

closed,  or  both.  Of  course,  the  continuity  of  the  nerve  with  the  organ  where 
its  activity  manifests  itself  must  be  maintained  intact.  The  changes  set  up 
by  the  current  in  the  different  nerve-trunks  are  probably  similar,  the  various 
sensations,  &c.,  produced  depending  on  the  different  terminal  organs  with 
which  the  nerves  are  connected.  * 

Sanderson  has  ascertained  that  the  movement  which  causes  the  Dioncea 
muscipula  (Venus'  Fly-trap),  one  of  what  are  called  carnivorous  plants,  to 
close  its  hairy  leaves  and  thereby  entrap  insects  which  alight  upon  it,  is 
accompanied  by  an  electrical  current  in  a  manner  analogous  to  that  mani- 
fested in  muscular  contraction.  The  manner  in  which  the  irritation  is  caused 
seems  immaterial. 

828.  Electrotonus. — In  a  living  nerve,  as  will  be  stated  more  fully  in 
Chapter  X.,  certain  parts  of  the  surface  are  electropositive  to  certain  other 
parts,  so  that  if  a  pair  of  electrodes  connected  with  a  galvanometer  be  applied 
to  these  two  points,  a  current  will  be  indicated  ;  if  now  another  part  of  the 
nerve  be  interposed  in  a  galvanic  circuit,  it  will  be  found  that,  if  this  extra- 
neous current  be  passing  in  the  same  direction  as  the  proper  nerve-current, 
the  latter  is  increased,  and  vice  versa  ;  and  this,  although  it  has  previously 
been  demonstrated  experimentally  that  none  of  the  battery  current  escapes 
down  the  nerve,  so  as  to  exert  any  influence  of  its  own  on  the  galvanometer. 
This  alteration  of  its  natural  electromotive  condition,  produced  through  the 
whole  of  a  nerve  by  the  passage  of  a  constant  current  through  part  of  it,  is 
known  as  the  electrotonic  state  ;  it  is  most  intense  near  the  extraneous,  or,  as 
it  is  called,  the  exciting  current.  It  continues  as  long  as  the  latter  is  pass- 
ing, and  is  attended  with  important  changes  in  the  excitability  of  the  nerve, 
or,  in  other  words,  the  readiness  with  which  the  nerve  is  thrown  into  a  state 
of  functional  activity  by  any  stimulus  applied  to  it.  Pfliiger,  who  has  inves- 
tigated these  changes,  has  named  the  part  of  the  nerve  through  which  the 
exciting  current  is  passing  the  intrapolar  region  ;  the  condition  of  the  nerve 
close  to  the  positive  pole  is  called  anelectrotonus  :  that  near  the  negative  pole, 
kathelectrotonus.  The  excitability  of  the  nerve  is  diminished  in  the  anelec- 
trotonic  region,  so  that  with  a  motor  nerve,  for  example,  a  stronger  stimulus 
than  before  would  need  to  be  applied  at  this  part,  in  order  to  obtain  a  mus- 
cular contraction  ;  in  the  kathelectrotonic  region,  on  the  contrary,  the  ex- 
citability of  the  nerve  is  heightened.  Moreover,  with  an  exciting  current  of 
moderate  strength  the  power  of  the  nerve  to  conduct  a  stimulus  is  lowered 
in  the  anelectrotonic  region,  and  increased  in  the  kathelectrotonic  ;  with 
strong  currents  it  is  said  to  be  diminished  in  both. 

These  facts  have  to  be  taken  into  account  in  the  scientific  application  of 
galvanism  to  medical  purposes  ;  if,  for  instance,  it  is  wished  to  diminish  the 
excitability  of  the  sensory  nerves  of  any  part  of  the  body,  the  current  should 
be  passed  in  such  a  direction  as  to  throw  the  nerves  of  that  part  into  a  state 
of  anelectrotonus — and  similarly  in  other  cases. 

If  a  powerful  electric  current  be  passed  through  the  body  of  a  recently 
killed  animal,  violent  movements  are  produced,  as  the  muscles  ordinarily 
retain  their  vitality  for  a  considerable  time  after  general  systematic  death  : 
by  this  means,  also,  life  has  been  re-established  in  animals  which  were  appa- 
rently dead — a  properly  applied  current  stimulating  the  respiratory  muscles 
to  contract. 


734  Dynamical  Electricity.  [829- 

829.  Heating  effects. — When  a  voltaic  current  is  passed  through  a  metal 
wire  the  same  effects  are  produced  as  by  the  discharge  of  an  electric  battery 
(790) ;  the  wire  becomes  heated,  and  even  incandescent  if  it  is  very  short  and 
thin.  With  a  powerful  battery  all  metals  are  melted,  even  iridium  and  plati- 
num, the  least  fusible  of  metals.  Carbon  is  the  only  element  which  has  not 
hitherto  been  fused  by  it.  Despretz,  however,  with  a  battery  composed  of 
600  Bunsen's  elements  joined  in  six  series  (825),  raised  rods  of  very  pure 
carbon  to  such  a  temperature  that  they  were  softened  and  could  be  welded 
together,  yielding  an  incipient  fusion. 

A  battery  of  30  to  40  Bunsen's  elements  is  sufficient  to  melt  and  volatilise 
fine  wires  of  lead,  tin,  zinc,  copper,  gold,  silver,  iron,  and  even  platinum,  with 
differently  coloured  sparks.  Iron  and  platinum  burn  with  a  brilliant  white 
light ;  lead  with  a  purple  light  ;  the  light  of  tin  and  of  gold  is  bluish  white  ; 


Fig.  689. 

the  light  of  zinc  is  a  mixture  of  white  and  gold  ;  finally,  copper  and  silver  give 
a  green  light. 

The  thermal  effects  of  the  voltaic  current  are  used  for  firing  mines  for 
military  purposes  and  for  blasting  operations.  The  following  arrangement 
was  devised  by  Colonel  Schaw  for  use  in  the  English  service : — Fig.  689 
represents  a  small  wooden  box  provided  with  a  lid.  Two  moderately  stout 
copper  wires,  b  b,  insulated  by  being  covered  with  gutta-percha,  are  deprived 
of  this  coating  at  the  ends,  which  are  then  passed  through  and  through  the 
box  in  the  manner  represented  in  the  figure.  The  distance  between  them  is 
|  of  an  inch,  and  a  very  fine  platinum  wire  (one  weighing  i  -92  grain  to  the 
yard,  is  the  regulation  size)  is  soldered  across.  The  object  of  arranging  the 
wires  in  this  manner  is  that  they  shall  not  be  in  contact,  and  that  the  strain 
which  they  exert  may  be  spent  on  the  box,  and  not  on  the  platinum  wire 
joining  them,  which,  being  extremely  thin,  would  be  broken  by  even  a  very 
slight  pull.  The  box  is  then  filled  with  fine-grained  powder,  and  the  lid  tied 
down.  The  wires  of  the  fuze  are  then  carefully  joined  to  the  long  conducting 
wires  which  lead  to  the  battery  ;  these  should  be  of  copper,  and  as  thick  as  is 
convenient,  so  as  to  offer  very  little  resistance  :  No.  16  gauge  copper  wire 


-830]       Laws  of  Heating  EffeUs.     Galvano-thermometer.       735 

is  a  suitable  size.  The  fuze  is  then  introduced  into  the  charge  to  be  fired  : 
if  it  is  for  a  submarine  explosion,  the  powder  is  contained  in  a  canister,  the 
neck  of  which,  after  the  introduction  of  the  fuze,  is  carefully  fastened  by 
means  of  cement.  When  contact  is  made  with  the  battery,  which  is  effected 
through  the  intervention  of  mercury  cups,  the  current  traversing  the  platinum 
wire  renders  it  incandescent,  which  fires  the  fuze  ;  and  thus  the  ignition  is 
communicated  to  the  charge  in  which  it  is  placed. 

The  heating  effect  depends  more  on  the  size  than  on  the  number  of  the 
plates  of  a  battery,  for  the  resistance  in  the  connecting  wires  is  small  (825). 
An  iron  wire  maybe  melted  by  a  single  Wollaston's  element,  the  zinc  of  which 
is  8  inches  by  6.  Hare's  battery  (805)  has  received  its  name  deflagrator  on 
account  of  its  greater  heating  effect  produced  by  the  great  surface  of  its 
plates. 

When  any  circuit  is  closed,  a  definite  amount  of  heat  is  produced 
throughout  the  entire  circuit ;  and  the  amount  of  heat  produced  in  any 
particular  part  of  the  circuit  is  greater,  the  greater  the  proportion  which  the 
resistance  of  this  part  bears  to  the  entire  circuit.  Hence,  in  firing  mines, 
the  wire  to  be  heated  should  be  of  as  small  section  and  of  as  small  con- 
ductivity as  practicable.  These  conditions  are  well  satisfied  by  platinum, 
which  has  over  iron  the  advantage  of  being  less  brittle  and  of  not  being 
liable  to  rust.  Platinum  too  has  a  slow  specific  heat,  and  is  thus  raised  to 
a  higher  temperature,  by  the  same  amount  of  heat,  than  a  wire  of  greater 
specific  heat. 

On  the  other  hand,  the  conducting  wires  should  present  as  small  a  resist- 
ance as  possible,  a  condition  satisfied  by  a  stout  copper  wire  ;  and  again,  as 
the  heating  effect  of  any  circuit  is  proportional  to  the  square  of  the  electro- 
motive force,  and  inversely  as  the  resistance,  a  battery  with  a  high 
electromotive  force  and  small  resistance,  such  as  Grove's  or  Bunsen's,  should 
be  selected. 

By  means  of  a  heated  platinum  wire,  parts  of  the  body  may  be  safely 
cauterised  which  could  not  begot  at  by  a  red-hot  iron  ;  the  removal  of  tumours 
may  be  effected  by  drawing  a  loop  of  platinum  round  their  base,  which  is  then 
gradually  pulled  together.  It  has  been  observed  that  when  the  temperature 
of  the  wire  is  about  600°  C,  the  combustion  of  the  tissues  is  so  complete  that 
there  is  no  haemorrhage  ;  while  at  1 500°  the  action  of  the  wire  is  like  that  of 
a  sharp  knife. 

830.  Laws  of  beating:  effects.  Galvano-thermometer. — Although  the 
thermal  effects  are  most  obvious  in  the  case  of  thin  wires,  they  are  by  no 
means  limited  to  them.  The  laws  of  the  heating  effect  were  investigated  by 
Lenz,  by  means  of  an  apparatus  called  the  Galvano-thermometer  (fig.  690).  A 
wide-mouthed  stoppered  bottle  was  fixed  upside  down  with  its  stopper,  B, 
in  a  wooden  box  ;  the  stopper  was  perforated  so  as  to  give  passage  to  two 
thick  platinum  wires,  connected  at  one  end  with  binding  screws,  ss,  while 
their  free  ends  were  provided  with  platinum  cones  by  which  the  wires  under 
investigation  could  be  affixed  ;  the  vessel  contained  alcohol,  the  temperature 
of  which  was  indicated  by  a  thermometer  fitted  in  a  cork  inserted  in  a  hole, 
made  in  the  bottom  of  the  vessel.  The  current  is  passed  through  the  platinum 
wires,  and  its  strength  measured  by  means  of  a  tangent  compass  interposed 
in  the  circuit.  By  observing  the  increase  of  temperature  in  the  thermometer  in 


736 


Dynamical  Electricity. 


[830- 


Fig.  690. 


a  given  time,  and  knowing  the  weight  of  the  alcohol,  the  mass  of  the  wire, 
the  specific  heat,  and  the  calorimetric  values  (453)  of  the  vessel,  and  of  the 

thermometer,  compared  with  alcohol,  the 
thermal  effect,  which  is  produced  by  the 
current  in  a  given  time,  can  be  calculated. 

By  apparatus  of  this  kind  the  laws  of  the 
thermal  effects  have  been  investigated  by 
Lenz,  Joule,  and  Becquerel.  They  are  as 
follows  : — 

I.  The  heat  disengaged  in  a  given  time 
is  directly  proportional  to  the  square  of  the 
strength  of  the  current,  and  to  the  resistance. 

II.  Whatever  be  the   length  of  a  wire, 
provided  its  diameter  remains  the  same,  and 
that  the  same  quantity  of  electricity  passes, 
the  increase  of  temperature  is  the  same  in  all 
parts  of  the  wire.. 

III.  For  the  same  quantity  of  electricity, 
the  increase  of  temperature  in  different  parts 

of  a  wire  is  inversely  as  the  fourth  power  of  the  diameter. 

If  the  current  passes  through  a  chain  of  platinum  and  silver  wire  of  equal 
sizes,  the  platinum  becomes  more  heated  than  the  silver  from  its  greater 
resistance  ;  and  with  a  suitable  current  the  platinum  may  become  incandes- 
cent while  the  silver  remains  dark.  This  experiment  was  devised  by 
Children. 

If  a  long  thin  platinum  wire  be  raised  to  dull  redness  by  passing  a  voltaic 
current  through  it,  and  if  part  of  it  be  cooled  down  by  ice,  the  resistance  of 
the  cooled  part  is  diminished,  the  intensity  of  the  current  increases,  and  the 
rest  of  the  wire  becomes  brighter  than  before.  If,  on  the  contrary,  a  part 
of  the  feeble  incandescent  wire  be  heated  by  a  spirit-lamp,  the  resistance  of 
the  heated  part  increases,  for  the  effect  is  the  same  as  that  of  introducing 
fresh  resistance,  the  intensity  of  the  current  diminishes,  and  the  wire 
ceases  to  be  incandescent  in  the  non-heated  part. 

The  cooling  by  the  surrounding  medium  exercises  an  important  influence 
on  the  phenomenon  of  ignition.  A  round  wire  is  more  heated  by  the  same 
current  than  the  same  wire  which  has  been  beaten  out  flat ;  for  the  latter 
with  the  same  section  offers  a  greater  surface  to  the  cooling  medium  than  the 
others.  For  the  same  reason,  when  a  wire  is  stretched  in  a  glass  tube  on 
which  two  brass  caps  are  fitted  air-tight,  and  the  wire  is  raised  to  dull  incan- 
descence by  the  passage  of  a  current,  the  incandescence  is  more  vivid  when 
the  air  has  been  pumped  out  of  the  tube,  because  it  now  simply  loses  heat 
by  radiation,  and  not  by  communication  to  the  surrounding  medium. 

Similarly,  a  current  which  will  melt  a  wire  in  air  will  only  raise  it  to  dull 
redness  in  ether,  and  in  oil  or  in  water  will  not  heat  it  to  redness  at  all,  for 
the  liquids  conduct  heat  away  more  readily  than  air  does. 

From  the  above  laws  it  follows  that  the  heating  effect  is  the  same  in  a 
wire  whatever  be  its  length,  provided  the  current  is  constant ;  but  it  must  be 
remembered  that  by  increasing  the  length  of  the  wire  we  increase  the  resist- 
ance, and  consequently  diminish  the  intensity  of  the  current ;  further,  in  a 


-832]        Relation  of  Heating  Effect  to  Work  of  a  Battery.       737 


wire  there  is  a  greater  surface,  and  hence  more  heat  is  lost  by  radiation 
and  by  conduction. 

831.   Graphical  representation  of  the  heating:  effects  in  a  circuit.  — 

The  law  representing  the  production  of  heat  in  a  circuit  in  the  unit  of  time  is 
very  well  seen  by  the  following  geometrical  construction  due  to  Professor 
Foster,  who  has  devised  several  similar  methods  of  graphically  representing 
electrical  laws. 

The  heat  H  produced  in  a  circuit  in  the  unit  of  time,  is  proportional  to 
the  square  of  the  strength  of  the  current  C,  and  to  the  resistance  R  (830), 


that  is  H  =  C-R  ;  but  since  C 


,  we  shall  have  H  =  ±;. 
R  R 


Draw  a  straight  line  DAB  (fig.  691),  and  from  any  point  A  in  it  draw  a 
line  AC,  at  right  angles  to  DAB,  and  of  a  length  proportional  to  the  electro- 
motive force  of  the  cell.  Lay  off  a  length  AB  proportional  to  the  resistance 
of  the  circuit.  Join  CB,  and  at  C  draw  a  line  at  right  angles  to  BC  and  let 
I)  be  the  point  where  this  line  cuts  the  line  DAB.  Then  the  length  AD  is 
proportional  to  the  heat  produced  in  the  whole  circuit  in  unit  time.  For  the 
triangles  ADC  and  ACB  are  similar,  and  therefore  AD  :  AC  =  AC  :  AB ;  that 

is,  AD  =  ^-^  that  is,  H  =  E 
AB  R 

By  drawing  figures  similar  to  the  above  it  will  be  found  that  for  a  given 
electromotive  force  the  heat  is  inversely  proportional  to  the  resistance,  and 


Fig.  691. 

for  a  given  resistance  directly  proportional  to  the  square  of  the  electromotive 
force.  That  is,  if  the  resistance  is  doubled,  the  heat  is  reduced  to  one  half; 
if  the  electromotive  force  is  doubled  the  heat  is  quadrupled. 

832.  Relation  of  heating:  effect  to  work  of  a  battery. — In  every 
closed  circuit  chemical  action  is  continuously  going  on ;  in  ordinary 
circuits,  the  most  common  action  is  the  solution  of  zinc  in  sulphuric  acid, 
which  may  be  regarded  as  an  oxidation  of  the  zinc  to  form  oxide  of  zinc,  and 
a  combination  of  this  oxide  of  zinc  with  sulphuric  acid  to  form  water  and 
zinc  sulphate.  It  is  a  true  combustion  of  zinc,  and  this  combustion  serves 
to  maintain  all  the  actions  which  the  circuit  can  produce,  just  as  all  the 
work  which  a  steam-engine  can  effect  has  its  origin  in  the  combustion  of 
fuel  (473). 

By  independent  experiments  it  has  been  found  that,  when  a  given  weight 
of  zinc  is  dissolved  in  sulphuric  acid,  a  certain  definite  measurable  quantity 
of  heat  is  produced,  which,  as  in  all  cases  of  chemical  action,  is  the  same, 
whatever  be  the  rapidity  with  which  this  solution  is  effected.  If  this  solution 


738  Dynamical  Electricity.  [832- 

takes  place  while  the  zinc  is  associated  with  another  metal  so  as  to  form  a 
voltaic  couple,  the  rapidity  of  the  solution  will  be  altered  and  the  whole  cir- 
cuit will  become  heated — the  liquid,  the  plates,  the  containing  vessel  as  well 
as  the  connecting  wire.  But  although  the  distribution  of  the  heat  is  thus 
altered,  its  quantity  is  not.  If  the  values  of  all  the  several  heating  effects 
in  the  various  parts  of  the  circuit  be  determined,  it  will  still  be  found  that, 
however  the  resistance  of  the  connecting  wire  be  varied,  this  sum  is  exactly 
equivalent  to  that  produced  by  the  solution  of  a  certain  weight  of  zinc. 

If  the  couple  be  made  to  do  external  mechanical  work  the  case  is  different. 
Joule  made  the  following  remarkable  experiment  : — A  small  zinc  and  copper 
couple  were  arranged  in  a  calorimeter  and  the  amount  of  heat  determined 
while  the  couple  was  closed  for  a  certain  length  of  time  by  a  short  thick  wire. 
The  couple  still  contained  in  the  calorimeter  was  next  connected  with  a 
small  electromagnetic  engine  (895),  by  which  a  weight  was  raised.  It  was 
thus  found  that  the  heat  produced  in  the  calorimeter  in  a  given  time — while 
therefore  a  certain  amount  of  zinc  was  dissolved — was  less  while  the  couple 
was  doing  work  than  when  it  was  not ;  and  the  amount  of  this  diminution 
was  the  exact  thermal  equivalent  of  the  work  performed  in  raising  the 
weight  (497). 

That  the  whole  of  the  chemical  work  and  disengagement  of  heat  in  the 
circuit  of  an  ordinary  cell  has  its  origin  in  the  solution  of  zinc  in  acid  is  con- 
firmed by  the  following  experiment  due  to  Favre  : — 

In  the  muffle  of  his  calorimeter  (456)  five  small  zinc  platinum  elements 
were  introduced  ;  the  other  muffle  contained  a  voltameter.  Now  when  the 
element  was  closed  until  one  equivalent  of  zinc  was  dissolved  in  the  whole  of 
the  cells,  |  of  an  equivalent  of  water  should  be  decomposed  in  the  voltameter 
(845);  which  was  found  to  be  the  case.  In  one  case  the  current  of  the 
battery  was  closed  without  inserting  the  voltameter,  and  the  heat  disengaged 
during  the  solution  of  one  equivalent  of  zinc  was  found  to  be  18796  thermal 
units ;  when,  however,  the  voltameter  was  introduced,  the  quantity  disengaged 
was  only  11,769  thermal  units.  Now  the  difference,  7027,  is  represented  by 
the  chemical  work  of  decomposing  \  of  an  equivalent  of  water  ;  this  agrees 

very  well  with  the  number,  6892  =  ^44  2?  which  represents  the  heat  dis- 
engaged during  the  formation  of  \  of  an  equivalent  of  water. 

833.  Luminous  effects. — In  closing  a  voltaic  battery  a  spark  is  obtained 
at  the  point  of  contact,  which  is  frequently  of  great  brilliancy.  A  similar 
spark  is  also  perceived  on  breaking  contact.  These  luminous  effects  are 
obtained,  when  the  battery  is  sufficiently  powerful,  by  bringing  the  two  elec- 
trodes very  nearly  in  contact ;  a  succession  of  bright  sparks  springs  some- 
times across  the  interval,  which  follow  each  other  with  such  rapidity  as  to 
produce  a  continuous  light.  With  eight  or  ten  of  Grove's  elements  brilliant 
luminous  sparks  are  obtained  by  connecting  one  terminal  of  the  battery 
with  a  file,  and  moving  its  point  along  the  teeth  of  another  file  connected 
with  the  other  terminal. 

The  most  beautiful  effect  of  the  electric  light  is  obtained  when  two  pencils 
of  charcoal  are  connected  with  the  terminals  of  the  battery  in  the  manner 
represented  in  fig.  692.  The  charcoal  b  is  fixed,  while  the  charcoal  a  can  be 
raised  and  lowered  by  means  of  a  rack  and  pinion  motion,  c.  The  two 
charcoals  being  placed  in  contact,  the  current  passes,  and  their  ends  soon 


-833] 


Luminous  Effects. 


739 


become  incandescent.  If  they  are  then  removed  to  a  distance  of  about  the 
tenth  of  an  inch,  according  to  the  strength  of  the  current,  a  luminous  arc 
extends  between  the  two  points,  which  has  an  exceedingly  brilliant  lustre, 
and  is  called  the  voltaic  arc. 

The  length  of  this  arc  varies  with  the  force  of  the  current.  In  air  it  may 
exceed  2  inches  with  a  battery  of  500  elements,  arranged  in  six  series  of  100 
each,  provided  the  positive  pole  is  uppermost,  as  represented  in  the  figure  ; 
if  it  is  undermost,  the  arc 
is  about  one-third  shorter. 
In  vacuo  the  distance  of 
the  charcoal  may  be 
greater  than  in  air  ;  in 
fact,  as  the  electricity 
meets  with  no  resistance, 
it  springs  between  the  two 
charcoals,  even  before 
they  are  in  contact.  The 
voltaic  arc  can  also  be 
produced  in  liquids,  but 
it  is  then  much  shorter, 
and  its  brilliancy  is 
greatly  diminished. 

The  voltaic  arc  has 
the  property  that  it  is 
attracted  when  a  magnet 
is  presented  to  it ;  a  con- 
sequence of  the  action  of 


Fig.  692. 


magnets  on  currents  (866). 

Some  physicists  have 
considered  the  voltaic  arc  as  formed  of  a  very  rapid  succession  of  bright 
sparks.  Its  colour  and  shape  depend  on  the  nature  of  the  conductors 
between  which  it  is  formed,  and  it  is  probably  due  to  the  incandescent 
particles  of  the  conductor,  which  are  volatilised  and  transported  in  the 
direction  of  the  current ;  that  is,  from  the  positive  to  the  negative  pole. 
The  more  easily  the  electrodes  are  disintegrated  by  the  current,  the  greater 
is  the  distance  at  which  the  electrodes  can  be  placed.  Charcoal,  which 
is  a  very  friable  substance,  is  one  of  the  bodies  which  gives  the  largest 
luminous  arc. 

Recent  researches  by  Edlund  have  shown  that  this  disintegration  of  the 
terminals  by  the  voltaic  arc  gives  rise  to  an  electromotive  force  opposed  in 
direction  to  that  of  the  main  current. 

Davy  first  made  the  experiment  of  the  electric  light,  in  1801,  by  means  of 
a  battery  of  2,000  plates,  each  4  inches  square.  He  used  charcoal  points 
made  of  light  wood  charcoal  which  had  been  heated  to  redness,  and  im- 
mersed in  a  mercury  bath  ;  the  mercury,  penetrating  into  the  pores  of  the 
charcoal,  increased  its  conductivity.  When  any  substance  was  introduced 
into  the  voltaic  arc  produced  by  this  battery,  it  became  incandescent ;  pla- 
tinum melted  like  wax  in  the  flame  of  a  candle  ;  sapphire,  magnesia,  lime, 
and  most  refractory  substances  were  fused.  Fragments  of  diamond,  of 


740 


Dynamical  Electricity. 


[833- 


charcoal,  and  of  graphite  rapidly  disappeared  without  undergoing  any 
previous  fusion. 

As  charcoal  rapidly  burns  in  air,  it  was  necessary  to  operate  in  vacuo, 
and.  hence  the  experiment  was  for  a  long  time  made  by  fitting  the  two  points 
in  an  electric  egg,  like  that  represented  in  fig.  645.  At  present  the  electrodes 
are  made  of  gas  graphite,  a  modification  of  charcoal  deposited  in  gas  retorts; 
this  is  hard  and  compact,  and  only  burns  slowly  in  air  :  hence  it  is  unnecessary 
to  operate  in  vacuo.  When  the  experiment  is  made  in  vacuo,  there  is  no 
combustion,  but  the  charcoal  wears  away  at  the  positive  pole,  while  it  is 
somewhat  increased  on  the  negative  pole,  indicating  that  there  is  a  transport 
of  solid  matter  from  the  positive  to  the  negative  pole. 

834.  Foucault's  experiment. — This  consists  in  projecting  on  a  screen 
the  image  of  the  charcoal  points  produced  in  the  camera  obscura  at  the 
moment  at  which  the  electric  light  is  formed  (fig.  693).  By  means  of  this 
experiment,  which  is  made  by  the  photo-electric  microscope  already  de- 
scribed (fig.  514),  the  two  charcoals  can  be  readily  distinguished,  and  the 
positive  charcoal  is  seen  to  become  somewhat  hollow  and  diminished,  while 
the  other  increases.  The  globules  represented  on  the  two  charcoals  arise 
from  the  fusion  of  a  small  quantity  of  silica  contained  in  the  charcoal.  When 
the  current  begins  to  pass,  the  negative  charcoal  first  becomes  luminous, 


but  the  light  of  the  positive  charcoal  is  the  brightest ;  as  it  also  wears  away 
about  twice  as  rapidly,  as  the  negative  electrode  it  ought  to  be  rather  the 
larger. 

835.  Regulator  of  the  electric  light, — When  the  electric  light  is  to  be 
used  for  illumination,  it  must  be  as  continuous  as  other  modes  of  lightning. 
For  this  purpose,  not  only  must  the  current  be  constant,  but  the  distance  of 
the  charcoals  must  not  alter,  which  necessitates  the  use  of  some  arrange- 
ment for  bringing  them  nearer  together  in  proportion  as  they  wear  away. 
One  of  the  best  modes  of  effecting  this  is  by  an  apparatus  invented  by 
Duboscq. 

In  this  regulator  the  two  charcoals  are  moveable,  but  with  unequal  veloci- 


-835]  Regulator  of  the  Electric  Light.  74 1 

ties,  which  are  virtually  proportional  to  their  waste.  The  motion  is  trans- 
mitted by  a  drum  placed  on  the  axis,  xy  (fig.  694).  This  turns,  in  the  direc- 
tion of  the  arrows,  two  wheels,  a  and  £,  the  diameters  of  which  are  as  i  :  2, 
and  which  respectively  transmit  their  motion  to  two  rackworks,  C'  and  C. 
C  lowers  the  positive  char- 
coal, p,  by  means  of  a  rod 
sliding  in  the  tube,  H,  while 
the  other  C'  raises  the  nega- 
tive charcoal,  «,  half  as 
rapidly.  By  means  of  the 
milled  head  y  the  drum  can 
be  wound  up,  and  at  the 
same  time  the  positive  char- 
coal moved  by  the  hand  ;  the 
milled  head  x  moves  the 
negative  charcoal  also  by  the 
hand,  and  independently  of 
the  first.  For  this  purpose 
the  axis,  xy,  consists  of  two 
parts  pressing  against  each 
other  with  some  force,  so 
that,  holding  the  milled  head 
x  between  the  fingers,  the 
other,  j,  may  be  moved, 
and  by  holding  the  latter  the 
former  can  be  moved.  But 
the  friction  is  sufficient  when 
the  drum  works  to  move  the 
two  wheels  a  and  b  and  the 
two  rackworks. 

The  'two  charcoals  being 
placed  in  contact,  the  cur- 
rent of  a  powerful  battery 
of  40  to  50  elements  reaches 
the  apparatus  by  means  of 
the  wires  E  and  E'.  The 
current  rising  in  H  descends 
by  the  positive  charcoal,  then 
by  the  negative  charcoal, 
and  reaches  the  apparatus,  but  without  passing  into  the  rackwork,  C, 
or  into  the  part  on  the  right  of  the  plate,  N  ;  these  pieces  being  insu- 
lated by  ivory  discs  placed  at  their  lower  part.  The  current  ultimately 
reaches  the  bobbin  B,  which  forms  the  foot  of  the  regulator,  and  passes 
into  the  wire,  E'.  Inside  the  bobbin  is  a  bar  of  soft  iron,  which  is 
magnetised  as  long  as  the  current  passes  in  the  bobbin,  and  demagnetised 
when  it  does  not  pass,  and  this  temporary' magnet  is  the  regulator.  For  this 
purpose  it  acts  attractively  on  an  armature  of  soft  iron,  A,  open  in  the  centre 
so  as  to  allow  the  rackwork  C'  to  pass,  and  fixed  at  the  end  of  a  lever,  which 
works  on  two  points,  ;;/;//,  and  transmits  a  slight  oscillation  to  a  rod,  d, 


742 


Dynamical  Electricity. 


[835- 


which,  by  means  of  a  catch,  z,  seizes  the  wheel  z,  as  is  seen  on  a  larger  scale 
in  figure  695.  By  an  endless  screw,  and  a  series  of  toothed  wheels,  the  stop 
is  transmitted  to  the  drum,  and  the  rackwork  being  fixed,  the  same  is  the 
case  with  the  carbons.  This  is  what  takes  place  so  long  as  the  magnetisa- 
tion in  the  bobbin  is  strong  enough  to  keep  down  the  armature,  A  ;  but  in 
proportion  as  the  carbons  wear  away,  the  current  becomes  feebler,  though 
the  voltaic  arc  continues,  so  that  ultimately  the  attraction  of  the  magnet  no 
longer  counterbalances  a  spring,  r,  which  continually  tends  to  raise  the 
armature.  It  then  ascends,  the  piece  d  disengages  the  stop  z,  the  drum 
works,  and  the  carbons  come  nearer  ;  they  do  not,  however,  touch,  because 
the  strength  of  the  current  gains  the  upper  hand,  the  armature  A  is  attracted, 
and  the  carbons  remain  fixed.  As  their  distance  only  varies  within  very 

narrow  limits,  a  regular  and  continuous 
light  is  obtained  with  this  apparatus 
until  the  carbons  are  quite  used. 

By  means  of  a  regulator,  Duboscq 
illuminates  the  photogenic  apparatus 
represented  in  fig.  514,  by  which  all  the 
optical  experiments  may  be  performed 
for  which  solar  light  was  formerly  neces- 
sary. 

836.  Browning's  regulator.  —  A 
much  simpler  apparatus,  represented  in 
fig.  696,  has  been  devised  by  Browning, 
which  is  less  costly  than  the  other 
lamps,  and  also  requires  a  smaller 
number  of  elements  to  work  it.  The 
current  enters  the  lamp  by  a  wire  at- 
tached to  a  binding  screw  on  the  base 
of  the  instrument,  passing  up  the  pillar 
by  the  small  electromagnet  to  the  centre 
pillar  along  the  top  of  the  horizontal 
bar,  down  the  left-hand  bar  through 
the  two  carbons,  and  away  by  a  wire 
attached  to  a  binding  screw  on  the  left 
hand.  A  tube  holding  the  upper  carbon 
slides  freely  up  and  down  a  tube  at  the 
end  of  the  cross-piece,  and  would  by 
its  own  weight  rest  on  the  lower  carbon, 
but  the  electromagnet  is  provided  with  a  keeper,  to  which  is  attached  a  rest 
that  encircles  the  carbon  tube  and  grasps  it.  When  the  electromagnet 
works  and  attracts  the  keeper,  the  rest  tightens  and  thereby  prevents  the 
descent  of  the  carbon.  When  the  keeper  is  not  attracted  the  rest  loosens, 
and  the  carbon-holder  descends. 

When  the  two  carbons  are  at  rest,  on  making  contact  with  a  battery  the 
current  traverses  both  carbons  and  no  light  is  produced.  But  if  the  upper 
carbon  be  raised  ever  so  little,  a  brilliant  light  is  emitted.  When  the  lamp 
is  thus  once  set  to  work,  the  rod  attached  to  the  upper  carbon  may  be  let 
go,  and  the  magnet  will  afterwards  keep  the  lamp  at  work.  For  when  some 


Fig.  696. 


Fig.   697. 


-837]          Properties  and  Intensity  of  the  Electric  Light.          743 

of  the  carbon  is  consumed,  and  the  interval  between  the  two  is  too  great  for 
the  current  to  pass,  the  magnet  loses  some  of  its  power,  the  keeper  loosens 
its  hold  on  the  carbon,  and  this  descends  by  its  own  weight.     When  they  are 
sufficiently  near,  but  before  they  are  in  contact,  the  current  is 
re-established  ;  the   magnet  again  draws  on  the  keeper,  and  I   t 

the  keeper  again  checks  the  descent  of  the  carbon,  and  so  forth.  _  jjcf 

Thus  the  points  are  retained  at  the  right  distances  apart,  and 
the  light  is  continuous  and  brilliant. 

Stohrer  has  devised  a  regulator  for  the  electrical  light  which 
is  very  simple  in  principle,  and  which  also  only  requires  a  few 
elements.  Its  essential  features  are  represented  in  fig.  697,  in 
which  b  is  a  cylinder  containing  glycerine  and  surrounded  by  the 
wire  of  the  circuit/  In  this  is  a  hollow  cylindrical  floater  «, 
nearly  as  wide  as  the  vessel ;  at  its  top  is  a  copper  tube  c, 
in  which  the  carbon  point  d  can  be  fixed.  A  stout  copper  wire 
fixed  to  the  bottom  of  the  float  dips  in  an  iron  tube  filled  with 
mercury,  with  which  is  connected  one  pole  of  the  battery ;  the 
other  pole  is  connected  with  the  carbon  d',  which  is  supported 
in  a  suitable  manner.  The  size  of  the  float  is  such  that  it  moves 
slowly  upwards,  so  that  the  carbon  ^presses  with  but  very  slight 
force  against  d'.  This  can  be  regulated  by  placing  small  weights 
in  the  collar  on  c. 

837.  Properties  and  intensity  of  the  electric  light. — The 
electric  light  has  similar  chemical  properties  to  solar  light  :  it  effects  the 
combination  cf  chlorine  and  hydrogen,  acts  chemically  on  chloride  of  silver, 
and  can  be  applied  in  photography,  though  not  for  taking  portraits,  as  it 
fatigues  the  sight  too  greatly. 

Passed  through  a  prism,  the  electric  light,  like  that  of  the  sun,  is  decom- 
posed and  gives  a  spectrum.  Wollaston,  and  more  especially  Fraunhofer, 
found  that  the  spectrum  of  the  electric  light  differs  from  that  of  other  lights, 
and  of  sunlight,  by  the  presence  of  several  very  bright  lines,  as  has  been 
already  stated  (578).  Wheatstone  was  the  first  to  observe  that  by  using 
electrodes  of  different  metals,  the  spectrum  and  the  lines  are  modified. 

Masson,  who  experimented  upon  the  light  of  the  electric  machine,  that  of 
the  voltaic  arc,  and  that  of  RuhmkorfiPs  coil,  found  the  same  colours  in  the 
electric  spectrum  as  in  the  solar  spectrum,  but  traversed  by  very  brilliant 
luminous  bands  of  the  same  shades  as  that  of  the  colour  in  which  they  occur. 
The  number  and  position  of  these  bands  do  not  depend  on  the  intensity  of 
the  light,  but,  as  we  have  seen  (833),  upon  the  substances  between  which 
the  voltaic  arc  is  formed. 

With  carbon  the  lines  are  remarkable  for  their  number  and  brilliancy  ; 
with  zinc  the  spectrum  is  characterised  by  a  very  marked  apple-green  tint  ; 
silver  produces  a  very  intense  green  ;  with  lead  a  violet  tint  predominates, 
and  so  on  with  other  metals. 

Bunsen,  in  experimenting  with  48  couples,  and  removing  the  charcoals  to 
a  distance  of  a  quarter  of  an  inch,  found  that  the  intensity  of  the  electric 
light  is  equal  to  that  of  572  candles. 

Fizeau  and  Foucault  compared  the  chemical  effects  of  the  solar  and  the 
electric  lights,  by  investigating  their  action  on  iodised  silver  plates.  Re- 


744 


Dynamical  Electricity. 


[837- 


presenting  the  intensity  of  the  sun's  light  at  midday  at  1000,  these  physicists 
found  that  that  of  46  Bunsen's  elements  was  235,  while  that  of  80  elements 
was  only  238.  It  follows  that  the  intensity  does  not  increase  to  any  material 
extent  with  the  number  of  the  couples  ;  but  experiment  shows  that  it  in- 
creases considerably  with  their  surface.  For  with  a  battery  of  46  elements, 
each  consisting  of  three  elements,  with  their  zinc  and  copper  respectively 
united  so  as  to  form  one  element  of  triple  surface  (825),  the  intensity  was 
385,  the  battery  working  for  an  hour  :  that  is  to  say,  more  than  a  third  of  the 
intensity  of  the  solar  light. 

Too  great  precautions  cannot  be  taken  against  the  effects  of  the  elec- 
tric light  when  they  attain  a  certain  intensity.  The  light  of  100  couples 
may  produce  very  painful  affections  of  the  eyes.  With  600,  a  single 
moment's  exposure  to  the  light  is  sufficient  to  produce  very  violent  head- 
aches and  pains  in  the  eye,  and  the  whole  frame  is  affected  as  by  a  powerful 
sunstroke. 

Renewed  attempts  have  recently  been 
made,  and  with  great  success,  to  render  the 
electric  light  more  applicable  to  purposes  of 
ordinary  illumination,  and  very  great  ad- 
vances have  been  made  both  in  the  manner 
in  which  the  arc  is  produced,  and  also  in  the 
means  by  which  the  electricity  is  generated. 
In  regard  to  the  latter,  some  form  of  magneto- 
electrical  machine  (915)  driven  by  water  or 
steam  power,  or  by  gas  engines,  is  employed  ; 
this  being  far  more  economical,  and  far  more 
convenient,  than  using  voltaic  batteries. 

Very  considerable  improvements  have 
been  made  in  the  lamp,  the  general  tendency 
of  which  has  been  to  supersede  the  more 
costly  and  expensive  forms  of  regulators. 
One  of  the  most  useful  is  known  as  the 
Jablochkoff  candle.  It  consists  (fig.  698)  of 
two  rods  of  gas  carbon,  a  and  b,  from  2  to 
4mm.  in  diameter,  separated  by  a  layer  of 
kaolin  or  Chinese  clay  about  2mm.  thick,  fixed 
respectively  in  the  supports,  to  which  the 
positive  and  negative  electrodes  A  B  are 
respectively  attached.  The  rods  are  insulated 
from  each  other  by  the  whole  being  bound 
by  some  insulating  material. 

The  current  is  started  by  a  small  piece  of 
carbon,  «,  placed  across  the  top.  As  the  arc 
passes,  the  kaolin  melts  away,  and  the  ar- 
rangement may  therefore  fitly  be  called  a  candle.  The  positive  electrode 
wears  away  twice  as  fast  as  the  negative,  which  would  soon  destroy  the  arc, 
but  by  using  alternating  currents  the  unequal  waste  of  the  carbons  is 
prevented. 

When  either  of  the  carbon  electrodes  which  produce  the  electric  light  is 


Fig.  698, 


-837]  Properties  of  the  Electric  Light.  745 

increased  in  size  its  increase  of  temperature  is  lessened,  while  that  of  the 
other  is  greater.  When  the  negative  electrode  is  large  the  light  of  the  posi- 
tive electrode  is  very  bright.  This  is  seen  in  Werdermanrfs  electric  lamp, 
which  consists  essentially  of  a  carbon  disc  about  2  inches  in  diameter  and  an 
inch  in  thickness,  which  is  connected  with  the  negative  pole  of  the  battery  ; 
the  positive  pole  is  a  rod  of  carbon  about  3  cm.  in  diameter,  of  any  suitable 
length  ;  it  slides  vertically  in  a  copper  tube,  which  serves  both  as  a  guide, 
and  as  a  contact  for  it ;  this  is  pressed  upwards  against  the  centre  by  a 
weight  passing  over  a  pulley.  The  current  can  be  passed  abreast  through 
as  many  as  ten  of  such  lamps,  though  it  seemed  that  the  total  illuminating 
power  of  this  arrangement  is  not  so  great  as  when  only  two  parallel  lights 
are  employed. 

Regnicr's  electric  lamp,  fig.  698^,  consists  of  a  rectangular  copper  rod  B, 
moving  in  a  copper  tube  A,  guided  by  four  pulleys  #,  of  which  only  two  are 
shown  ;  to  B  a  cross  piece  holding  a  thin  carbon  pencil  a 
is  fixed,  the  lower  part  of  which  passes  through  a  silver 
guide,  and  its  end  presses,  but  not  quite  over  the  centre, 
against  a  carbon  disc  /«,  which  moves  about  a  horizontal 
axis.  The  piece  supporting  this  is  insulated  from  A,  but 
is  connected  with  the  negative  pole  by  a  wire  b.  The 
positive  current,  entering  by  A,  passes  by  C  to  a  small 
block  of  carbon  0,  which  presses  against  the  pencil.  Thus 
the  current  only  passes  through  a  very  small  portion  of 
this  pencil,  and  it  is  this  small  portion  which  becomes 
incandescent  and  forms  the  arc.  The  rod,  as  it  burns 
away  and  sinks  by  its  own  weight,  rotates  the  disc  ;;/ 
slowly  and  prevents  its  being  irregularly  worn  away. 

The  advantages  of  the  electric  light  over  gas  are  its 
greater  cheapness,  the  perfect  purity  of  its  colour,  no  con- 
sumption of  oxygen,  and  no  formation  of  carbonic  acid  ; 
no  danger  of  fire  or  explosion,  and  no  evil  smells  such  as 
arise  from  the  escape  of  coal  gas. 

Schwendler  has  devised  a  new  unit  of  luminous  in- 
tensity which  he  calls  the  platinum  light  standard,  spe- 
cially for  use  with  the  electric  light.  It  is  the  incandescence 
produced  by  a  current  of  known  strength  (6-15  webers) 
passing  through  a  U~snaPed  strip  of  platinum  foil  36'28mm 
in  length,  2mm  in  breadth,  and  0*017  in  thickness.  The  circuit  contains  a 
rheostate  and  a  galvanometer  by  which  the  constancy  of  the  current  can  be 
ensured  and  observed.  When  the  strength  of  the  current  is  constant  the 
intensity  of  the  light,  radiated  by  the  platinum,  is  constant  also,  and  fulfils 
all  the  conditions  of  a  standard  measure  of  light  as  it  can  always  be  repro- 
duced in  exactly  the  same  form  from  pure  platinum. 

From  a  comparison  of  the  electrical  arc  with  that  of  the  oxy-hydrogen 
flame,  Dewar  infers  that  the  temperature  of  the  former  is  6,000°  C. 

The  resistance  of  the  voltaic  arc  was  found  by  Ayrton  and  Perry  to 
be  12,  1 6,  and  30  ohms,  according  as  60,  80,  or  122  Grove's  cells  were  em- 
ployed to  produce  it.  The  resistance  should  increase  with  the  number  of 

KK 


FIG.  698  a. 


746  Dynamical  Electricity.  [837- 

the  cells,  seeing  that  a  larger  arc  is  thereby  produced.  In  the  above  case  the 
resistance  of  each  cell  was  found  to  be  approximately  0*2  of  an  ohm  ;  hence 
the  numbers  show  that  the  total  internal  is  nearly  equal  to  the  total  external 
resistance. 

838.  Mechanical  effects  of  the  battery. — Under  this  head  may  be  in- 
cluded the  motion  of  solids  and  liquids  effected  by  the  current.  An  example 
of  the  former  is  found  in  the  voltaic  arc,  in  which  there  is  a  passage  of  the 
molecules  of  carbon  from  the  positive  to  the  negative  pole  (834). 

The  mechanical  action  of  the  current  may  be  shown  by  means  of  the 
following  experiment  (fig.  699).  A  glass  tube  AB  bent  at  the  two  ends,  about 
50  cm.  in  length  and  i  cm.  in  diameter,  is  almost  filled  with  dilute  sulphuric 
acid,  and  a  globule  of  mercury,  ;/z,  is  introduced.  The  whole  is  fixed  in  a 
support,  and  the  level  of  the  tube  can  be  adjusted  by  the  screw  ;z,  the  drop 
of  mercury  itself  serving  as  index. 

When  the  two  poles  of  a  battery  of  4  or  5  cells  are  introduced  into  the 
two  ends,  the  globule  of  mercury  elongates  and  moves  towards  the  negative 
pole  with  a  velocity  which  increases  with  the  number  of  elements.  With 
24,  a  long  column  of  mercury  can  be  moved  through  a  tube  a  metre  in 
length  ;  with  50,  the  velocity  is  greater  and  the  mercury  divides  into  globules, 

all  moving  in  the  same  direc- 
tion. If  the  direction  of  the 
current  is  reversed,  the  mer- 
cury first  remains  stationary 
and  then  moves  in  the  oppo- 
site direction. 

If  the  tube  is  gently  in- 
clined towards  the  positive 
pole,  the  mercury  is  still 
moved  with  the  current  ;  and 
a  moment  is  at  length  reached 
at  which  there  is  equilibrium 
between  the  impulsive  force 
of  the  current  and  the  weight 
of  the  mercury.  The  com- 
ponent of  this  weight  parallel  to  the  plane  may  then  be  taken  as  representing 
the  mechanical  action  of  the  current  which  traverses  the  globule  of  mercury. 
A  similar  phenomenon,  known  as  electiical  endosmose,  is  observed  in 
the  following  experiment,  due  to  Porret.  Having  divided  a  glass  vessel 
into  two  compartments  by  a  porous  diaphragm,  he  poured  water  into 
the  two  compartments  to  the  same  height,  and  immersed  two  platinum 
electrodes  in  connection  with  a  battery  of  80  elements.  As  the  water 
became  decomposed,  part  of  the  liquid  was  carried  in  the  direction  of  the 
current  through  the  diaphragm,  from  the  positive  to  the  negative  compart- 
ment, where  the  level  rose  above  that  in  the  other  compartment.  A  solution 
of  blue  vitriol  is  best  for  these  experiments,  because  then  the  disturbing 
influence  of  the  disengagement  of  gas  at  the  negative  electrode  is  avoided. 

The  converse  of  these  phenomena  is  observed  when  a  liquid  is  forced 
through  a  diaphragm  by  mechanical  means.  Such  currents,  which  were  dis- 
covered by  Quincke,  are  called  diaphragm  currents. 


_839] 


Electro-capillaiy  Phenomena. 


747 

A  porous  diaphragm  p  is  fixed  in  a  glass  tube  (fig.  700),  in  which  are  also 
fused  two  platinum  wires  terminating  in  platinum  electrodes,  a  and  b ;  on 
forcing  a   liquid   through    the 
diaphragm  the  existence  of  a 
current  is  evidenced  by  a  gal-^ 
vanometer  with  which  the  wires 

are  connected,  the  direction  of  a     fa     ° 

which  is  that  of  the  flow  of  the 

liquid.     The  difference  of  potential  due  to  this  flow  is  proportional  to  the 
pressure. 

According  to  Zollner,  all  circulatory  motions  in  liquids,  especially  when 
they  take  place  in  partial  contact  with  solids,  are  accompanied  by  electrical 
currents  which  have  generally  the  same  direction  as  that  in  which  the  cur- 
rent flows. 

Wertheim  found  that  the  elasticity  of  metal  wires  is  diminished  by  the 
current,  and  not  by  the  heat  alone,  but  by  the  electricity ;  he  has  also  found 
that  the  cohesion  is  diminished  by  the  passage  of  a  current. 

To  the  mechanical  effects  of  the  current  may  be  assigned  the  sounds  pro- 
duced in  soft  iron  when  submitted  to  the  magnetising  action  of  a  discon- 
tinuous current — a  phenomenon  which  will  be  subsequently  described. 

839.  Electro-capillary  phenomena. — If  a  drop  of  mercury  be  placed  in 
dilute  sulphuric  acid  containing  a  trace  of  chromic  acid,  and  the  end  of  a 
bright  iron  wire  be  so 
fixed  that  it  dips  in  the 
acid  and  just  touches  the 
edge  of  the  mercury,  the 
latter  begins  a  series  of 
regular  vibrations  which 
may  last  for  hours.  The 
explanation  of  this  phe- 
nomenon, which  was 
first  observed  by  Kiihne, 
is  as  follows  :  —  When 
the  iron  first  touches 
the  mercury,  an  iron- 
mercury  couple  is 
formed,  in  consequence 
of  which  the  surface  of 
the  mercury  is  polarised 
by  the  deposition  of  an 
invisible  layer  of  hydro- 
gen ;  this  polarisation 
(806)  increases  the  sur- 
face-tension of  the  mer- 
cury (138),  it  becomes 
rounder,  and  contact 
with  the  iron  is  broken  ; 


Fig.  701. 


the  chromic  acid  present  depolarises  the  mercury,  its  original  shape  is  re- 
stored, the  couple  is  again  formed,  and  the  process  repeats  itself  continuously. 


K  K  2 


748 


Dynamical  Electricity. 


[839- 


Lippmann  has  been  led  by  the  observation  of  this  phenomenon  to  a  series 
of  interesting  experimental  results,  which  have  demonstrated  a  relation 
between  capillary  and  electrical  phenomena.  Of  these  results  the  most 
important  is  the  construction  of  a  capillary  electrometer. 

A  glass  tube,  A  (fig.  701),  is  drawn  out  on  a  fine  point,  and  is  filled 
with  mercury  :  its  lower  end  dips  in  a  glass  vessel  B,  containing  mercury 
at  the  bottom  and  dilute  sulphuric  acid  at  the  top.  Platinum  wires  are 
fused  in  the  tubes  A  and  B,  and  terminate  in  the  binding  screws  a  and  b 
respectively. 

Now  at  the  beginning  of  the  experiment  the  position  of  the  mercury  in  the 
drawn-out  tube  is  such  that  the  capillary  action  due  to  the  surface  tension 
at  the  plane  of  separation  of  the  mercury  in  the  tube  and  the  liquid  is  suffi- 
cient to  counterbalance  the  pressure  of  the  column  A.  This  position  is 
observed  by  means  of  a  microscope,  the  focus  of  which  is  at  the  fiducial 
mark  on  the  glass  at  which  the  mercury  stops.  If  now  a  difference  of 
potential  be  established,  by  connecting  the  poles  of  a  cell  with  the  wires  a 
and  £,  the  surface-tension  is  increased,  the  mercury  ascends  in  the  capillary 
tube,  and  in  order  to  bring  the  meniscus  back  to  its  former  position,  the 
pressure  on  A  must  be  increased.  This  is  most  simply  effected  by  means  of 
a  thick  caoutchouc  tube  T,  connected  with  the  top  of  A,  and  with  a  mano- 
meter H  ;  and  which  can  be  more  or  less  compressed  by  means  of  a  screw 
E.  The  difference  in  level  of  the  two  legs  of  the  manometer  is  thus  a 
measure  of  the  increase  of  the  surface  tension,  and  therewith  of  the  difference 
of  potential.  Lippmann  found  by  special  experiments  that  this  increase  is 
almost  directly  proportional  to  the  electromotive  force,  up  to  about  0-9  of  a 
Daniell's  element.  Each  electrometer  requires  a  special  table  of  graduation, 
but  when  once  this  is  constructed  it  can  be  directly  used  for  determining 
electromotive  forces.  It  should  not  be  used  for  greater  electromotive  forces 
than  0-6  of  a  Daniell ;  but  it  can  estimate  the  one-thousandth  part  of  this 
quantity,  and,  as  its  electrical  capacity  is  very  small,  it  can  show  rapid 
changes  of  potential,  which  ordinary  electrometers  cannot  do.  For  very 

small  electromotive  forces,  the 
pressure  is  kept  constant,  and  the 
displacement  of  the  meniscus  is 
measured  by  the  microscope. 

840.  Chemical  effects. — These 
are  among  the  most  important  of 
all  the  actions,  either  of  the  simple 
or  compound  circuit.  The  first 
decomposition  effected  by  the  bat- 
tery was  that  of  water  in  1800 
by  Carlisle  and  Nicholson  by  means 
of  a  voltaic  pile.  Water  is  rapidly 
decomposed  by  4  or  5  Bunsen's 
cells ;  the  apparatus  (fig.  702)  is 

very  convenient  for  the  purpose.  It  consists  of  a  glass  vessel  fixed  on 
a  wooden  base.  In  the  bottom  of  the  vessel  two  platinum  electrodes, 
h  and  n,  are  fitted,  communicating  by  means  of  copper  wires  with  the 
binding  screws.  The  vessel  is  filled  with  water  to  which  some  sulphuric  acid 


Fig.  702. 


-841"!  Electrolysis.  749 

has  been  added  to  increase  its  conductivity,  for  pure  water  is  a  very  imperfect 
conductor  ;  two  glass  tubes  filled  with  water  are  inverted  over  the  electrodes, 
and  on  interposing  the  apparatus  in  the  circuit  of  a  battery,  decomposition  is 
rapidly  set  up,  and  gas  bubbles  rise  from  the  surface  of  each  pole.  The 
volume  of  gas  liberated  at  the  negative  pole  is  about  double  that  at  the 
positive,  and  on  examination  the  former  gas  is  found  to  be  hydrogen  and  the 
latter  gas  oxygen.  This  experiment  accordingly  gives  at  once  the  qualitative 
and  quantitative  analysis  of  water.  The  oxygen  thus  obtained  has  the 
peculiar  and  penetrating  odour  observed  when  an  electrical  machine  is 
worked  (793),  and  which  is  due  to  ozone.  The  water  contains  at  the  same 
time  peroxide  of  hydrogen,  in  producing  which  some  oxygen  is  consumed. 
Moreover,  oxygen  is  somewhat  more  soluble  in  water  than  hydrogen. 
Owing  to  these  causes  the  volume  of  oxygen  is  less  than  that  required  by  the 
composition  of  water,  which  is  two  volumes  of  hydrogen  to  one  of  oxygen. 
Hence  voltametric  measurements  are  most  exact  when  the  hydrogen 
alone  is  determined,  and  when  this  is  liberated  at  the  surface  of  a  small 
electrode. 

841.  Electrolysis. — The  term  electrolyte  was  applied  to  those  sub- 
stances which,  like  water,  are  resolved  into  their  elements  by  the  voltaic 
current,  by  Faraday,  to  whom  the  principal  discoveries  in  this  subject  and 
the  nomenclature  are  due.  Electrolysis  is  the  decomposition  by  the  voltaic 
battery  ;  the  positive  electrode  was  by  Faraday  called  the  anode,  and  the 
negative  electrode  the  kathode.  The  products  of  decomposition  are  iones  • 
katione,  that  which  appears  at  the  kathode  ;  and  anione,  that  which  appears 
at  the  anode. 

By  means  of  the  battery,  the  compound  nature  of  several  substances 
\rhich  had  previously  been  considered  as  elements  has  been  determined.  By 
means  of  a  battery  of  250  couples,  Davy,  shortly  after  the  discovery  of  the 
decomposition  of  water,  succeeded  in  decomposing  the  alkalies  potass  and 
soda,  and  proved  that  they  were  the  oxides  of  the  hitherto  unknown  metals 
potassium  and  sodium.  The  decomposition  of  potass  may  be  demonstrated 
with  the  aid  of  a  battery  of  4 
to  6  elements  in  the  following 
manner ;  a  small  cavity  is 
made  in  a  piece  of  solid  caustic 
potass,  which  is  moistened,  and 
a  drop  of  mercury  placed  in  it 
(fig.  703).  The  potass  is  placed 
on  a  piece  of  platinum  con- 
nected with  the  positive  pole  of 
the  battery.  The  mercury  is 
then  touched  with  the  negative 
pole.  When  the  current  passes, 

the  potass  is  decomposed,  oxygen  is  liberated  at  the  positive  pole,  while  the 
potassium  liberated  at  the  negative  pole  amalgamates  with  the  mercury.  On 
distilling  this  amalgam  out  of  contact  with  air,  the  mercury  passes  off 
leaving  the  potassium. 

The  decomposition  of  binary  compounds — that  is,  bodies  containing  two 


75°  Dynamical  Electricity.  [841- 

elements — is  quite  analogous  to  that  of  waterand  of  potass  ;  one  of  the  ele- 
ments goes  to  the  positive,  and  the  other  to  the  negative  pole.  The  bodies 

separated  at  the  positive  pole  are  called  electro- 
negative elements,  because  at  the  moment  of 
separation  they  are  considered  to  be  charged 
with  negative  electricity,  while  those  separated 
at  the  negative  pole  are  called  electropositive 
elements.  One  and  the  same  body  may  be 
electronegative  or  electropositive,  according  to 
the  body  with  which  it  is  associated.  For  in- 
stance, sulphur  is  electronegative  towards 
hydrogen,  but  is  electropositive  towards  oxygen. 
The  various  elements  may  be  arranged  in  such 
Fi  a  series  that  any  one  in  combination  is  electro- 

negative  to  any  following,  but  electropositive 

towards  all  preceding  ones.  This  is  called  the  electrochemical  series,  and 
begins  with  oxygen  as  the  most  electronegative  element,  terminating  with 
potassium  as  the  most  electropositive. 

The  decomposition  of  hydrochloric  acid  into  its  constituents,  chlorine  and 
hydrogen,  may  be  shown  by  means  of  the  apparatus  represented  in  fig.  704. 
Carbon  electrodes  must,  however,  be  substituted  for  those  of  platinum, 
which  is  attacked  by  the  liberated  chlorine  ;  a  quantity  of  salt  also  must 
be  added  to  the  hydrochloric  acid,  in  order  to  dimmish  the  solubility  of 
the  liberated  chlorine.  The  decomposition  of  potassium  iodide  may  be 
demonstrated  by  means  of  a  single  element.  For  this  purpose  a  piece  of 
bibulous  paper  is  soaked  with  a  solution  of  starch,  to  which  potassium 
iodide  is  added.  On  touching  this  paper  with  the  electrodes,  a  blue  spot  is 
produced  at  the  positive  pole,  due  to  the  action  of  the  liberated  iodine  on 
the  starch. 

842.  Decomposition  of  salts. — Ternary  salts  in  solution  are  decomposed 
by  the  battery,  and  then  present  effects  varying  with  the  chemical  affinities 
and  the  intensity  of  the  current.  In  all  cases  the  acid,  or  the  body  which  is 
chemically  equivalent  to  it,  is  electronegative  in  its  action  towards  the  other 
constituent.  The  decomposition  of  salts  may  be  readily  shown  by  means  of 
the  bent  tube  represented  in  fig.  704.  This  is  nearly  filled  with  a  saturated 
solution  of  a  salt,  say  sodium  sulphate,  coloured  with  tincture  of  violets. 
The  platinum  electrodes  of  a  battery  of  four  Bunsen's  elements  are  then 
placed  in  the  two  legs  of  the  tube.  After  a  few  minutes  the  liquid  in  the  posi- 
tive leg,  A,  becomes  of  a  red,  and  that  in  the  negative  leg,  B,  of  a  green 
colour,  showing  that  the  salt  has  been  resolved  into  acid  which  has  passed 
to  the  positive,  and  into  a  base  which  has  gone  to  the  negative  pole,  for  these 
are  the  effects  which  a  free  acid  and  a  free  base  respectively  produce  on 
tincture  of  violets. 

In  a  solution  of  copper  sulphate,  free  acid  and  oxygen  gas  appear  at 
the  positive  electrode,  and  metallic  copper  is  deposited  at  the  negative  elec- 
trode. In  like  manner,  with  silver  nitrate,  metallic  silver  is  deposited  on 
the  negative,  while  free  acid  and  oxygen  appear  at  the  positive  electrode. 

This  decomposition  of  salts  was  formerly  explained  by  saying  that  the 
acid  was  liberated  at  the  positive  electrode  and  the  base  at  the  negative.  Thus 


-843]  Transmissions  effected  by  the  Current.  751 

potassium  sulphate,  K2OSO3,  was  considered  to  be  resolved  into  sulphuric 
acid,  SO3,  and  potash,  K2O.  This  view  regarded  salts  composed  of  three 
elements  as  different  in  their  constitution  from  binary  or  haloid  salts.  Their 
electrolytic  deportment  has  led  to  a  mode  of  regarding  the  constitution  of 
salts  which  brings  all  classes  of  them  under  one  category.  In  potassium 
sulphate,  for  instance,  the  electropositive  element  is  potassium,  while  the 
electronegative  element  is  a  complex  of  sulphur  and  oxygen,  which  is  regarded 
as  a  single  group,  SO4,  and  to  which  the  name  oxy-sulphion  may  be  assigned. 
The  formula  of  potassium  sulphate  would  thus  be  K2SO4,  and  its  decom- 
position would  be  quite  analogous  to  that  of  potassium  chloride,  KC1, 
lead  chloride,  PbCl2,  potassium  iodide,  KI.  The  electronegative  group 
SO4  corresponds  to  a  molecule  of  chlorine  or  iodine.  In  the  decomposition 
of  potassium  sulphate,  the  potassium  liberated  at  the  negative  pole  decom- 
poses water,  forming  potash  and  liberating  hydrogen.  In  like  manner  the 
electronegative  constituent  SO4,  which  cannot  exist  in  the  free  state,  decom- 
poses into  oxygen  gas,  which  is  liberated,  and  into  anhydrous  sulphuric  acid, 
SO3,  which  immediately  combines  with  water  to  form  ordinary  sulphuric  acid, 
H2SO4.  In  fact,  where  the  action  of  the  battery  is  strong,  these  gases  are 
liberated  at  the  corresponding  poles  ;  in  other  cases  they  combine  in  the 
liquid  itself,  reproducing  water.  The  constitution  of  copper  sulphate, 
CuSO4,  and  of  silver  nitrate,  AgNO3,  and  their  decomposition,  will  be 
readily  understood  from  these  examples. 

843.  Transmissions  effected  by  the  current. —  In  chemical  decomposi- 
tions effected  by  the  battery'  there  is  not  merely  a  separation  of  the  elements, 
but  a  passage  of  the  one  to  the  positive  and  of  the  other  to  the  negative 
electrode.  This  phenomenon  was  demonstrated  by  Davy  by  means  of 
several  experiments,  of  which  the  two  following  are  examples  : — 

i.  He  placed  solution  of  sodium  sulphate  in  two  capsules  connected  by 
a  thread  of  asbestos  moistened  with  the  same  solution,  and  immersed  the 
positive  electrode  in  one  of  the  capsules,  and  the  negative  electrode  in  the 
other.  The  salt  was  decomposed,  and  at  the  expiration  of  some  time  all  the 
sulphuric  acid  was  found  in  the  first  capsule,  and  the  soda  in  the  second. 

ii.  Having  taken  three  glasses,  A,  B,  and  C  (fig.  705),  he  poured  into  the 
first  solution  of  sodium  sulphate,  into  the  second  dilute  syrup  of  violets, 
and  into  the  third  pure  water 
and  connected  them  by  mois- 
tened threads  of  asbestos.  The 
current  was  then  passed  in  the 
direction  from  C  to  A.  The  sul- 
phate in  the  vessel  A  was  de-  /^ 
composed,  and  in  the  course  of  I" 
time  there  was  nothing  but  soda 
in  this  glass,  which  formed  the 
negative  end,  while  all  the  acid 

had  been  transported  to  the  glass  C,  which  was  positive.  If,  on  the  contrary, 
the  current  passed  from  A  to  C,  the  soda  was  found  in  C,  while  all  the  acid 
remained  in  A  ;  but  in  both  cases  the  remarkable  phenomenon  was  seen 
that  the  syrup  of  violets  in  B  neither  became  red  nor  green  by  the  passage  of 


752  Dynamical  Electricity.  [843- 

the  acid  or  base  through  its  mass,  a  phenomenon  the  explanation  of  which 
is  based  on  the  hypothesis  enunciated  in  the  following  paragraph. 

844.  Crrothiiss's  hypothesis. — Grothtiss  has  given  the  following  explana- 
tion of  the  chemical  decompositions  effected  by  the  battery.  Adopting  the 
hypothesis  that  in  every  binary  compound,  or  body  which  acts  as  such,  one 
of  the  elements  is  electropositive,  and  the  other  electronegative,  he  assumes 
that,  under  the  influence  of  the  contrary  electricities  of  the  electrodes,  there 
is  effected,  in  the  liquid  in  which  they  are  immersed,  a  series  of  successive 
decompositions  and  recompositions  from  one  pole  to  the  other.  Hence  it  is 
only  the  elements  of  the  terminal  molecules  which  do  not  recombine,  and  re- 
maining free  appear  at  the  electrodes.  Water,  for  instance,  is  formed  of  one 
atom  of  oxygen  and  two  atoms  of  hydrogen,  the  first  gas  being  electronegative, 
the  second  electropositive.  Hence  when  the  liquid  is  traversed  by  a  suffi- 
ciently powerful  current,  the  molecule  a  in  contact  with  the  positive  pole 
arranges  itself  as  shown  in  fig.  706,  that  is,  the  oxygen  is  attracted  and 
the  hydrogen  repelled.  The  oxygen  of  this  molecule  is  then  given-  off  at 
the  positive  electrode,  the  liberated  hydrogen  immediately  unites  with  the 
oxygen  of  the  molecule  £,  the  hydrogen  of  this  with  the  oxygen  of  the  mole- 
cule c,  and  so  on,  to  the  negative  electrode,  where  the  last  atoms  of  hydrogen 
become  free  and  appear  on  the  poles.  The  same  theory  applies  to  the 
metallic  oxides,  to  the  acids  and  salts,  and  explains  why  in  the  experiment 

mentioned  in  the  preceding  para- 
graph the  syrup  of  violets  in  the 
vessel  B  becomes  neither  red  nor 
green.  The  reason  why,  in  the 
fundamental  experiment,  the  hy- 
drogen is  given  off  at  the  nega- 
tive pole  when  the  circuit  is  closed 
will  be  readily  understood  from  a  consideration  of  this  hypothesis. 

Clausius  objects  that,  according  to  this  theory,  a  very  great  force  must 
be  required  for  overcoming  the  affinity  for  each  other  of  the  oppositely 
electrolysed  particles  of  the  compound  ;  and  that  below  a  certain  minimum 
strength  of  current  no  decomposition  could  occur.  Now  Buff  has  shown  that 
the  action  of  even  the  feeblest  currents  continued  for  a  long  time  can  pro- 
duce decomposition.  Again,  when  the  necessary  strength  of  the  current  is 
obtained,  it  should  be  sudden  and  complete ;  whereas  we  know  it  to  be  pro- 
portional to  the  strength  of  the  current. 

To  overcome  this  difficulty  Clausius  applies  the  theory  now  generally 
admitted  of  the  constitution  of  liquids  (292).  The  particles  of  a  compound 
liquid  have  not  the  rigid  unalterable  condition  of  a  solid  body  ;  they  are  in  a 
perpetual  state  of  separation  and  reunion,  so  that  we  must  suppose  compound 
bodies  and  their  elementary  constituents  to  coexist  with  each  other  in  a  liquid. 
Water,  for  instance,  contains  particles  of  water,  together  with  particles  of 
oxygen  and  of  hydrogen  ;  the  former  are  being  continually  decomposed 
and  the  latter  continually  reunited.  When  the  voltaic  current  passes  it 
acts  on  the  motion  of  the  molecules  in  such  a  manner  that  the  negatively 
electrical  particles  of  oxygen  pass  to  the  positive  electrodes,  and  the  positively 
electrical  particles  of  hydrogen  to  the  negative  electrode.  Hence  the  cur- 


-845]  Laws  of  Electrolysis.  753 

rent  does  not  bring  about  the  decomposition,  but  utilises  it,  to  give  definite 
direction  to  the  particles  which  are  already  separated. 

845.  Laws  of  electrolysis. — The  laws  of  electrolysis  were  discovered  by 
Faraday  :  the  most  important  of  them  are  as  follows  : 

I.  Electrolysis  cannot  take  place  unless  the  electrolyte  is  a    conductor. 
Hence  ice  is  not  decomposed  by  the  battery,  because  it  is  a  bad  conductor. 
Other  bodies,  such  as  lead  oxide,  silver  chloride,  etc.,  are  only  electrolysed 
in  a  fused  state — that  is,  when  they  can  conduct  the  current. 

I 1.  The  energy  of  the  electrolytic  action  of  the  current  is  the  same  in  all 
its  parts. 

III.  The  same  quantity  of  electricity — that  is,  the  same  electric  current — 
decomposes  chemically  equivalent  quantities  of  all  the  bodies  which  it  tra- 
verses; from  which  it  follows,  that  the  weights  of  elements  separated  in  these 
electrolytes  are  to  each  other  as  their  chemical  equivalents. 

In  a  circuit  containing  a  voltameter  V,  Faraday  introduced  a  tube,  A  B, 
containing  tin  chloride  kept  in  a  state  of  fusion  by  the  heat  of  a  spirit 
lamp  (fig.  707).  In  the  bottom  of  this  the  negative  pole  was  fused,  while  the 


positive  electrode  consisted  of  a  rod  of  graphite  ;  when  the  current  passed 
chlorine  was  liberated  at  the  positive,  while  tin  collected  at  the  negative 
pole  ;  in  like  manner  lead  oxide  was  electrolysed  and  yielded  lead  at  the 
negative  and  oxygen  at  the  positive  pole.  Comparing  the  quantities  of 
substances  liberated,  they  are  found  to  be  in  a  certain  definite  relation. 
Thus  for  every  18  parts  of  water  decomposed  in  the  voltameter  there  will  be 
liberated  2  parts  of  hydrogen,  207  parts  of  lead,  and  117  of  tin  at  the 
respective  negative  electrodes,  and  16  parts  of  oxygen,  and  71  (or  2  x  35*5) 
parts  of  chlorine  at  the  corresponding  positive  electrode.  Now  these 
numbers  are  exactly  as  the  equivalents  (not  as  the  atomic  weights)  of  the 
bodies. 

It  will  further  be  found  that  in  each  of  the  cells  of  the  battery  65  parts  by 
weight  of  zinc  have  been  dissolved,  for  every  two  parts  by,  weight  of  hydrogen 
liberated  ;  that  is,  that  for  every  equivalent  of  a  substance  decomposed  in  the 
circuit  one  equivalent  of  zinc  is  dissolved.  This  is  the  case  whatever  be  the 
number  of  cells.  An  increase  in  the  number  only  has  the  effect  of  over- 
coming the  great  resistance  which  many  electrolytes  offer,  and  of  accelerating 
the  decomposition.  It  does  not  increase  the  quantity  of  electrolyte  decom- 

K  K  3 


754 


Dynamical  Electricity. 


[845- 


posed.  If  in  any  of  the  cells  more  than  65  parts  of  zinc  are  dissolved  for 
every  two  parts  of  hydrogen  liberated,  this  arises  from  a  disadvantageous 
local  action  ;  and  the  more  perfect  the  battery,  the  more  nearly  does  it 
approach  this  ratio. 

IV.  It  follows  from  the  above  law,  that  the  quantity  of  a  body  decomposed 
in  a  given  time  is  proportional  to  the  strength  of  the  current.  On  this  is 
founded  the  use  of  Faraday's  voltameter,  in  which  the  intensity  of  a  current 
is  ascertained  from  the  quantity  of  water  which  it  decomposes  in  a  given 
time.  It  consists  of  a  glass  vessel,  in  which  two  platinum  electrodes  are 
fixed.  In  the  neck  of  a  vessel  a  bent  delivery  tube  is  fitted,  and  the  mixed 
gases  are  collected  in  a  graduated  cylinder,  so  that  their  volume  can  be  deter- 
mined, which,  reduced  to  a  constant  temperature  and  pressure,  is  a  measure 
of  their  quantity. 

The  use  of  this  voltameter  appears  simple  and  convenient ;  and  hence 
some  physicists  have  proposed  as  unit  of  the  strength  of  the  current,  that 
current  which  in  one  minute  yields  a  cubic  centimetre  of  mixed  gas  reduced 
to  the  temperature  o°  and  the  pressure  760  mm.  Yet,  for  reasons  mentioned 
before  (840),  the  measurements  should  be  based  on  the  volume  of  hydrogen 
liberated. 

A  convenient  form  of  this  instrument  is  that  represented  in  fig.  708. 
The  vessel  a  is  that  in  which  the  water  is  decomposed,  and  contains  two  plati- 
num plates,  and  is  in  connection  with  the 
flask  b,  which  contains  water.  In  this  is  a 
lateral  delivery  tube  c,  which  is  inclined 
until  the  level  of  the  liquid  in  it  is  the  same 
as  in  the  funnel  tube  n.  The  air  is  then  under 
the  same  pressure  as  the  atmosphere.  When 
the  battery  is  connected  with  the  decom- 
posing cell  a,  the  gases  disengaged  expel  a 
corresponding  volume  of  water  through  the 
delivery  tube  c  ;  at  the  conclusion  of  the  ex- 
periment, this  tube  is  inclined  until  the 
liquid  is  at  the  same  level  in  the  tube  n, 
and  in  the  flask.  The  weight  of  the  liquid 
expelled  is  then  a  direct  measure  of  the 
volume  of  the  disengaged  gases. 

Poggendorff  s  silver  voltameter,  fig.  709, 
is  an  instrument  for  measuring  the  strength 
of  the  current.  A  solution  of  silver  nitrate 
of  known  strength  is  placed  in  a  platinum 
dish  which  rests  on  a  brass  plate  that  can 
be  connected  with  the  negative  pole  of  the 

battery  by  means  of  the  binding  screw  b.  In  this  solution  dips  the  positive 
pole,  which  consists  of  a  rod  of  silver  wrapped  round  with  muslin,  and 
suspended  to  an  adjustable  support.  When  the  current  passes  silver  sepa- 
rates at  the  negative  pole,  and  is  washed,  dried,  and  weighed  ;  and  the  weight 
thus  produced  in  a  given  time  is  a  very  accurate  measure  of  the  strength  of 
the  current.  Some  silver  particles  which  are  apt  to  become  detached  from 
the  positive  pole  are  retained  in  the  muslin. 


a 


-846] 


Tangent  Galvanometer  and  Voltameter. 


755 

The  current  from  the  electrical  machine,  which  is  of  very  high  potential, 
is  capable  of  traversing  any  electrolyte,  but  the  quantity  which  it  ran 
decompose  is  extremely  small  as  com- 
pared with  even  the  smallest  voltaic 
apparatus,  and  the  quantity  of  electricity 
developed  by  the  frictional  machine  is 
very  small  as  compared  with  that  de- 
veloped by  chemical  action. 

It  has  been  calculated  by  Weber, 
that  if  the  quantity  of  positive  electricity 
required  to  decompose  a  grain  of  water 
were  accumulated  on  a  cloud  at  a  dis- 
tance of  3,000  feet  from  the  earth's  sur- 
face, it  would  exert  an  attractive  force 
upon  the  earth  of  upwards  of  1,500  tons. 

846.  Comparison  between  the  tan- 
gent galvanometer  and  the  volta- 
meter.— There  are  several  objections 
to  the  use  of  the  voltameter.  In  the 
first  place,  it  does  not  indicate  the 
strength  at  any  given  moment,  for  in 
order  to  obtain  measurable  quantities 
of  gas  the  current  must  be  continued 
for  some  time.  Again,  the  voltameter  Fis-  7°9- 

gives  no  indications  of  the  changes  which  take  place  in  this  time,  but  only 
the  mean  intensity.  It  offers  also  great  resistance,  and  can  thus  only  be 
used  in  the  case  of  strong  currents ;  for  such  currents  either  do  not 
decompose  water,  or  only  yield  quantities  too  small  for  accurate  measure- 
ment. In  addition  to  this,  the  indications  of  the  voltameter  depend  not 
only  on  the  intensity  of  the  current,  but  on  the  acidity  of  the  water,  and  on 
the  distance  and  size  of  the  electrodes. 

The  magnetic  measurements  are  preferable  to  the  chemical  ones.  Not 
only  are  they  more  delicate  and  offer  less  resistance,  but  they  give  the  in- 
tensity at  any  moment.  On  the  other  hand,  indications  furnished  by  the 
tangent  galvanometer  hold  only  for  one  special  instrument.  They  vary 
with  the  diameter  of  the  ring  and  the  number  of  turns  ;  moreover,  one 
and  the  same  instrument  will  give  different  indications  on  different  places, 
seeing  that  the  force  of  the  earth's  magnetism  varies  from  one  place  to 
another  (701). 

The  indications  of  the  two  instruments  may,  however,  be  readily  com- 
pared with  one  another.  For  this  purpose  the  voltameter  and  the  tangent 
galvanometer  are  simultaneously  inserted  in  the  circuit  of  a  battery,  and 
the  deflection  of  the  needle  and  the  amount  of  gas  liberated  in  a  given  time 
are  noted.  In  one  special  set  of  experiments  the  following  results  were 
obtained  : — 


Dynamical  Electricity. 


[846- 


Number  of 
Elements. 

Deflection. 

Gas  liberated  in 
three  minutes. 

1  2 

28-5° 

I25CC. 

8 

24-8 

1  06 

6 

22  'O 

93 

3 

1375 

56 

2 

6-9 

24 

If  we  divide  the  tangents  of  the  angles  into  the  corresponding  volumes 
of  gas  liberated  in  one  minute,  we  should  obtain  a  constant  magnitude  which 
represents  how  much  gas  is  developed  in  a  minute  by  a  current  which  could 
produce  on  the  tangent  galvanometer  the  deflection  45°,  for  tang.  45°— i. 
Making  this  calculation  with  the  above  observations,  we  obtain  a  set  of 
closely  agreeing  numbers,  the  mean  of  which  is  76'5.  The  gas  was  measured 
under  a  pressure  of  737  mm.  and  at  a  temperature  of  15°,  and  therefore 
under  normal  conditions  (332)  its  volume  would  be  70  cubic  centimetres. 
That  is  to  say,  this  is  the  volume  of  gas  which  corresponds  to  a  deflection 
of  45°. 

Hence  in  chemical  measure  the  strength  C  of  a  current  which  produces 
in  this  particular  tangent  galvanometer  a  deflection  of  <p°  is 

C  =  70  tang.  0. 

For  instance,  supposing  a  current  produced  in  this  tangent  galvanometer 
a  deflection  of  54°,  this  current,  if  it  passed  through  a  voltameter,  would  liber- 
ate in  a  minute  70  x  tang.  54°  =  70  x  i  -376  =  96-32  cubic  centimetres  of  gas. 

If  once  the  reduction  factor  for  a  tangent  galvanometer  has  been  deter- 
mined, the  strength  of  any  current  may  be  readily  calculated  in  chemical 
measure  by  a  simple  reading  of  the  angle  of  deflection.  This  reduction  factor 
of  course  only  holds  for  one  special  instrument,  and  for  experiments  in  the 
same  place,  seeing  that  the  force  of  the  earth's  magnetism  varies  in  different 
places. 

The  indications  of  the  sine-compass  may  be  compared  with  those  of  the 
galvanometer  in  a  similar  manner. 

847.  Polarisation. — When  the  platinum  electrodes,  which  have  been 
used  in  decomposing  water,  are  disconnected  from  the  battery,  and  con- 
nected with  a  galvanometer,  the  existence  of  a  current  is  indicated  which  has 
the  opposite  direction  to  that  which  had  previously  passed.  This  phenome- 
non is  explained  by  the  fact  that  oxygen  has  been  condensed  on  the  surface 
of  the  positive  plate,  and  hydrogen  on  the  surface  of  the  negative  plate,  ana- 
logous to  what  has  been  already  seen  in  the  case  of  the  non-constant  batteries 
(806).  The  effect  of  this  is  to  produce  two  different  electromotors,  which 
produce  a  current  opposed  in  direction  to  the  original  one,  and  which,  there- 
fore, must  weaken  it.  As  the  two  electrodes  thus  become  the  poles  of  a  new 
current,  they  are  said  to  be  polai  ised,  and  the  current  is  called  a  polarisation- 
current.  The  degree  of  polarisation  is  considerable  ;  it  increases  with  the 
strength  of  the  current,  attaining  the  force  of  2*6  volts  with  platinum  plates 
in  dilute  sulphuric  acid.  It  constitutes  a  negative  electromotive  force  and 
must  be  allowed  for  in  Ohm's  formula. 


-848] 


Groves  Gas  Battery. 


75? 


On  this  principle  batteries  may  be  constructed  of  pieces  of  metal  of  the 
same  kind — for  instance,  platinum — which  otherwise  gives  no  current.  A 
piece  of  moistened  cloth  is  interposed  between  each  pair,  and  each  end  of 
this  system  is  connected  with  the  poles  of  a  battery.  After  some  time  the 
apparatus  has  received  a  charge,  and  if  separated  from  the  battery  can  itself 
produce  all  the  effects  of  a  voltaic  battery.  Such  batteries  are  called  second- 
ary batteries.  Their  action  depends  on  an  alteration  of  the  surface  of  the 
metal  produced  by  the  electric  current  ;  the  constituents  of  the  liquid  with 
which  the  cloth  is  moistened  having  become  accumulated  on  the  opposite 
plates  of  the  circuit. 

To  this  class  belongs  Plant^s  secondary  battery,  which  consists  of  two 
concentric  cylinders  of  sheet  lead,  which  do  not  touch,  and  are  immersed  in 
dilute  acid.  They  are  charged  by  being  placed  in  contact  with  a  battery  of 
two  or  three  cells,  and  there  is  an  arrangement  by  which  they  can  be  de- 
tached from  the  battery  and  their  current  utilised.  They  serve  in  a  certain 
sense  to  store  up  and  transform  the  power  of  the  primary  battery,  and  pro- 
duce effects  of  great  intensity. 

A  dry  pile  which  has  become  inactive  may  be  used  as  a  secondary  battery. 
\Vhen  a  current  is  passed  through  it,  in  a  direction  contrary  to  that  which 
the  active  battery  yields,  it  then  regains  its  activity. 

848.  Grove  g  gas  battery. — On  the  property,  which  metals  have,  of  con- 
densing gases  on  their  surfaces,  Grove  constructed  his  gas  battery,  fig.  710. 


Fig.  71 


A  single  cell  consists  of  two  glass  tubes,  B  and  A,  in  each  of  which  is  fused 
a  platinum  electrode,  provided  on  the  outside  with  binding  screws.  These 
electrodes  are  made  more  efficient  by  being  covered  with  finely  divided  pla- 
tinum. One  of  the  tubes  is  partially  filled  with  hydrogen,  and  the  other  par- 
tially with  oxygen,  and  they  are  inverted  over  dilute  sulphuric  acid,  so  that 
half  the  platinum  is  in  the  liquid  and  half  in  gas.  On  connecting  the  elec- 
trodes with  a  galvanometer,  the  existence  of  a  current  is  indicated,  whose 
direction  in  the  connecting  wire  is  from  the  platinum  in  oxygen  to  that  in 
hydrogen  ;  so  that  the  latter  is  negative  towards  the  former.  As  the  current 
passes  through  water  this  is  decomposed  ;  oxygen  is  separated  at  the  positive 


758  Dynamical  Electricity.  [848- 

plate  and  hydrogen  at  the  other.  These  gases  unite  with  the  gases  condensed 
on  their  surface,  so  that  the  volume  of  gas  in  the  tubes  gradually  diminishes, 
but  in  the  ratio  of  one  volume  of  oxygen  to  two  volumes  of  hydrogen.  These 
elements  can  be  formed  into  a  battery  (fig.  710)  by  joining  the  dissimilar 
plates  with  one  another  just  as  they  are  joined  in  an  ordinary  battery.  One 
element  of  such  a  battery  is  sufficient  to  decompose  potassium  iodide,  and 
four  will  decompose  water. 

849.  Passive  state  of  iron. — With  polarisation  is  probably  connected  a 
very  remarkable  chemical  phenomenon,  which  many  metals  exhibit,  but  more 
especially  iron.     When  this  is  immersed  in  concentrated  nitric  acid    it  is 
unattacked.     This  condition  of  iron  is  called  the  passive  state,  and  upon  it 
depends  the  possibility  of  the  zinc-iron  battery  (810)      It  is  probable  that  in 
the  above  experiment  a  thin  superficial  layer  of  proto-sesquioxide  of  iron  is 
formed,  which  is  then  negative  towards  platinum. 

850.  Nobili's  rings. — When  a  drop  of  acetate  of  copper  is  placed  on  a 
silver  plate,  and  the  silver  is  touched  in  the  middle  of  a  drop  with  a  piece 
of  zinc,  there  are  formed  around  the  point  of  contact  a  series  of  copper  rings 
alternately  dark  and  light.     These  are  Nobili's  coloured  rings.     They  may 
be  obtained  in  beautiful  iridescent  colours  by  the  following  process  :  A  solu- 
tion of  lead  oxide  in  potash  is  obtained  by  boiling  finely  powdered  litharge 
in  a  solution  of  potash.     In  this  solution  is  immersed  a  polished  plate  of 
silver  or  of  German  silver,  which  is  connected  with  the  positive  electrode  of 
a  battery  of  eight   Bunsen's  elements.     With  the  negative  pole  is  connected 
a  fine  platinum  wire  fused  in  glass,  so  that  only  its  point  projects  ;  and  this 
is  placed  in  the  liquid  at  a  small  distance  from  the  plate.     Around  this  point 
binoxide  of  lead  is  separated  on  the  plate  in  very  thin  concentric  layers,  the 
thickness  of  which  decreases  from  the  middle.     They  show  the  same  series 
of  colours  as  Newton's  coloured  rings  in  transmitted  light.     The  binoxide  of 
lead  owes  its  origin  to  a  secondary  decomposition  ;  by  the  passage  of  the 
current  some  lead  oxide  is  decomposed  into  metallic  lead,  which  is  depo- 
sited at  the  negative  pole,  and  oxygen  which  is  liberated  at  the  positive  ;  and 
this  oxygen  combines  with  some   oxide  of  lead  to  form  binoxide,  which  is 
deposited  on  the  positive  pole  as  the  decomposition  proceeds. 

The  effects  are  also  well  seen  if  a  solution  of  copper  sulphate  is  placed 
on  a  silver  plate,  which  is  touched  with  a  zinc  rod,  the  point  of  which  is 
in  the  solution  ;  for  then  a  current  is  formed  by  these  metals  and  the  liquid. 

851.  Arbor  Saturni,  or  lead  tree.    Arbor  Dianae. — When,  in   a  solu- 
tion of  a  salt,  is  immersed  a  metal  which  is  more  oxidisable  than  the  metal 
of  the  salt,  the  latter  is  precipitated  by  the  former,  while  the  immersed  metal 
is  substituted  equivalent  for  equivalent  for  the  metal  of  the  salt.     This  pre- 
cipitation of  one  metal  by  another  is  partly  attributable  to  the  difference 
in  their  affinities,  and  partly  to  the  action  of  a  current  which  is  set  up  as 
soon  as  a  portion  of  the  less  oxidisable  metal   has  been  deposited.     The 
action  is  promoted  by  the  presence  of  a  slight  excess  of  acid  in  the  solution. 

.  A  remarkable  instance  of  the  precipitation  of  one  metal  by  another  is 
the  Arbor  Saturni.  This  name  is  given  to  a  series  of  brilliant  ramified 
crystallisations  obtained  by  zinc  in  solutions  of  lead  acetate.  A  glass 
flask  is  filled  with  a  clear  solution  of  this  salt,  and  the  vessel  closed  with  a 
cork,  to  which  is  fixed  a  piece  of  zinc  in  contact  with  some  copper  wire. 


-852]  '  Electrometallurgy.  759 

The  flask,  being  closed,  is  left  to  itself.  The  copper  wire  at  once  begins  to 
be  covered  with  a  moss-like  growth  of  metallic  lead,  out  of  which  brilliant 
crystallised  laminae  of  the  same  metal  continue  to  form  ;  the  whole  pheno- 
menon has  great  resemblance  to  the  growth  of  vegetation,  from  which  indeed 
the  old  alchemical  name  is  derived.  For  the  same  reason  the  name  arbor 
Diana;  has  been  given  to  the  metallic  deposit  produced  in  a  similar  manner 
by  mercury  in  a  solution  of  silver  nitrate. 


ELECTROMETALLURGY. 

852.  Electrometallurgy- — The  decomposition  of  salts  by  the  battery 
has  received  a  most  important  application  in  electrometallurgy,  or  galvano- 
plastics,  or  the  art  of  precipitating  certain  metals  from  their  solutions  by  the 
slow  action  of  a  galvanic  current,  by  which  means  the  salts  of  certain 
metals  are  decomposed,  the  metal  being  deposited  on  the  negative  pole, 
while  the  acid  is  liberated  at  the  positive.  The  art  was  discovered  inde- 
pendently by  Spencer  in  England,  and  by  Jacobi  in  Petersburg. 

In  order  to  obtain  a  galvanoplastic  reproduction  of  a  medal  or  any  other 
object,  a  mould  must  first  be  made,  on  which  the  layer  of  metal  is  deposited 
by  the  electric  current. 

For  this  purpose  several  substances  are  in  use,  and  one  or  the  other 
is  preferred  according  to  circumstances.  For  medals  and  similar  objects 
which  can  be  submitted  to  pressure,  gutta-percha  may  be  used  with  advan- 
tage. The  gutta-percha  is  softened  in  hot  water,  pressed  against  the  object 
to  be  copied,  and  allowed  to  cool,  when  it  can  be  detached  without  difficulty. 
For  the  reproduction  of  engraved  woodblocks  or  type,  wax  moulds  are 
now  commonly  used.  They  are  prepared  by  pouring  into  a  narrow  flat  pan 
a  suitable  mixture  of  wax,  tallow,  and  Venice  turpentine,  which  is  allowed  to 
set,  and  is  then  carefully  brushed  over  with  very  finely  powdered  graphite. 
While  this  composition  is  still  somewhat  soft,  the  woodblock  or  type  is 
pressed  upon  it  either  by  a  screw  press,  or,  still  better,  by  hydraulic  pressure. 
If  plaster  of  Paris  moulds  are  to  be  made  use  of,  it  is  essential  that  they  be 
first  thoroughly  saturated  with  wax  or  tallow  so  as  to  become  impervious  to 
water. 

In  all  cases,  whether  the  moulds  be  of  gutta-percha,  of  wax,  or  any  non- 
conducting substance,  it  is  of  the  highest  importance  that  the  surface  be 
brushed  over  very  carefully  with  graphite,  and  so  made  a  good  conductor. 
The  conducting  surface  thus  prepared  must  also  be  in  metallic  contact  with 
a  wire  or  a  strip  of  copper  by  which  it  is  connected  with  the  negative  elec- 
trode. Sometimes  the  moulds  are  made  of  a  fusible  alloy  (338),  which  may 
consist  of  5  parts  of  lead,  8  of  bismuth,  and  3  of  tin.  Some  of  the  melted 
alloy  is  poured  into  a  shallow  box,  and  just  as  it  begins  to  solidify,  the  medal 
is  placed  horizontally  on  it  in  a  fixed  position.  When  the  alloy  has  become 
cool,  a  slight  shock  is  sufficient  to  detach  the  medal.  A  copper  wire  is  then 
bound  round  the  edge  of  the  mould,  by  which  it  can  be  connected  with  the 
negative  electrode  of  the  battery,  and  then  the  edge  and  the  back  are  covered 
with  a  thin  non-conducting  layer  of  wax,  so  that  the  deposit  is  only  formed 
on  the  mould  itself. 


760 


Dynamical  Electricity. 


[852- 


The  most  suitable  arrangement  for  producing  an  electro-deposit  of  copper 
consists  of  a  trough  of  glass,  slate,  or  of  wood,  lined  with  india-rubber  or  coated 
with  marine  glue  (fig.  711).  This  contains  an  acid  solution  of  copper 
sulphate,  and  across  it  are  stretched  copper  rods,  B  and  D,  connected  respec- 
tively with  the  negative  and  positive  poles  of  a  battery.  By  their  copper 
conductors  the  moulds,  ;;?,  are  suspended  in  the  liquid  from  the  negative  rod 
B,  whilst  a  sheet  of  copper,  C,  presenting  a  surface  about  equal  to  that  of  the 
moulds  to  be  covered,  is  suspended  from  the  positive  rod  D,  at  the  distance 
of  about  2  inches,  directly  opposite  to  them. 

The  battery  employed  for  the  electric  deposition  of  metals  ought  to  be  one 
of  great  constancy,  and  Daniell's  and  Smee's  are  mostly  in  use.  The  currents 
of  electricity  furnished  by  magneto-electrical  machines  of  a  special  construc- 
tion are  also  used  in  large  establishments  (715). 

The  copper  plate  suspended  from  the  positive  pole  serves  a  double 
purpose  ;  it  not  only  closes  the  current,  but  it  keeps  the  solution  in  a  state  of 


Fig.  711. 

concentration,  for  the  acid  liberated  at  the  positive  pole  dissolves  the  copper, 
and  reproduces  a  quantity  of  copper  sulphate  equal  to  that  decomposed  by 
the  current. 

Another,  and  very  simple,  process  for  producing  the  electric  deposit  of 
copper  consists  in  making  use  of  what  is  in  effect  a  Daniell's  cell.  A  porous 
pot,  or  a  glass  cylinder  covered  at  the  bottom  with  bladder,  or  with  vegetable 
parchment,  is  immersed  in  a  vessel  of  larger  capacity  containing  a  concen- 
trated solution  of  copper  sulphate.  The  porous  vessel  contains  acidulated 
water,  and  in  it  is  suspended  a  piece  of  amalgamated  zinc  of  suitable  form  ; 
and  having  a  surface  about  equal  to  that  of  the  mould.  The  latter  is  attached 
to  an  insulated  wire  connected  with  the  zinc,  and  is  immersed  in  the  solution 
of  copper  sulphate  in  such  a  position  that  it  is  directly  opposite  to  the 
diaphragm.  The  action  commences  by  the  mould  becoming  covered  with 
copper,  commencing  at  the  point  of  contact  with  the  conductor,  and  gradually 
increasing  in  thickness  in  proportion  to  the  action  of  the  Daniell's  element 
thus  formed.  It  is  of  course  essential  in  the  process  to  keep  the  solution  of 
copper  sulphate  at  a  uniform  strength,  which  is  done  by  suspending  in  it 
muslin  bags  filled  with  crystals  of  this  salt. 

How  great  is    the   delicacy    which    such    electric    deposits    can  attain 


-854]  Electrosilvenng. 

appears  from  the  fact  that  galvanoplastic  copies  can  be  made  of  daguerreo- 
types, which  are  of  the  greatest  accuracy. 

853.  Biectrogildlnr The  old  method  of  gilding  was  by  means  of  mer- 
cury. It  was  effected  by  an  amalgam  of  gold  and  mercury,  which  was 
applied  on  the  metal  to  be  gilt.  The  objects  thus  covered  were  heated  in  a 
furnace,  the  mercury  volatilised,  and  the  gold  remained  in  a  very  thin  layer 
on  the  objects.  The  same  process  was  used  for  silvering  ;  but  they  were 
expensive  and  unhealthy  methods,  and  have  now  been  entirely  replaced  by 
electrogilding  and  electrosilvering.  Electrogilding  only  differs  from  the 
process  described  in  the  previous  paragraph  in  that  the  layer  is  thinner  and 
adheres  more  firmly.  Brugnatelli,  a  pupil  of  Volta,  appears  to  have  been 
the  first,  in  1803,  to  observe  that  a  body  could  be  gilded  by  means  of  the 
battery  and  an  alkaline  solution  of  gold ;  but  De  la  Rive  was  the  first  who 
really  used  the  battery  in  gilding.  The  methods  both  of  gilding  and  silvering 
owe  their  present  high  state  of  perfection  principally  to  the  improvements  of 
Elkington,  Ruolz,  and  others, 

The  pieces  to  be  gilt  have  to  undergo  three  processes  before  gilding. 

The  first  consists  in  heating  them  so  as  to  remove  the  fatty  matter  which 
has  adhered  to  them  in  previous  processes. 

As  the  objects  to  be  gilt  are  usually  of  what  is  called  gilding  metal  or  red 
brass,  which  is  a  special  kind  of  brass  rich  in  copper,  and  their  surface 
during  the  operation  of  heating  becomes  covered  with  a  layer  of  cupric 
or  cuprous  oxide,  this  is  removed  by  the  second  operation.  For  this  purpose 
the  objects,  while  still  hot,  are  immersed  in  very  dilute  nitric  acid,  where 
they  remain  until  the  oxide  is  removed.  They  are  then  rubbed  with  a  hard 
brush,  washed  in  distilled  water,  and  dried  in  gently  heated  sawdust. 

To  remove  all  spots  they  must  undergo  the  third  process,  which  consists 
in  rapidly  immersing  them  in  ordinary  nitric  acid,  and  then  in  a  mixture  of 
nitric  acid,  bay  salt,  and  soot. 

When  thus  prepared  the  objects  are  attached  to  the  negative  pole  of  a 
batter}-,  consisting  of  three  or  four  Bunsen's  or  DanielPs  elements.  They  are 
then  immersed  in  a  bath  of  gold,  as  previously  described.  They  remain  in 
the  bath  for  a  time  which  depends  on  the  thickness  of  the  desired  deposit. 
There  is  a  great  difference  in  the  composition  of  the  baths.  That  most  in 
use  consists  of  I  part  ot  gold  chloride,  and  10  parts  of  potassium  cyanide, 
dissolved  in  200  parts  of  water.  In  order  to  keep  the  bath  in  a  state  of  con- 
centration, a  piece  of  gold  is  suspended  from  the  positive  electrode,  which 
dissolves  in  proportion  as  the  gold  dissolved  in  the  bath  is  deposited  on  the 
objects  attached  to  the  negative  pole. 

The  method  which  has  just  been  described  can  also  be  used  for  silver, 
bronze,  German  silver,  etc.  But  other  metals  such  as  iron,  steel,  zinc,  tin, 
and  lead,  are  very  difficult  to  gild  well.  To  obtain  a  good  coating,  they  must 
first  be  covered  with  a  layer  of  copper,  by  means  of  the  battery  and  a  bath 
of  copper  sulphate  ;  the  copper  with  which  they  are  coated  is  then  gilded, 
as  in  the  previous  case. 

8  54.  Electrosilvering — What  has  been  said  about  gilding  applies  exactly 
to  the  process  of  electrosilvering.  The  difference  is  in  the  composition  of  the 
bath,  which  consists  of  two  parts  of  silver  cyanide,  and  two  parts  of  potas- 
sium cyanide,  dissolved  in  250  parts  of  water.  To  the  positive  electrode  is 


762  Dynamical  Electricity.  [854- 

suspended  a  plate  of  silver,  which  prevents  the  bath  from  becoimng  poorer ; 
the  pieces  to  be  silvered,  which  must  be  well  cleaned,  are  attached  to  the 
negative  pole.  It  may  here  be  observed  that  these  processes  succeed  best 
with  hot  solutions. 

855.  Electric  deposition  of  iron  and  nickel. — One  of  the  most  valuable 
applications  of  the  electric  deposition  of  metals  is  to  what  is  called  the 
steeling  (acierage)  of  engraved  copper  plates.  The  bath  required  for  this 
purpose  is  obtained  by  suspending  a  large  sheet  of  iron,  connected  with  the 
positive  pole  of  a  battery,  in  a  trough  filled  with  a  saturated  solution  of  sal- 
ammoniac  ;  whilst  a  thin  strip  of  iron,  also  immersed,  is  connected  with  the 
negative  pole.  By  this  means  iron  from  the  large  plate  is  dissolved  in  the 
sal-ammoniac,  while  hydrogen  is  given  off  on  the  surface  of  the  small  one. 
When  the  bath  has  thus  taken  up  a  sufficient  quantity  of  iron,  an  engraved 
copper  plate  is  substituted  for  the  small  negative  strip.  A  bright  deposit  of 
iron  begins  to  form  on  it  at  once,  and  the  plate  assumes  the  colour  of  a 
polished  steel  plate.  The  deposit  thus  obtained  in  the  course  of  half  an  hour 
is  exceedingly  thin,  and  an  impression  of  the  plate  thus  covered  does  not 
seem  different  from  an  uncovered  plate  ;  it  possesses,  however,  an  extra- 
ordinary degree  of  hardness,  so  that  a  very  large  number  of  impressions  can 
be  taken  from  such  a  plate  before  the  thin  coating  of  iron  is  worn  off.  When, 
however,  this  is  the  case,  the  film  of  iron  is  dissolved  off  by  dilute  nitric  acid 
and  the  plate  is  again  covered  with  the  deposit  of  iron. 

An  indefinite  number  of  perfect  impressions  may,  by  this  means,  be 
obtained  from  one  copper  plate,  without  altering  the  original  sharp  condition 
of  the  engraving. 

The  covering  of  metals  by  a  deposit  of  nickel  has  of  late  come  into  use. 
The  process  is  essentially  the  same  as  that  just  described.  The  bath  used 
for  the  purpose  can,  however,  be  made  more  directly  by  mixing,  in  suitable 
proportions,  salts  of  nickel  with  those  of  ammonia.  The  positive  pole  con- 
sists of  a  plate  of  pure  nickel.  A  special  difficulty  is  met  with  in  the  electric 
deposition  of  nickel  owingtothe  tendency  of  this  metal  to  deposit  in  an  uneven 
manner ;  and  then  to  become  detached.  This  is  got  over  by  frequently 
removing  the  articles  from  the  bath,  and  submitting  them  to  a  polishing 
process. 

Objects  coated  with  nickel  show  a  highly  polished  surface  of  the  charac- 
teristic bright  colour  of  this  metal.  The  coating  is  moreover  very  hard  and 
durable,  and  is  not  affected  either  by  the  atmosphere  or  even  by  sulphuretted 
hydrogen. 


-856] 


Electrodynamics. 


763 


CHAPTER   IV. 

ELECTRODYNAMICS.      ATTRACTION   AND  REPULSION   OF  CURRENTS   BY 

CURRENTS. 

856.  Electrodynamics. — Under  electrodynamics  is  understood  the  laws 
of  electricity  in  a  state  of  motion,  or  the  action  of  electric  currents  upon  each 
other  and  upon  magnets,  while  electrostatics  deals  with  the  laws  of  electricity 
in  a  state  of  rest. 

The  action  of  one  electrical  current  upon  another  was  first  investigated 
by  Ampere,  shortly  after  the  discovery  of  Oersted's  celebrated  fundamental 


Fig.  712. 


experiment  (820).     All  the  phenomena,  even  the  most  complicated,  follow 
from  two  simple  laws,  which  are — 

I.  Tu>o  currents  which  are  parallel,  and  in  the  same  direction,  attract  one 
another. 

I 1.  Two  currents  parallel,  but  in  contrary  direction,  repel  one  another. 

In  order  to  demonstrate  these  laws,  the  circuit  which  the  current  traverses 
must  consist  of  two  parts,  one  fixed  and  the  other  moveable.    This  is  effected 


764 


Dynamical  Electricity. 


[856- 


713- 


by  the  apparatus  (fig.   712),  which  is  a  modified  and  improved  form  of  one- 
originally  devised  by  Ampere. 

It  consists  of  two  brass  columns,  A  and  D,  between  which  is  a  shorter 
one.  The  column  D  is  provided  with  a  multiplier  (821)  of  20  turns,  MN  (fig., 
712),  which  greatly  increases  the  sensitiveness  of  the  instrument.  This  can> 
be  adjusted  at  any  height,  and  in  any  position,  by  means  of  a  universal  screw 
clamp  (see  figs.  712,  714-718). 

The  short  column  is  hollow,  and  in  its  interior  slides  a  brass  tube  ter- 
minating in  a  mercury  cup,V,  which  can  be  raised  or  lowered.  On  the 
column  A  is  another  mercury  cup  represented  in 
section  at  fig.  713  in  its  natural  size.  In  the 
bottom  is  a  capillary  aperture  through  which  passes 
the  point  of  a  sewing  needle  fixed  to  a  small  copper 
ball.  This  point  extends  as  far  as  the  mercury, 
and  turns  freely  in  the  hole.  The  movable  part 
of  the  circuit  consists  of  a  copper  wire  proceeding 
from  a  small  ball,  and  turning  in  the  direction  of 
the  arrows  from  the  cup  a  to  the  cup  c.  The  two  lower  branches  are  fixed 
to  a  thin  strip  of  wood,  and  the  whole  system  is  balanced  by  two  copper 
balls,  suspended  to  the  ends. 

The  details  being  known,  the  current  of  a  Bunsen's  battery  of  4  or  5  cells 
ascending  by  the  column  A  (fig.  712)  to  the  cup  <2,  traverses  the  circuit  BC, 

reaches  the  cup  c,  descends 
the  central  column,  and 
thence  passes  by  a  wire,  P, 
to  the  multiplier  MN,  from 
whence  it  returns  to  the  bat- 
tery by  the  wire  O.  Now  if, 
before  the  current  passes, 
the  movable  circuit  has 
been  arranged  in  the  plane 
of  the  multiplier,  with  the 
sides  B  and  M  opposite  each 
other,  when  the  current 
passes,  the  side  B  is  repelled, 
which  demonstrates  the  se- 
cond law  ;  for  in  the  branches 
B  and  M  the  currents,  as 
indicated  by  the  arrows,  are 
proceeding  in  opposite  directions. 

To  demonstrate  the  first  law  the  experiment  is  arranged  as  in  figure  714 
— that  is,  the  multiplier  is  reversed  ;  the  current  is  then  in  the  same  direc- 
tion both  in  the  multiplier  and  in  the  movable  part ;  and  when  the  latter  is 
removed  out  of  the  plane  of  the  multiplier,  so  long  as  the  current  passes  it 
tends  to  return  to  it,  proving  that  there  is  attraction  between  the  two  parts. 

857.  Regret's  vibrating:  spiral. — The  attraction  of  parallel  currents  may 
also  be  shown  by  an  experiment  known  as  that  of  Rogefs  -vibrating  spiral. 
A  copper  wire  about  07  mm.  in  diameter  is  coiled  in  a  spiral  of  about  30 
coils  of  25  mm.  in  diameter.  At  one  end  it  is  hung  vertically  from  a  binding 


-858] 


Laws  of  Angular  Currents. 


765. 


Fig.  715- 


screw,  while  the  other  just  dips  in  a  mercury  cup.     On  passing  the  current 
of  a  battery  of  3  to  5  Grove's  cells  through  the  spiral  by  means  of  the  mer- 
cury cup  and  the  binding  screw,  its  coils  are  traversed  by  parallel  currents ; 
they  therefore  attract  one  another,  and  rise,  and  thus  the  contact  with  the 
mercury  is  broken. 
The  current  having 
thus    ceased,    the 
coils     no     longer 
attract  each  other, 
they  fall  by  their 
own   weight,  con- 
tact with  the  mer- 
cury   is    re-estab- 
lished,    and     the 
series    of    pheno- 
mena  are    indefi- 
nitely     produced. 
The  experiment  is 
still  more  striking 
if    a     magnetised 
rod   the  thickness 
of  a  pencil  is  intro- 
duced into  the  interior.     This  will  be  intelligible  if  we  consider  the  action 
between  the  parallel  Amperian  currents  of  the  magnet  and  of  the  helix. 

858.  Xiaws  of  angular  currents. — I.    Two  rectilinear  currents,  the  direc- 
tions of  which  firm  an  angle  with  each  oilier,  attract  one  another  when  both 
approach,    or    re- 
cede from,  the  apex 
of  the  angle. 

II.  They  repel 
one  another,  if  one 
approaches  and  the 
other  recedes  from 
the  apex  of  the 
angle. 

These  two  laws 
may  be  demon- 
strated by  means 
of  the  apparatus 
above  described, 
replacing  the  mov- 
able circuit  by  the 
circuit  BC  (fig.  715).  If  then  the  multiplier  is  placed  horizontally,  so  that 
its  current  is  in  the  same  direction  as  in  the  movable  current,  if  the  latter 
is  removed  and  the  current  passes  so  that  the  direction  is  the  same  as  in  the 
movable  part,  on  removing  the  latter  it  quickly  approaches  the  multiplier, 
which  verifies  the  first  law. 

To  prove  the  second  law,  the  multiplier  is  turned  so  that  the  currents  are 
in  opposite  directions,  and  then  repulsion  ensues  (fig.  716). 


Fig.  716. 


766 


Dynamical  Electricity. 


[858- 


In  a  rectilinear  current  each  element  of  the  current  repels  the  succeeding 
one,  and  is  itself  repelled. 

This  is  an  important  consequence  of  Ampere's  law,  and  may  be  experi- 
mentally demonstrated  by  the  fol- 
lowing arrangement,  which  was 
devised  by  Faraday.  A  (J -shaped 
piece  of  copper  wire,  whose  ends 
dip  in  two  separate  deep  mercury 
cups,  is  suspended  from  one  end  of 
a  delicate  balance  and  suitably 
equipoised.  When  the  mercury 
cups  are  connected  with  the  two 
poles  of  a  battery,  the  wire  rises 
very  appreciably,  and  sinks  again 
to  its  original  position  when  the 
current  ceases  to  pass.  The  current 
passes  into  the  mercury  and  into 
the  wire  ;  but  from  the  construction 
of  the  apparatus  the  former  is  fixed, 
while  the  latter  is  movable,  and  is 
accordingly  repelled. 

The  repulsion  may  also  be  shown 
by  means  of  the  following  experi- 
ment. A  rod  of  charcoal,  C  (fig. 
717),  drawn  out  to  a  fine  point,  is 
fixed  horizontally  in  a  support.  In 
contact  with  it  is  another  similar 


Fig.  717. 


pointed  rod,  C',  counterpoised  by  the  weight  K  at  the  end  of  a  light  hori- 
zontal rod,  A  ;  this  rod  is  suspended  by  a  wire,  and  is  in  metallic  connection 

with  a  mercury  cup,  M.  If 
now  C  and  C'  be  connected 
with  the  poles  F  and  F'  of  a 
battery,  the  movable  cone 
C'  is  repelled  from  C.  As 
the  wire  thereby  'experiences 
some  torsion,  a  stable  equili- 
brium is  established,  and  the 
point  C'  is  kept  at  a  fixed 
distance  from  C.  At  the 
same  time  the  voltaic  arc 
(833)  is  formed  between  C 
and  C'. 

859.  laws  of  sinuous 
currents. —  The  action  of  a 
sinuous  current  is  equal  to 
that  of  a  rectilinear  ciirrent 

of  the  same  length  in  projection.  This  principle  is  demonstrated  by  ar- 
ranging the  multiplier  vertically  and  placing  near  it  a  movable  circuit  of 
insulated  wire  half  sinuous  and  half  rectilinear  (fig.  718).  It  will  be  seen 


-860] 


Direction  of  Currents  by  Currents. 


767 


that  there  is  neither  attraction  nor  repulsion,  showing  that  the  action  of  the 
sinuous  portion  mn  is  equalled  by  that  of  the  rectilinear  portion. 

An  application  of  this  principle  will  presently  be  met  with  in  the  appa- 
ratus called  solenoids  (872),  which  are  formed  of  the  combination  of  a  sinuous 
with  a  rectilinear  current. 


DIRECTION   OF  CURRENTS   BY  CURRENTS. 

860.  Action  of  an  infinite  current  on  a  current  perpendicular  to  its 
direction. —  From  the  action  exerted  between  two  angular  currents  (869)  the 
action  of  a  fixed  and  infinite  rectilinear  current,  PQ  (fig.  719),  on  a  movable 


>5t 

.a,::'... ...:.--, 


R: 


o 

Fig.  719. 


0 
Fig.  720. 


current,  KH,  perpendicular  to  its  direction,  can  be  determined.  Let  OK  be 
the  perpendicular  common  to  KH  and  PQ,  which  is  null  if  the  two  lines  PC 
and  KH  meet.  The  current  PQ  flowing  from  Q  to  P  in  the  direction  of  the 
arrows,  let  us  first  consider  the  case  in  which  the  current  KH  approaches  the 
current  QP.  From  the  first  law  of  angular  currents  (858)  the  portion  GO  ot 
the  current  PQ  attracts  the  current  KH,  because  they  both  flow  towards  the 
summit  of  the  angle  formed  by  their  direccions.  The  portion  PO,  on  the  con- 
trary, will  repel  the  current  KH,  for  here  the  two  currents  are  in  opposite 
directions  at  the  summit  of  the  angle.  If  then  mq  and  ;;//  stand  for  the  two 
forces,  one  attractive  and  the  other  repulsive,  which  act  on  the  current  KH, 
and  which  are  necessarily  of  the  same  intensity,  since  they  are  symmetrically 
arranged  in  reference  to  the  two  sides  of  the  point  O,  these  two  forces  may 
be  resolved  into  a  single  force,  mn,  which  tends  to  move  the  current  KH 
parallel  to  the  current  QP,  but  in  a  contrary  direction. 

A  little  consideration  will  show  that  when  the  current  KH  is  below  the 
current  PQ,  its  action  will  be  the  opposite  of  what  it  is  when  above. 

On  considering  the  case  in  which  the  current  KH  moves  away  from  PQ 
(fig.  720),  it  will  be  readily  seen  from  similar  considerations  that  it  moves 
parallel  to  this  current,  but  in  the  same  direction. 

Hence  follows  this  general  principle.  A  finite  movable  current  -which 
approaches  a  fixed  infinite  current  is  acted  on  so  as  to  move  in  a  direction 
parallel  and  opposite  to  that  of  the  fixed  current;  if  the  movable  current 
tends  from  the  fixed  current,  it  is  acted  on  so  as  to  move  parallel  to  the 
current  and  in  the  same  direction. 

It  follows  from  this,  that  if  a  vertical  current  is  movable  about  an  axis, 
XV,  parallel  to  its  direction  (figs.  721  and  722),  any  horizontal  current,  PQ, 
will  have  the  effect  of  turning  the  movable  current  about  its  axis,  until  the 
plane  of  the  axis  and  of  the  current  have  become  parallel  to  PQ  ;  the  vertical 


;68 


Dynamical  Electricity. 


[860- 


current  stopping,  in  reference  to  its  axis,  on  the  side  from  which  the  current 
PQ  comes  (fig.  721),  or  on  the  side  towards  which  it  is  directed  (fig.   722), 


Fig.  721. 


Fig.  722. 


according  as  the  vertical  current  descends  or  ascends — that  is,  according  as  it 
approaches  or  moves  from  the  horizontal  axis. 

It  also  follows  from  this  principle  that  a  system  of  two  vertical  currents 
rotating  about  a  vertical  axis  (figs.  723  and  724)  is  directed  by  a  horizontal 

current,    PQ,   in 
X:  a  plane   parallel 

to  this  current 
when  one  of 
the  vertical  cur- 
rents is  ascend- 
ing and  the  other 
descending  (fig, 
—  723) ;  but  that  if 

Fig.  723.  Fig.  724.  tney are  botn  as- 

cending  or  both 
descending  (fig.  724),  they  are  not  directed. 

861.  Action  of  an  infinite  rectilinear  current  on  a  rectangular  or 
circular  current. — It  is  easy  to  see  that  a  horizontal  infinite  current  exercises 
the  same  directive  action  on  a  rectangular  current  movable  about  a  vertical 

axis  (fig.  725)  as 

•A.] ^^o  T-I  sL'< 

— tj  -J-4a 

>&          nA 


what  has  been 
above  stated.  For, 
from  the  direction 
of  the  currents 
indicated  by  the 
arrows,  the  part 
Q  Y  acts  by  at- 
traction not  only 
on  the  horizontal 
portion  YD  (law 
of  angular  cur- 
rents}, but  also  on 
The  same  action 
Hence, 


Fig.  725. 


Fig.  726. 


the  vertical  portion  AD  (law  of  perpendicular  currents}. 

evidently  takes  place  between  the  part  PY  and  the  parts  CY  and  BC. 

the  fixed  current  PQ  tends  to  direct  the  movable  rectangular  current  ABCD 

into  a  position  parallel  to  PQ,  and  such  that  in  the  wires  CD  and  PQ  the 

direction  of  the  two  currents  is  the  same. 


-863] 


Rotation  of  Currents  by  Currents. 


769 


This  principle  is  readily  demonstrated  by  placing  the  circuit  ABCD  on 
the  apparatus  with  two  supports  (fig.  725),  so  that  at  first  it  makes  an  angle 
with  the  plane  of  the  supports.  On  passing  below  the  circuit,  a  somewhat 
powerful  current  in  the  same  plane  as  the  supports,  the  movable  part  passes 
into  that  plane.  It  is  best  to  use  the  circuit  in  fig.  734,  which  is  astatic, 
while  that  of  fig.  725  is  not. 

What  has  been  said  about  the  rectangular  current  in  fig.  725  applies 
also  to  the  circular  current  of  fig.  726,  and  is  demonstrated  by  the  same 
experiments. 


ROTATION   OF  CURRENTS   BY  CURRENTS. 


862.  Rotation  of  a  finite  horizontal  current  by  an  infinite  horizontal 
rectilinear    current. — The   attractions  and    repulsions  which    rectangular 
currents  exert  on  one  another : 

may  readily  be  transformed 
into  a  continuous  circular  mo- 
tion. Let  OA  (fig.  727)  be  a 
current  movable  about  the 
point  O  in  a  horizontal  plane, 
and  let  PQ  be  a  fixed  infinite 

current  also  horizontal.      As    - —  ^ 

these  two  currents  flow  in  the  p^g  ?27  Fig  ?28 

direction  of  the  arrows,  it  fol- 
lows that  in  the  position  OA,  the  moveahrfe  current  is  attracted  by  the  current 
PQ,  for  they  are  in  the  same  direction.  Having  reached  the  position  OA', 
the  movable  current  is  attracted  by  the  part  NO  of  the  fixed  current,  and 
repelled  by  the  part  PN.  Similarly,  in  the  position  OA",  it  is  attracted  by 
MO  and  repelled  by  PM,  and  so  on  ;  from  which  follows  a  continuous  rota- 
tory' motion  in  the  direction  AA'A"Am.  If  the  movable  current,  instead 
of  being  directed  from  O  towards  A,  were  directed  from  A  towards  O,  it  is 
easy  to  see  that  the  rotation  would  take  place  in  the  contrary  direction. 
Hence,  by  the  action  of  a  fixed  infinite  current,  PQ,  the  movable  current  OA 
tends  to  a  continuous  motion  in  a  direction  opposite  that  of  the  fixed  current . 
If,  both  currents  being  horizontal,  the  fixed  current  were  circular  instead 
of  being  rectilinear,  its  effect  would  still  be  to  produce  a  continuous  circular 
motion.  For,  let  ABC  (fig.  728)  be  a  fixed  circular  current,  and  mn  a  rec- 
tilinear current  moveable  about  the  axis  //,  both  currents  being  horizontal. 
These  currents,  flowing  in  the  direction  of  the  arrows,  would  attract  one 
another  in  the  angle  «AC,  for  they  both  flow  towards  the  summit  (858).  In 
the  angle  ;iAB,  on  the  contrary,  they  repel  one  another,  for  one  goes  towards 
the  summit  and  the  other  moves  from  it.  Both  effects  coincide  in  moving 
the  wire  ///;/  in  the  same  direction  ACB. 

863.  Rotation  of  a  vertical  current  by  a  horizontal  circular  current. 

A  horizontal  circular  current,  acting  on  a  rectilinear  vertical,  also  imparts  to 
it  a  continuous  rotatory  motion.  In  order  to  show  this,  the  apparatus  repre- 
sented in  fig.  729  is  used. 

L  L 


770 


Dynamical  Electricity. 


[863- 


Fig.  729 


It  consists  of  a  brass  vessel,  round  which  are  rolled  several  coils  of  in- 
sulated copper  wire,  through  which  a  current  passes.  In  the  centre  of  the 
vessel  is  a  brass  support,  a,  terminated  by  a  small  cup  containing  mercury. 
In  this  dips  a  pivot  supporting  a  copper  wire,  bb,  bent  at  its  ends  in  two  ver- 
tical branches,  which  are  soldered  to  a  very  light  copper  ring  immersed  in 

acidulated  water 

/(l    ^^^^^  contained  in  the 

01  _«jr          ]/  ,        A 

vessel  A  cur- 
rent  entering 

through  the  wire 
/;/,  reaches  the 
wire  A,  and 
having  made 
several  circuits, 
terminates  at  B, 
which  is  con- 
nected by  a  wire 

underneath  with  the  lower  part  of  the  column  a.  Ascending  in  this  column, 
it  passes  by  the  wires  bb  into  the  copper  ring,  into  the  acidulated  water,  and 
into  the  sides  of  the  vessel,  whence  it  returns  to  the  battery  by  the  strip  D. 
The  current  being  thus  closed,  the  circuit  bb  and  the  ring  tend  to  turn  in  a 

direction  con- 
trary to  that  of 
the  fixed  cur- 
rent, a  motion 
due  to  the  action 
of  the  circular 
current  on  the 
current  in  the 
vertical  bran- 
ches bb  ;  for,  as 
follows  from  the 
two  laws  of  an- 
Ifgular  currents, 
If  the  branch  b  on 
the  right  is  at- 
tracted by  the 
portion  A  of  the 
fixed  current, 

and  the  branch  b  on  the  left  is  attracted  in  the  contrary  direction' by  the 
opposite  part,  and  these  t\vo  motions  coincide  in  giving  the  ring  a  continuous 
rotatory  motion  in  the  same  direction.  The  action  of  the  circular  current 
on  the  horizontal  part  of  the  circuit  bb  would  tend  to  turn  it  in  the  same 
direction  ;  but  from  its  distance  it  may  evidently  be  neglected. 

864.  Rotation  of  magnets  by  currents.— Faraday  proved  that  currents 
impart  the  same  rotatory  motions  to  magnets  which  they  do  to  currents. 
This  may  be  shown  by  means  of  the  apparatus  represented  in  fig.  730.  It 
consists  of  a  large  glass  vessel,  almost  filled  with  mercury.  In  the  centre  of 
this  is  immersed  a  magnet,  A,  about  eight  inches  in  length,  which  projects  a 
little  above  the  surface  of  the  mercury;  and  is  loaded  at  the  bottom  with  a 


Fig.  730. 


-865] 


Directive  Action  of  Magnets  on  Currents. 


771 


platinum  cylinder.  At  the  top  of  the  magnet  is  a  small  cavity  containing 
mercury  ;  the  current  ascending  the  column  m  passes  into  this  cavity  by  the 
rod  C.  From  the  magnet  it  passes  by  the  mercury  to  a  copper  ring,  G,  whence 
it  emerges  by  the  column  ;/.  When  this  takes  place  the  magnet  begins  to 
rotate  round  its  own  axis  with  a  velocity  depending  on  its  magnetic  power 
and  on  the  intensity  of  the  current. 

Instead  of  making  the  magnet  rotate  on  its  axis,  it  may  be  caused  to 
rotate  round  a  line  parallel  to  its  axis  by  arranging  the  experiment  as  shown 
in  fig.  731. 

This  rotatory  motion  is  readily  intelligible  on  Ampere's  theory  of  mag- 
netism, which  will  be  subsequently  explained  (877),  according  to  which, 
magnets  are  traversed  on  their  surface  by  an  infinity  of  circular  currents  in 
the  same  direction,  in  planes  perpendicular  to  the  axis  of  the  magnet.  At 
the  moment  at  which  the  current  passes  from  the  magnet  into  the  mercury, 
it  is  divided  on  the  surface  of  the  mercury  into  an  infinity  of  rectilinear 
currents  proceeding 
from  the  axis  of  the 
magnet  to  the  cir- 
cumference of  the 
glass.  Figs.  732  and 

c/-^ 


733,  which  corre- 
spond respectively  to 
figs.  73oand  731,  give 
on  a  larger  scale,  and 
on  a  horizontal  plane 
passing  through  the 
surface  of  the  mer- 
cury, the  direction  of 
the  currents  to  which  the  rotation  is  due.  In  figure  732  the  north  pole  being 
at  the  top,  the  Amperian  currents  pass  round  the  magnet  in  the  reverse 
direction  to  that  of  the  hands  of  a  watch,  as  indicated  by  the  arrow  z  (877), 
while  the  currents  which  radiate  from  the  rod  C  towards  the  metal  ring  GG', 
have  the  direction  CD,  CE.  Thus  (858)  any  given  element  e  of  the  mag- 
netic current  of  the  bar  A  is  attracted  by  the  current  CE  and  repelled  by 
the  current  CD  ;  hence  results  a  rotation  of  the  bar  about  its  axis  in  the 
same  direction  as  the  hands  of  a  watch. 

In  fig.  733  the  currents  CD,  CE  being  in  the  opposite  direction  to  those 
of  the  bar  would  repel  the  latter,  which  would  be  attracted  by  the  currents 
CE,  CA.  Hence  the  bar  rotates  in  a  circular  direction,  shown  by  the  arrow 
j,  about  the  vertical  axis  which  passes  through  the  rod  C. 

If  the  north  pole  is  below,  or  if  the  direction  of  the  current  be  altered,  the 
rotation  of  the  magnet  is  in  the  opposite  direction. 


Fig.  732. 


Fig-  733- 


ACTION   OF  THE  EARTH   AND   OF   MAGNETS  ON   CURRENTS. 

865.  Directive  action  of  magnets  on  currents. —  Not  only  do  currents 
act  upon  magnets,  but  magnets  also  act  upon  currents.  In  Oersted's  funda- 
mental experiment  (fig.  677),  the  magnet  being  movable  while  the  current  is 

L  L  2 


772  Dynamical  Electricity,  [865- 

tixed,  the  former  is  directed  and  sets  at  right  angles  with  the  current.     If, 
on  the  contrary,  the  magnet   is  fixed  and  the  current  movable,  the  latter  is 

directed  and  sets 
across  the  direc- 
tion of  the  mag- 
net. This  may  be 
illustrated  by  the 
apparatus  repre- 
sented in  fig.  734. 
This  is  the  origi- 
nal form  of  Am- 
pere's stand  and 
is  frequently  used 
in  experimental 
demonstration.  It 
needs  no  explana- 
tion. The  circuit 
which  the  current 
traverses  is  mov- 
able, and  below 


F'g.  734- 


its  lower  branch 


a  powerful  bar  magnet  is  placed  ;  the  circuit 
immediately  begins  to  turn,  and  stops  after 
some  oscillations  in  a  plane  perpendicular  to 
the  axis  of  the  magnet. 

For  demonstrating  the  action  of  magnets 
upon  currents,  and  indeed  for  establishing  the 
fundamental  laws  of  electrodynamics,  a  small 
apparatus,  known  as  De  la  Rive's  floating 
battery,  is  well  adapted.  It  consists  of  a  small 
Daniell's  element,  contained  in  a  glass  tube 
attached  to  a  cork,  so  that  it  can  float  freely  on 
water.  The  plates  are  connected  with  minute 
mercury  cups  on  the  cork  float  ;  and  with  these 
can  be  connected  either  circular  or  rectangular 
wires,  coils,  or  solenoids  ;  they  are  then  tra- 
versed by  a  current,  and  can  be  subjected  to 
the  action  either  of  magnets  or  of  currents. 

866.  Rotation  of  currents  by  mag-nets. — 
Not  merely  can  currents  be  directed  by  mag- 
nets, but  they  may  also  be  made  to  rotate,  as 
is  seen  from  the  following  experiment,  devised 
by  Faraday,  fig.  735.  On  a  base  with  levelling 
screws,  and  resting  on  an  ivory  support,  is  a 
copper  rod,  BD.  It  is  surrounded  in  part  of 
its  length  by  a  bundle  of  magnetised  wire,  AB, 
and  at  the  top  is  a  mercury  cup.  A  copper 
circuit,  EF,  balanced  on  a  steel  point,  rests  in 

the  cup,  and  the  other  ends  of  the  circuit,  which  terminate  in  steel  points, 

dip  in  an  annular  reservoir  full  of  mercury. 


Fig.  735- 


-867]  Electrodynaiuic  and  Electromagnetic  Rotation  of  Liquids.  773 

The  apparatus  being  thus  arranged,  the  current  from  4  or  5  Bunsen's 
elements  enters  at  the  binding  screw  b :  it  thence  ascends  in  the  rod,  I), 
i  edescends  by  the  two  branches,  reaches  the  mercury  by  the  steel  points, 
whence  it  passes  by  the  framework,  which  is  of  copper,  to  the  battery  by  the 
binding  screw  a.  If  now  the  magnetised  bundle  be  raised,  the  circuit  EF 
rotates,  either  in  one  direction  or  the  other,  according  to  the  pole  by  which 
it  is  influenced.  This  rotation  is  due  to  currents  assumed  to  circulate  round 
magnets  ;  currents  which  act  on  the  vertical  branches  EF  in  the  same  way 
as  the  circular  current  on  the  arm  in  fig.  ^30. 

In  this  experiment  the  magnetised  bundle  may  be  replaced  by  a  solenoid 
(872)  or  by  an  electromagnet,  in  which  case  the  two  binding  screws  in  the 
base  of  the  apparatus  on  the  left  give  entrance  to  the  current  which  is  to 
traverse  the  solenoid  or  electromagnet. 

867.  Electrodynamic  and  electromagnetic  rotation  of  liquids. — In 
the  experiments  hitherto  discussed  rotation  is  produced  by  causing  a  fixed 
current  to  act  upon  a  movable  linear  current.  The  condition  of  a  linear 
current  is  not  necessary.  Fig.  736  represents  an  apparatus  devised  by  Bertin 
to  show  the  electrodynamic  and  electromagnetic  rotation  of  liquids.  This 
apparatus  consists  of  an  annular  earthen  vessel,  VV  ;  that  is  to  say,  it  is 
open  in  the 
centre  so  as  to 
be  traversed  by 
a  coil,  H.  it 
rests  on  a  board 
which  can  be 
raised  along  two 
columns,  E  and 
I,  and  which 
are  fixed  by 
means  of  the 
screws  KK. 
Round  the  ves- 
sel VV  is  a  se- 
cond larger  coil, 
G,  fixed  on  the 
columns  SS'. 
The  vessel  VV 
rests  on  the 
lower  plane.  In 

the  centre  of  the  coil  there  is  a  bar  of  soft  iron,  JIT,  which  makes  an  electro- 
magnet. 

The  vessel  VV  contains  acidulated  water,  and  in  the  liquid  are  plunged 
two  cylindrical  copper  plates  c  and  /,  soldered  to  copper  wires,  e'  and  /', 
which  convey  the  current  of  a  battery  of  four  couples  through  the  rods  E 
and  I. 

The  whole  system  is  arranged  on  a  larger  base,  on  the  left  of  which  is  a 
commutator  represented  afterwards  on  a  larger  scale  (fig.  737).  With  the 
base  of  the  columns  E,  I,  S  and  S',  are  connected  four  copper  strips,  three 
of  which  lead  to  the  commutator  and  the  fourth  to  the  binding  screw  A, 
which  receives  the  wire  from  the  positive  pole. 


774  Dynamical  Electricity.  [867- 

These  details  being  premised,  the  following  three  effects  may  be  obtained 
with  this  apparatus  : — (i),  the  action  of  the  coil  G  alone  ;  (2),  the  action  of 
the  electromagnet  H  alone  ;  (3),  the  simultaneous  action  of  the  coil  and  of 
the  electromagnet. 

I.  Fig.  736  represents  the  apparatus  arranged  for  the  first  effect.     The 
current  coming  by  the  binding  screw  A  attains  the  column  S',  which  leads  it 
to  the  coil  G,  with  regard  to  which  it  is  left — that  is,  in  a  contrary  direction 
to  the  hands  of  a  watch.     Then  descending  by  the  column  S,  it  reaches  the 
commutator,  which  leads  it  by  the  plate  marked  centripete  to  the  column  E 
and  to  the' electrode  e'.     The  current  here  traverses  the  liquid  from  the  cir- 
cumference to  the  centre,  attains  the  electrode  z,  the  column  I,  and  by  the 
intervention  of  the  plate  centrifuge  the  central  piece  of  the  commutator.  This 
transmits  it  finally  to  the  negative  binding  screw,  which  leads  it  to  the 
battery.     The  liquid  then  commences  a  direct  rotatory  motion — that   is  to 
say,  in  the  same  direction  as  the  coil. 

If  the  direction  of  the  current  in  the  liquid  is  centrifugal — that  is,  proceeds 
from,  the  centre  to  the  circumference — the  rotation  is  inverse  ;  that  is,  is  in 
the  opposite  direction  to  that  of  the  coil.  In  both  cases  the  rotations  may 
be  shown  to  those  at  a  distance  by  means  of  small  flags,  f,  f,  fixed  on  discs 
of  cork  which  float  on  the  liquid,  and  which  are  coated  with  lampblack  to 
prevent  adherence  by  capillary  attraction  between  the  discs  and  the  elec- 
trodes e  and  z. 

II.  To  experiment  with  the  electromagnet  alone,  the  positive  wire  of  the 
battery  is  joined  with  the  binding  screw  C,  and  the  binding  screws  D  and  B 
are  joined  by  a  copper  wire.     The  current  first  passes  into  the  electromagnet 
H,  then,  reaching  the  commutator  by  the  binding  screw  B,  passes  into  the 
centripetal  plate,  whence  it  rises  in  the  column  E,  traverses  the  liquid  in  the 
same  direction  as  at  first,  reascends  by  the  column  I,  and  from  thence  to  the 
centre  of  the  commutator  and  the  negative  binding  screw  which  leads  it  to 
the  battery. 

If  the  north  pole  of  the  electromagnet  is  at  the  same  height  as  the  glass 
vessel,  as  in  the  figure,  the  Amperian  currents  move  in  the  opposite  direction 
to  the  hands  of  a  watch,  and  the  floats  then  move  in  the  same  direction  as 
above  ;  and  if  the  electromagnet  is  raised  until  the  neutral  line  is  at  the  same 
height  as  the  vessel,  the  floats  stop  ;  if  it  is  above  them,  the  floats  move 
again,  but  in  the  opposite  direction. 

III.  To  cause  the  coil  and  the  electromagnet  to  act  simultaneously,  the 
positive  wire  of  the  battery  is  attached  at  C,  and  the  binding  screws  D  and 
A  are  connected  by  a  conductor.     Hence,  after  having  traversed  the  coil  H, 
the  current  arrives  from  D,  and  the  binding  screw  A,  whence  it  traverses 
exactly  the  same  circuit  as  in  the  first   experiments.     The  effects  are  the 
same,  though  more  intense  ;  the  action  of  the  coil  and  the  electromagnet 
being  in  the  same  direction. 

868.  Ber tin's  commutator.— Commutators  are  apparatus  by  which  the 
direction  of  currents  may  be  changed  at  pleasure,  or  by  which  they  may  be 
opened  or  closed.  Bert-in's  has  the  advantage  of  at  once  showing  the  direc- 
tion of  the  current.  It  consists  of  a  small  base  of  hard  wood  on  which  is 
an  ebonite  plate,  which,  by  means  of  the  handle  in  (fig.  737),  is  turned 
about  a  central  axis,  between  two  stops,  c  and  c'.  On  the  disc  are  fixed  two 


-869]    Directive  Action  of  t  fie  ^Earth  on  Vertical  Currents.      775 

copper  plates,  one  of  which,  o,  is  always  positive,  being  connected  by  the 

axis  and  by  a  plate,  +  ,  with  the  binding  screw  P,  which  receives  the  positive 

electrode  of  the  battery  ; 

the  other,  i  e,  bent  in  the 

form  of  a  horse-shoe,  is 

connected  by  friction  be- 

low the  disc  with  a  plate 

—  which  passes  to  the  ne- 

gative  electrode  N.     On 

the  opposite  side  of  the 

board    are    two    binding 

screws,  b  and  £',  to  which 

are  adapted    two   elastic 

metal  plates,  r  and  r'. 


These    details    being 


premised,  the  disc  being  turned  as  shown  in  the  figure,  the  current  coming 
by  the  binding  screw  P  passes  into  the  piece  0,  the  plate  r  and  the  binding 
screw  b,  which  by  a  second  plate,  or  by  a  copper  wire,  leads  it  to  the  appa- 
ratus of  fig.  736,  or  any  other.  Then  returning  to  the  binding  screw  b',  the 
current  attains  the  plate  r\  the  piece  /  e,  and  ultimately  the  binding  screw 
N,  which  returns  it  to  the  batten-. 

If  the  disc  is  turned  so  that  the  handle  is  halfway  between  c  and  r',  the 
pieces  o  and  /  e  being  no  longer  in  contact  with  the  plates  r  and  r1  ,  the 
current  does  not  pass.  If  ;//  is  turned  as  far  as  c,  the  plate  o  touches  r', 
the  current  thus  passes  first  to  b'  and  returns  by  b  ;  it  is  therefore  reversed. 

869.  Directive  action  of  tlie  earth  on  vertical  currents.  —  The  earth 
which  exercises  a  directive  action  on  magnets  (690),  acts  also  upon  currents 


738. 


giving  them,  in  some  cases,  a  fixed  direction,  in  others  a  continuous  rotatory 
motion,  according  as  their  currents  are  arranged  in  a  vertical  or  horizontal 
direction. 

The  first  of  these  two  actions  may  be  thus  enunciated  :  Every  vertical 
current  movable  about  an  axis  parallel  to  itself,  places  itself  under  the  direc- 
tive action  of  the  earth  in  a  plane  through  this  axis  perpendicular  to  the 


Dynamical  Electricity. 


[869- 


7/6 

magnetic  meridian,  and  stops  after  some  oscillations,  on  the  east  of  its  axis 
of  rotation  when  it  is  descending,  and  on  the  west  when  it  is  ascending, 

This  may  be  demonstrated  by  means  of  the  apparatus  represented  in 
fig.  739,  which  consists  of  two  brass  vessels  of  somewhat  different  diameters. 
The  larger,  a,  about  13  inches  in  diameter,  has  an  aperture  in  the  centre, 
through  which  passes  a  brass  support,  b,  insulated  from  the  vessel  a,  but 
communicating  with  the  vessel  K.  This  column  terminates  in  a  small  cup, 
in  which  a  light  wooden  rod  rests  on  a  pivot.  At  one  end  of  this  rod  a  fine 
wire  is  coiled,  each  end  of  which  dips  in  acidulated  water,  with  which  the 
two  vessels  are  respectively  filled. 

The  current  arriving  by  the  wire  in  passes  to  a  strip  of  copper,  which  is 
connected  underneath  the  base  of  the  apparatus  with  the  bottom  of  the 
column  b.  Ascending  in  this  column,  the  current  reaches  the  vessel  K,  and 
the  acidulated  water  which  it  contains  ;  it  ascends  from  thence  in  the  wire 
c,  redescends  by  the  wire  e,  and  traversing  the  acidulated  water,  it  reaches 
the  sides  of  the  vessel  a,  and  so  back  to  the  battery  through  the  wire  ;/. 

The  current  being  thus  closed,  the  wire  e  moves  round  the  column  b,  and 
stops  to  the  east  of  it,  when  it  descends,  as  is  the  case  in  the  figure  ;  but  if 

it  ascends,  which  is  effected 
by  transmitting  the  current 
by  the  wire   n,  the   wire   e 
stops    to    the   west    of   the 
column  //>,in  a  position  directly 
opposite  to  that  which  it  as- 
sumes when  it  is  descending. 
If  the  rod  with  a  single 
wire,  in  fig.  739,  be  replaced 
by  one  with  two  wires,  as  in 
fig-    738,   the    rod   will    not 
move,  for  as  each  wire  tends  to  place  itself  on  the  east  of  the  column  b,  two 
equal  and  contrary  effects  are  produced,  which  counterbalance  one  another. 
870.  Action  of  the  earth  on  horizontal   currents   movable  about   a 
vertical  axis.— The  action  of  the  earth  on  horizontal  currents  is  not  direc- 
tive,  but  gives  them   a   contimious   rotatory 
motion  from  the  east  to  the  west  wlien  the  hori- 
zontal current  moves  away  from  the  axis  of 
rotation  and  from  the  west  to  the  east  when  it 
is  directed  towards  this  axis. 

This  may  be  illustrated  by  means  of  the 
apparatus  represented  in  fig.  740,  which  only 
differs  from  that  of  fig.  739  in  having  but  one 
vessel.  The  current  ascending  by  the  column 
a,  traverses  the  two  wires  cc,  and  descends  by 
the  wires  bb,  from  which  it  regains  the  pile  ; 
the  circuit  bccb  then  begins  a  continuous  rota- 
tion, either  from  the  east  to  the  west,  or  from 
the  west  to  the  east,  according  as  in  the  wires  cc 
the  current  goes  from  the  centre,  as  is  the  case  in  the  figure,  or  according  as 
it  goes  towards  it,  which  is  the  case  when  the  current  enters  by  the  wire  m 


Fig.  740. 


Fig.  741. 


872] 


Structure  of  a  Solenoid. 


777 


instead  of  by  //.  But  we  have  seen  (869)  that  the  action  of  the  earth  on  the 
vertical  wires  bb  is  destroyed  :  hence  the  rotation  is  that  produced  by  the 
action  on  the  horizontal  branches  cc.  This  rotatory  action  of  the  terrestrial 
current  on  horizontal  currents  is  a  consequence  of  the  rotation  of  a  finite 
horizontal  by  an  infinite  horizontal  current  (862). 

871.  Directive  action  of  the  earth  on  closed  currents  movable  about 
a  vertical  axis. —  If  the  current  on  which  the  earth  acts  is  closed,  whether 
it  be  rectangular  or  circular,  the  result  is  not  a  continuous  rotation,  but  a 
directive  action,  as  in  the  case  of  vertical  currents  (869),  in  virtue  of  which 
tlie  current  places  itself  in  a  plane  perpendicular  to  the  magnetic  meridian, 
so  that,  for  an  observer  looking  at  the  north,  it  is  descending  on  the  east  of 
its  axis  ofictation,  and  ascending  on  the  west. 

This  property,  which  can  be  shown  by  means  of  the  apparatus  repre- 
sented in  fig.  741,  is  a  consequence  of  what  has  been  said  about  horizontal 
and  vertical  currents.  For  in  the  closed  circuit  BA,  the  current  in  the 
upper  and  lower  parts  tends  to  turn  in  opposite  directions,  from  the  law  of 
horizontal  currents  (860)  ;  and  hence  is  in  equilibrium,  while  in  the  lateral 
parts  the  current  on  the  one  side  tends  towards  the  east,  and  on  the  other 
side  to  the  west,  from  the  law  of  vertical  currents  (854). 

From  the  directive  action  of  the  earth  on  currents,  it  is  necessary,  in  most 
experiments,  to  obviate  this  action.  This  is  effected  by  arranging  the 

movable   circuit    symmetrically   about    its 

axis  of  rotation,  so  that  the  directive  action 
of  the  earth  tends  to  turn  them  in  opposite 
directions,  and  hence  destroys  them.    This 
condition  is  fulfilled  in  the  circuit  in  fig.  734. 
astatic  circuits. 

872.  Structure   of  a  solenoid.— A  solenoid  is  a  system  of  equal  and 
parallel  circular  currents  formed  of  the  same  piece  of  covered  copper  wire 
and  coiled  in  the  form  of  a  helix  or  spiral,  as  represented  in  fig.  742.    A  sole- 
noid, however,  is  only  com- 
plete when  part  of  the  wire 

BC  passes  in  the  direction  of 
the  axis  in  the  interior  of  the 
helix.  With  this  arrange- 
ment, when  the  circuit  is 
traversed  by  a  current,  it 
follows  from  what  has  been 
said  about  sinuous  currents 
(859)  that  the  action  of  a 
solenoid  in  a  longitudinal 
direction,  AB,  is  counter- 
balanced by  that  of  the  recti- 
linear current  BC.  This  ac- 
tion is  accordingly  null  in  the 
direction  of  the  length,  and  the  action  of  a  solenoid  in  a  direction  per- 
pendicular to  its  axis  is  exactly  equivalent  to  that  of  a  series  of  equal  parallel 
currents. 

Li-3 


Fig.  742. 

Such  circuits  are  hence  called 


743- 


778 


Dynamical  Electricity. 


[873- 


873.  Action    of  currents   on   solenoids. — What  has  been  said  of  the 
action  of  fixed  rectilinear  currents  on  finite  rectangular,  or  circular  currents 
(862),  applies  evidently  to  each  of  the  circuits  of  a  solenoid,  and  hence  a 
rectilinear  current  must  tend  to  direct  these  circuits  parallel  to  itself.     To 
demonstrate  this  fact  experimentally,  a  solenoid  is  constructed  as  shown  in 
fig.  743,  so  that  it  can  be  suspended  by  two  pivots  in  the  cups  a  and  c  of  the 
apparatus  represented  in  fig.   734.     The  solenoid  is  then  movable  about  a 
vertical  axis,  and  if  beneath  it  a  rectilinear  current  OP  be  passed,  which  at 
the  same  time  traverses  the  wires  of  the  solenoid,  the  latter  is  seen  to  turn 
and  set  at  right  angles  to  the  lower  current— that  is,  in  such  a  position  that 
its  circuits  are  parallel  to  the  fixed  current  ;  and,  further,  in  the  lower  part 
of  each  of  the  circuits  the  current  is  in  the  same  direction  as  in  the  recti- 
linear wire. 

If,  instead  of  passing  a  rectilinear  current  below  the  solenoid,  it  is  passed 
vertically  on  the  side,  an  attraction  or  repulsion  will  take  place,  according 
as  in  the  vertical  wire,  and  in  the  nearest  part  of  the  solenoid,  the  two 
currents  are  in  the  same  or  in  contrary  directions. 

874.  Directive  action  of  the  earth  on   solenoids. — If  a  solenoid   be 
suspended  in  the  two  cups  (fig.  734),  not  in  the  direction  of  the  magnetic 
meridian,  and  a  current   be  passed  through  the  solenoid,   the  latter  will 
begin  to  move,  and  will  finally  set  in  such  a  position  that  its  axis  is  in  the 
direction  of  the  magnetic  meridian.     If  the  solenoid   be  removed,  it  will, 
after  a  few  oscillations,  return,  so  that  its  axis  is  in  the  magnetic  meridian. 
Further,  it  will  be  found  that  in  the  lower  half  of  the  coils  of  which  the 
solenoid  consists,  the  direction  of  the  current  is  from  east  to  west  ;  in  other 
words,  the  current  is  descending  on  that  side  of  the  coil  turned  towards  the 
east  and  ascending  -on  the  west.      The  directive  action   of  the   earth  on 
solenoids  is  accordingly  .a  consequence  of  that  which  it  exerts  on  circular 
currents.     In  this  experiment  the  solenoid  is  directed  like  a  magnetic  needle, 
and  the  north  pole,  as  in  magnets,  is  that  end  which  points  towards  the 
florth,  and  the  south  fiole  that  which  points  towards  the  south.     This  experi- 
ment may  be  made  by  means  of  a  solenoid  fitted  on  a  De  la  Rive's  floating 
battery. 


Fig-  744 


875.  Mutual  action  of  magnets  and   solenoids.— Exactly  the    same 
phenomena  of  attraction  and  repulsion  exist  between  solenoids  and  magnets 


-877]  Amperes  Theory  of  Magnetism.  779 

as  between  magnets  themselves.  For  if  one  of  the  poles  of  a  magnet  be  pre- 
sented to  a  movable  solenoid,  traversed  by  a  current,  attraction  or  repulsion 
will  take  place,  according  as  the  poles  of  the  magnet  and  of  the  solenoid  are 
of  contrary  or  of  the  same  name.  The  same  phenomenon  takes  place 
when  a  solenoid  traversed  by  a  current  and  held  in  the  hand  is  presented 
to  a  movable  magnetic  needle.  Hence  the  law  of  attractions  and  repulsions 
applies  exactly  to  the  case  of  the  mutual  action  of  solenoids  and  of  magnets. 

876.  Mutual  action  of  solenoids. — When  two  solenoids  traversed  by  a 
powerful  current  are  allowed  to  act  on  each  other,  one  of  them  being  held 
in  the  hand,  and  the  other  being  movable  about  a  vertical  axis,  as  shown 
in  fig.  744,  attraction  and  repulsion  will  take  place  just  as  in  the  case  of  two 
magnets.     These  phenomena  are  readily  explained  by  reference  to  what  has 
been  said  about  the  mutual  action  of  the  currents,  bearing  in  mind  the  direc- 
tion of  the  currents  in  the  extremities  presented  to  each  other. 

877.  Ampere's  theory  of  magnetism. — Ampere  propounded  a  theory, 
based  on  the  analogy  between  solenoids  and  magnets,  by  which  all  magnetic 
phenomena  may  be  referred  to  electrodynamical  principles. 

Instead  of  attributing  magnetic  phenomena  to  the  existence  of  two  fluids 
Ampere  assumed  that  each  individual  molecule  of  a  magnetic  substance  is 
traversed  by  a  closed  electric  current,  and  further  that  these  molecular  cur- 
rents are  free  to  move  about  their  centres.  The  coercive  force,  however, 
which  is  little  or  nothing  in  soft  iron,  but  considerable  in  steel,  opposes  this 
motion,  and  tends  to  keep  them  in  any  position  in  which  they  happen  to  be. 
When  the  magnetic  substance  is  not  magnetised,  these  molecular  currents, 
under  the  influence  of  their  mutual  attractions,  occupy  such  positions  that 
their  total  action  on  any  external  substance  is  null.  Magnetisation  consists 
in  giving  to  these  molecular  currents  a  parallel  direction,  and  the  stronger 
the  magnetising  force  the  more  perfect  the  parallelism.  The  limit  of  mag- 
netisation is  attained  when  the  currents  are  completely  parallel. 

The  resultant  of  the  actions  of  all  the  molecular  currents  is  equivalent  to 
that  of  a  single  current  which  traverses  the  outside  of  a  magnet.  For  by- 
inspection  of  fig.  745  in  which 
the  molecular  currents  are  re- 
presented by  a  series  of  small 
internal  circles  in  the  two  ends 
of  a  cylindrical  bar,  it  will  be 
seen  that  the  adjacent  parts  of 
the  currents  oppose  one  another 
and  cannot  exercise  any  external 
electrodynamic  action.  This  is 
not  the  case  with  the  surface  ; 
there  the  molecular  currents  at 
ab  are  not  neutralised  by  other 
currents,  and  as  the  points  abc 

are  infinitely  near,  they  form  a  series  of  elements  in  the  same  direction 
situated  in  planes  perpendicular  to  the  axis  of  the  magnet,  and  which  consti- 
tute a  true  solenoid. 

The  direction  of  these  currents  in  magnets  can  be  ascertained  by  con- 
sidering the  suspended  solenoid  (fig.  743).  If  we  supposed  it  traversed  by  a 


780  Dynamical  Electricity.  {877- 

current,  and  in  equilibrium  in  the  magnetic  meridian,  it  will  set  in  such  a 
position  that  in  the  lower  half  of  each  coil  the  current  flows  from  east  to 
west.  We  have  then  the  following  rule.  At  the  north  pole  of  magnet,  the 
direction  of  the  Ampeiian  currents  is  opposite  that  of  the  hands  of  a  'watch, 
and  at  the  south  pole  the  direction  is  the  same  as  that  of  'the  hands. 

878.  Terrestrial  current. — In  order  to  explain  on  this  supposition 
terrestrial  magnetic  effects,  the  existence  of  electrical  currents  is  assumed, 
which  continually  circulate  round  our  globe  from  east  to  west  perpendicular 
to  the  magnetic  meridian.  The  resultant  of  their  action  is  a  single  current 
traversing  the  magnetic  equator  from  east  to  west.  They  are  supposed  by 
some  to  be  thermoelectric  currents  due  to  the  variations  of  temperature 
caused  by  the  successive  influence  of  the  sun  on  the  different  parts  of  the 
globe  from  east  to  west. 

These  currents  direct  magnetic  needles ;  for  a  suspended  magnetic 
needle  comes  to  rest  when  the  molecular  currents  on  its  under  surface  are 
parallel  and  in  the  same  direction  as  the  terrestrial  currents.  As  the 
molecular  currents  are  at  right  angles  to  the  direction  of  its  length,  the 
needle  places  its  greatest  length  at  right  angles  to  east  and  west,  or  north 
and  south.  Natural  magnetisation  is  probably  imparted  in  the  same  way  to 
iron  minerals. 

878^.  Ball's  experiment. — In  the  actions  of  magnets  on  currents  which 
have  been  described  in  the  foregoing,  we  have  been  concerned  with  the 
action  of  the  magnet  on  the  body  conveying  the  current. 

Professor  Hall  of  Baltimore  has  made  the  following  experiment  to 
determine  whether  the  path  of  a  current  in  the  body  of  a  conductor  is  or  is 
not  deflected  when  it  is  exposed  to  the  direct  action  of  a  magnetic  field. 
A  strip  of  gold  leaf,  9  centimetres  in  length  by  2  centimetres  broad,  was 
fastened  on  a  glass  plate,  which  was  placed  between  the  poles  of  an  electro- 
magnet in  such  a  manner  that  the  plane  of  the  strip  was  at  right  angles  to 
the  lines  of  force  of  the  magnetic  field.  The  ends  of  this  strip  were  in 
connection  with  the  poles  of  a  Bunsen's  cell.  Two  wires  leading  to  a 
Thomson's  galvanometer  were  connected  with  two  isopotential  points  at 
the  opposite  edges  of  the  strip  ;  that  is  to  say,  in  two  points,  found  by  trial, 
in  which  there  was  no  deflection  of  the  galvanometer  (748).  When  now  the 
electromagnet  was  excited  by  passing  a  current  through  it,  a  distinct  deflec- 
tion was  produced  in  the  galvanometer,  showing  that  the  path  of  the  current 
in  the  conducting  strip  had  been  deflected.  This  deflection  was  permanent, 
and  could  not  therefore  be  due  to  induction,  and  its  direction  was  reversed 
when  the  current  in  the  magnet  was  reversed. 

The  magnetic  field  acts  thus  upon  the  current  in  the  gold  leaf  in  such 
a  manner  as  to  displace  it  from  one  edge  towards  the  other,  and  to  cause  a 
small  portion  to  pass  through  the  circuit  of  the  galvanometer. 

This  experiment  has  greatly  interested  physicists  from  its  theoretical 
bearings,  as  leading  to  a  method  of  determining  the  velocity  of  electricity  in 
absolute  measure. 


-879] 


Magnetisation  by  Currents. 


781 


CHAPTER   V. 

MAGNETISATION    BY  CURRENTS.      ELECTROMAGNETS. 
ELECTRIC  TELEGRAPHS. 

879.  Magnetisation  by  current*.— From  the  influence  which  currents 
exert  upon  magnets,  turning  the  north  pole  to  the  left  and  the  south  pole  to 
the  right,  it  is  natural  to  think  that  by  acting  upon  magnetic  substances  in 
the  natural  state  the  currents  would  tend  to  separate  the  two  magnetisms. 
In  fact,  when  a  wire  traversed  by  a  current  is  immersed  in  iron  filings,  they 
adhere  to  it  in  large  quantities,  but  become  detached  as  soon  as  the  current 
ceases,  while  there  is  no  action  on  any  other  non-magnetic  metal. 

The  action  of  currents  on  magnetic  substances  is  well  seen  in  an  experi- 
ment due  to  Ampere,  which  consists  in  coiling  an  insulated  copper  wire  round 
a  glass  tube,  in  which  there  is  an  unmagnetised  steel  bar.  If  a  current  be 
passed  through  the  wire,  even  for  a  short  time,  the  bar  becomes  strongly 
magnetised. 

If,  as  we  have  already  seen,  the  discharge  of  a  Leyden  jar  be  transmitted 
through  the  wire,  by  connecting  one  end  with  the  outer  coating,  and  the 


Fig.  746. 

other  with  the  inner  coating,  the  bar  is  also  magnetised.     Hence  both  voltaic 
and  frictional  electricity  can  be  used  for  magnetising. 

If  in  this  experiment  the  wire  be  coiled  on  the  tube  in  such  a  manner 
that  when  it  is  held  vertically  the  downward  direction  of  the  coils  is  from 
right  to  left  on  the  side  next  the  observer,  this  constitutes  a  right-handed  or 
dextrorsal  spiral  or  helix  (fig.  746),  of  which  the  ordinary  screw  is  an 
example.  In  a  left-handed  or  sinistrorsal  helix  the  coiling  is  in  the  opposite 
direction,  that  is  from  left  to  right  (fig.  747). 


747- 


In  a  right-handed  spiral  the  north  pole  is  at  the  end  at  which  the  current 
emerges,  and  the  south  pole  at  the  end  at  which  it  enters  ;  the  reverse  is  the 
case  in  a  left-handed  spiral.  But  whatever  the  direction  of  the  coiling,  the 


Dynamical  Electricity. 


[87S- 


polarity  is  easily  found  by  the  following  rule  :  If  a  person  swimming  in  the 
current  look  at  the  axis  of  the  spiral,  the  north  pole  is  always  on  his  left. 

If  the  wire  be  not  coiled  regularly,  but 
if  its  direction  be  reversed,  at  each 
change  of  direction  a  consequent  pole 
(68 1)  is  formed  in  the  magnet.  The 
simplest  method  of  remembering  the 
polarity  produced  is  as  follows  : 
Whatever  be  the  nature  of  the  helix, 
either  right  or  left  handed,  if  the  end 
facing  the  observer  has  the  current 
flowing  in  the  direction  of  the  hands 
of  a  watch,  it  is  a  south  pole,  and  vice 
versa.  The  same  polarity  is  produced, 
whether  or  not  there  is  an  iron  core 
within  the  helix. 

The  nature  of  the  tube  on  which 
the  helix  is  coiled  is  not  without  in- 
fluence. Wood  and  glass  have  no 
effect,  but  a  thick  cylinder  of  copper 
may  greatly  affect  the  action  of  the 
current  unless  the  copper  be  slit  longi- 
tudinally. This  action  will,  be  subse- 
quently explained.  The  same  is  the 
case  with  iron,  silver,  and  tin. 

In  order  to  magnetise  a  steel  bar 
by  means  of  electricity,  it  need  not  be 
•  748.  placed  in  a  tube,  as  shown  in  figs.  746 

and  747.  It  is  sufficient  to  coil  round  it  a  copper  wire,  covered  with  silk, 
cotton,  or  gutta-percha  in  order  to  insulate  the  circuits  from  one  another. 
The  action  of  the  current  is  thus  multiplied,  and  a  feeble  current  is  sufficient 
to  produce  a  powerful  magnetising  effect. 

880.  Electromagnets. — Electromagnets  are  bars  of  soft  iron  which,  under 
the  influence  of  a  voltaic  current,  become  magnets  ;  but  this  magnetism  is 
only  temporary,  for  the  coercive  force  of  perfectly  soft  iron  is  null,  and  the 
two  magnetisms  neutralise  each  other  as  soon  as  the  current  ceases  to  pass 
through  the  wire.  If,  however,  the  iron  is  not  quite  pure,  it  retains  more  or 
less  traces  of  magnetism.  Electromagnets  have  the  horse-shoe  form,  as 
shown  in  fig.  746,  and  a  copper  wire,  covered  with  silk  or  cotton,  is  rolled 
several  times  round  them  on  the  two  branches,  so  as  to  form  two  bobbins, 
A  and  B.  In  order  that  the  two  ends  of  the  horse-shoe  may  be  of  opposite 
polarity,  the  winding  on  the  two  limbs  A  and  B  must  be  such  that  if  the 
horse-shoe  were  straightened  out,  it  would  be  in  the  same  direction. 

Electromagnets,  instead  of  being  made  in  one  piece,  are  frequently  con- 
structed of  two  cylinders,  firmly  screwed  to  a  stout  piece  of  the  same  metal. 
Such  are  the  electromagnets  in  Morse's  telegraph  (886),  the  electromagnetic 
motor  (895).  The  helices  on  them  must  be  such  that  the  current  shall  flow 
in  the  same  direction  as  the  hands  of  a  watch  as  seen  from  the  south  pole, 
and  against  the  hands  of  a  watch  as  seen  from  the  north  pole. 


-880]  Electromagnets.  783 

The  results  at  which  various  experimenters  have  arrived  as  regards  the 
force  of  electromagnets  are  often  greatly  divergent,  which  is  partly  due  to 
the  different  senses  they  have  attached  to  the  notion  of  electromagnetic  force. 
For  this  may  mean  (I.)  the  induction  current  which  the  development  and 
disappearance  of  the  magnetism  of  an  iron  core  indicate  in  a  spiral  which 
surrounds  it;  this  is  the  excited  magnetism;  or  (II.)  the  free  magnetism 
measured  by  the  action  on  a  magnetic  needle,  oscillating  at  a  distance  : 
(1 1 1.)  the  attractive  force ',  or  the  force  required  to  hold  an  armature  at  a 
distance  from  the  electromagnet ;  (IV.)  the  lifting  power  measured  by  the 
force  with  which  an  armature  is  held  in  direct  contact  with  the  pole. 

The  most  important  results  which  have  been  arrived  at  are  the  follow- 
ing: 

(i.)  Using  the  term  electromagnetic  force  in  the  first  two  senses,  it  is 
proportional  to  the  strength  of  the  current.  This  only  applies  when  the  cur- 
rents are  not  very  powerful,  and  to  stout  bars  ;  for  in  each  bar  there  is,  as 
Muller  has  found,  a  maximum  of  magnetisation  which  cannot  be  exceeded. 

(ii.)  Taking  into  account  the  resistance,///^  electromagnetic  force  is  in- 
dependent of  the  nature  and  thickness  of  the  'wire.  Thus,  the  strength  of  the 
current,  and  the  number  of  coils  being  the  same,  thick  and  thin  wires  produce 
the  same  effect. 

(iii.)  With  the  same  current  the  electromagnetic  force  is  independent  of 
the  width  of  the  coils,  provided  the  iron  projects  beyond  the  coils,  and  the 
diameter  of  the  coil  is  small  compared  with  its  length. 

(iv.)  The  temporary  magnetic  moment  of  an  iron  bar  is,  within  certain 
limits,  proportional  to  the  number  of  windings.  The  product  of  the  intensity 
into  the  number  of  turns  is  usually  spoken  of  as  the  magnetising  power  of 
the  spiral.  The  greatest  magnetising  power  is  obtained  when  the  resistance 
in  the  magnetising  spiral  is  equal  to  the  sum  of  the  other  resistances  in  the 
circuit,  those  of  the  battery  included,  and  the  length  and  diameter  of  the 
wire  must  be  so  arranged  as  to  satisfy  these  conditions. 

(v.)  The  magnetism  in  solid  and  in  hollow  cylinders  of  the  same  dia- 
meters is  the  same,  provided  in  the  latter  case,  there  is  sufficient  thickness 
of  iron  for  the  development  of  the  magnetism. 

(vi.)  The  attraction  of  an  armature  by  an  electromagnet  is  proportional 
to  the  square  of  the  intensity  of  the  current  so  long  as  the  magnetic  moment 
does  not  attain  its  maximum.  Two  unequally  strong  electromagnets  attract 
each  other  with  a  force  proportional  to  the  square  of  the  sum  of  both  cur- 
rents. 

(vii.)  For  powerful  currents  the  length  of  the  branches  of  an  electro- 
magnet  is  with Jl|^  influence  on  the  weight  which  it  can  support. 

Beetz  observecl  that,  for  the  same  strength  of  current,  electromagnetism 
is  produced  more  rapidly  in  circuits  with  great  resistance  and  great  electro- 
motive force  than  in  circuits  with  small  resistance  and  correspondingly  smaller 
electromotive  force  ;  in  the  latter  case  the  reverse  currents  which  occur  in 
the  coils  of  the  electromagnet  come  into  play  more  in  the  latter  case  than 
in  the  former. 

As  regards  the  quality  of  the  iron  used  for  the  electromagnet,  it  must  be 
pure,  and  be  made  as  soft  as  possible  by  being  reheated  and  cooled  a  great 
many  times  ;  it  is  polished  by  means  of  a  file  so  as  to  avoid  twisting.  If 


784  Dynamical  Electricity.  [880- 

this  is  not  the  case,  the  bar  retains,  even  after  the  passage  of  the  current,  a 
quantity  of  magnetism  ^vhich  is  called  the  remanent  magnetism.  A  bundle 
of  soft  iron  wires  loses  its  magnetism  more  rapidly  than  a  massive  bar  of 
the  same  size.  According  to  Stone,  iron  wires  may  be  materially  improved 
for  electromagnetic  experiments  by  forming  them  into  bundles  by  tying 
them  round  with  wire  ;  these  bundles  are  then  dipped  in  paraffine  and  set 
fire  to. 

During  magnetisation  the  volume  of  a  magnet  does  not  vary.  This  has 
been  established  by  placing  the  bar  to  be  magnetised  with  its  helix  in  a  sort 
of  water  thermometer,  consisting  of  a  flask  provided  with  a  capillary  tube. 
On  magnetising,  no  alteration  in  the  position  of  the  water  is  observed.  But 
the  dimensions  vary  ;  the  diameter  is  somewhat  lessened,  and  the  length 
increased  :  according  to  Joule  to  the  extent  of  about  2?uboo»  ^  ^ie  bar 
magnetised  to  saturation. 

88 1.  Vibratory  motion  and  sounds  produced  by  currents. — When  a 
rod  of  soft  iron  is  magnetised  by  a  strong  electric  current,  it  gives  a  very 
distinct  sound,  which,  however,  is  only  produced  at  the  moment  of  closirg 
or  opening  the  current.     This  phenomenon,  which  was  first  observed  by 
Page  in  America,  and  by  Delezenne  in  France,  has  been  particularly  inves- 
tigated by  De  la  Rive,  who  attributed  it  to  a  vibratory  motion  of  the  mole- 
cules of  iron  in  consequence  of  a  rapid  succession  of  magnetisations  and 
demagnetisations. 

When  the  current  is  broken  and  closed  at  very  short  intervals,  De  la  Rive 
observed  that  whatever  be  the  shape  or  magnitude  of  the  iron  bars,  two 
sounds  may  always  be  distinguished  ;  one,  which  is  musical,  corresponds  to 
that  which  the  rod  would  give  by  vibrating  transversely  ;  the  other,  which 
consists  of  a  series  of  harsh  sounds,  corresponding  to  the  interruptions  of 
the  current,  is  compared  by  De  la  Rive  to  the  noise  of  rain  falling  on  a 
metal  roof.  The  most  marked  sound,  says  he,  is  that  obtained  by  stretch: 
ing,  on  a  sounding-board,  pieces  of  soft  iron  wire,  well  annealed,  from  i  to  2 
mm.  in  diameter,  and  i  to  2  yards  long.  These  wires  being  placed  in  the 
axis  of  one  or  more  bobbins  traversed  by  powerful  currents,  send  forth  a 
number  of  sounds,  which  produce  a  surprising  effect,  and  much  resemble 
that  of  a  number  of  church  bells  heard  at  a  distance. 

Wertheim  has  obtained  the  same  sounds  by  passing  a  discontinuous  cur- 
rent, not  through  the  bobbins  surrounding  the  iron  wires,  but  through  the 
wires  themselves.  The  musical  sound  is  then  stronger  and  more  sonorous 
in  general  than  in  the  previous  experiment.  The  hypothesis  of  a  molecular 
movement  in  the  iron  wires  at  the  moment  of  their  magnetisation,  and  of 
their  demagnetisation,  is  confirmed  by  the  researches  of  Wertheim,  who  has 
found  that  their  elasticity  is  then  diminished. 

882.  Reis's  telephone. — The  essential  features  of  this  instrument  (fig. 
749)  are  a  sort  of  box,  B,  one  side  of  which  is  closed  by  a  membrane  C, 
while  there  is  a  mouthpiece,  A,  in  another  side.     On  the  membrane  is  a 
piece  of  thin  metal-foil  C,  which  is  connected  with  a  wire  leading  to  one 
pole  of  the  battery  G,  the  other  pole  of  which  is  put  to  earth.     Just  above 
the  foil,  and  almost  touching  it,  is  a  metal  point  D,  which  is  connected  by 
the  line  wire  (893)  with  one  end  of  a  coil  of  insulated  wire  surrounding  an 
iron  wire,  the  other  end  of  which  is  put  to  earth. 


-883] 


Electric  Telegraphs. 


-85 


When  the  mouthpiece  is  spoken  or  sung  into,  the  sounds  set  the  mem- 
brane in  vibration  ;  this  alternately  opens  and  closes  the  current,  and  these 


Litim 


1 


Fig.  749. 

makes  and  breaks  being   transmitted   through  the   circuit  to  the  electro- 
magnet F,  produce  the  corresponding  sounds. 


ELECTRIC   TELEGRAPH. 

883.  Electric  telegraph. — These  are  apparatus  by  which  signals  can  be 
transmitted  to  considerable  distances  by  means  of  voltaic  currents  propa- 
gated in  metallic  wires.  Towards  the  end  of  the  last  century,  and  at  the 
beginning  of  the  present,  many  philosophers  proposed  to  correspond  at  a 
distance  by  means  of  the  effects  produced  by  electrical  machines  when  pro- 
pagated in  insulated  conducting  wires.  In  1811,  Sremmering  invented  a 
telegraph,  in  which  he  used  the  decomposition  of  water  for  giving  signals. 
In  1820,  at  a  time  when  the  electromagnet  was  unknown,  Ampere  proposed 
to  correspond  by  means  of  magnetic  needles,  above  which  a  current  was  sent, 
as  many  wires  and  needles  being  used  as  letters  were  required.  In  1834, 
Gausst  and  Weber  constructed  an  electromagnetic  telegraph,  in  which  a  voltaic- 
current  transmitted  by  a  wire  acted  on  a  magnetised  bar,  the  oscillations  of 
which  under  its  influence  were  observed  by  a  telescope.  They  succeeded  in 
thus  sending  signals  from  the  Observatory  to  the  Physical  Cabinet  in  Got- 
tingen,  a  distance  of  a  mile  and  a  quarter,  and  to  them  belongs  the  honour  of 
having  first  demonstrated  experimentally  the  possibility  of  electrical  com- 
munication at  a  considerable  distance.  In  1837,  Steinheil  in  Munich,  and 
Wheatstone  in  London,  constructed  telegraphs  in  which  several  wires  each 
acted  on  a  single  needle  ;  the  current  in  the  first  case  being  produced  by  an 
electromagnetic  machine,  and  in  the  second  by  a  constant  battery. 

Every  electric  telegraph  consists  essentially  of  three  parts  ;  i,  a  circuit 
consisting  of  a  metallic  connection  between  two  places,  and  an  electromotor 
for  producing  the  current ;  2,  a  communicator  for  sending  the  signals  from 
the  one  station  ;  and,  3,  an  indicator  tor  receiving  them  at  the  other  station. 
The  manner  in  which  these  objects,  more  especially  the  last  two,  are  effected 
can  be  greatly  varied,  and  we  shall  limit  ourselves  to  a  description  of  the 
three  principal  methods. 

One  form  of  electromotor  still  sometimes  used  in  England  is  a  modifica- 


786 


Dynamical  Electricity. 


[883- 


tion  of  Wollaston's  battery.  It  consists  of  a  trough  divided  into  compartments 
in  each  of  which  is  an  amalgamated  zinc  plate  and  a  copper  plate  ;  these 
plates  are  usually  about  4*  inches  in  height  by  3*  in  breadth.  The  compart- 
ments are  filled  with  sand,  which  is  moistened  with,  dilute  sulphuric  acid. 
This  battery  is  inexpensive  and  easily  worked,  only  requiring  from  time  to 
time  the  addition  of  a  little  acid  ;  but  it  has  very  low  electromotive  force 
and  considerable  resistance,  and  when  it  has  been  at  work  for  some  time 
the  effects  of  polarisation  begin  to  be  perceived.  On  the  telegraphs  of  the 

South-Eastern  Railway,  the  platinised 
graphite  (811)  battery,  invented  by  Mr. 
C.  V.  Walker,  is  used  with  success. 
On  circuits  on  which  there  is  constant 
work  some  form  of  UanielPs  battery  is 
used,  and  for  other  circuits  Leclanche's 
cell  is  coming  into  more  extended  use. 
In  France,  Daniell's  battery  is  used  for 
telegraphic  purposes. 

The  connection  between  two  sta- 
tions is  made  by  means  of  galvanised 
iron  wire  suspended  by  porcelain  sup- 
ports (fig.  750),  which  insulate  and  pro- 
tect them  against  the  rain,  either  on  posts  or  against  the  sides  of  buildings. 
In  England  and  other  moist  climates  special  attention  is  required  to  be  paid 
to  the  perfection  of  the  insulation.  In  towns,  wires  covered  with  gutta-percha 
are  placed  in  tubes  laid  in  the  ground.  Submarine  cables,  where  great 
strength  is  required  combined  with  lightness  and  high  conducting  power, 
are  formed  on  the  general  type  of  one  of  the  Atlantic  cables,  a  longitudinal 
view  of  which  is  given  in  fig.  751,  while  fig.  752  represents  a  cross  section 


Fig.  751- 


Fig.  752. 


In  the  centre  is  the  core,  which  is  the  conductor  ;  it  consists  of  seven  copper 
wires,  each  one  i  mm.  in  diameter,  twisted  in  a  spiral  strand  and  covered  with 
several  layers  of  gutta-percha,  between  each  of  which  is  a  coating  of 
Chattertorfs  compound — a  mixture  of  tar,  resin,  and  gutta-percha.  This 
forms  the  insulator  proper,  and  it  should  have  great  resistance  to  the  passage 
of  electricity,  combined  with  low  specific  inductive  capacity  (748).  Round 
the  insulator  is  a  coating  of  hemp,  and  on  the  outside  is  wound  spirally  a 
protecting  sheath  of  steel  wire,  each  of  which  is  spun  round  with  hemp. 

At  the  station  which  sends  the  -despatch,  the  line  is  connected  with  the 
positive  pole  of  a  battery,  the  current  passes  by  the  line  to  the  other  station, 
and  if  there  were  a  second  return  line,  it  would  traverse  it  in  the  opposite 


-884]      WJicatstone's  and  Cooke V Single  Needle  Telegraph.       787 

direction  to  return  to  the  negative  pole.  In  1837,  Steinheil  made  the  very 
important  discovery  that  the  earth  might  be  used  for  the  return  conductor, 
thereby  saving  the  expense  of  the  second  line.  For  this  purpose  the  end  of 
the  conductor  at  the  one  station,  and  the  negative  pole  of  the  battery  at  the 
other,  are  connected  with  large  copper  plates,  which  are  sunk  to  some  deptlj 
in  the  ground.  The  action  is  then  the  same  as  if  the  earth  acted  as  a  return 
wire.  The  earth  is,  indeed,  far  superior  to  a  return  wire ;  for  the  added 
resistance  of  such  a  wire  would  be  considerable,  whereas  the  resistance  of 
the  earth  beyond  a  short  distance  is  absolutely  nil.  The  earth  really  dissi- 
pates the  electricity,  and  does  not  actually  return  the  same  current  to  the 
battery. 

884.  Wheatstone's  and  Cooke's  single  needle  telegraph. — This  con- 
sists essentially  of  a  vertical  multiplier  (821)  with  an  astatic  needle,  the 
arrangement  of  which  is 
seen  in  fig.  754,  while  fig. 
753  gives  a  front  view  of 
the  case  in  which  the  ap- 
paratus is  placed.  A  (fig. 
754)  is  the  bobbin,  con- 
sisting of  about  400  feet 
of  fine  copper  wire,  wound 
in  a  frame  in  two  con- 
nected coils.  Instead  of 
an  astatic  needle,  Mr. 
Walker  has  found  it  ad- 
vantageous to  use  a  single 
needle  formed  of  several 
pieces  of  very  thin  steel 
strongly  magnetised ;  it 
works  with  the  bobbin, 
and  a  light  index  joined 
to  it  by  a  horizontal  axis 
indicates  the  motion  of 
the  needle  on  the  dial. 

The  signs  are  made 
by  transmitting  the  cur- 
rent in  different  directions 
through  the  multiplier,  by 
which  the  needle  is  deflec- 
ted either  to  the  right  or 
left,  according  to  the  will 
of  the  operator.  The  instrument  by  which  this  is  effected  is  a  commutator 
or  key,  G;  its  construction  is  shown  in  fig.  754,  while  fig.  755  shows  on  a 
large  scale  how  two  stations  are  connected.  It  consists  of  a  cylinder  of 
boxwood  with  a  handle,  which  projects  in  front  of  the  case  (fig.  753).  On 
its  circumference  parallel  to  the  axis  are  seven  brass  strips  (fig.  755),  the 
spaces  between  which  are  insulated  by  ivory ;  these  strips  are  connected 
at  the  end  by  metallic  wires,  also  insulated  from  each  other,  in  the  following 
manner  :  a  with  b  and  c,f  with  </,  and  e  with  g.  Four  springs  press  against 


Fig.  753- 


;88 


Dynamical  Electricity. 


[884- 


the  cylinder  ;  x  and  y  are  connected  with  the  poles  of  the  battery,  m   with 
the  earth  plate,  and  n  with  one  end  of  the  multiplier,  N. 

When  not  at  work  the  cylin- 
der and  the  handle  are  in  a 
vertical  position,  as  seen  on  the 
left  of  the  diagram.  The  circuit 
is  thus  open,  for  the  pole  springs, 
x  and  y,  are  not  connected  with 
the  metal  of  the  commutator. 
But  if,  as  in  the  figure  on  the 
right,  the  key  is  turned  to  the 
righK,  the  battery  is  brought  into 
the  circuit,  and  the  current 
passes  in  the  following  direc- 
tion :  +  pole  x'a'b'n'Wq'N) 
conductor  qp^&nacufiLp,  earth 
P'}L'm'e'gry',  —  pole.  The  coils  N 
and  N'  are  so  arranged  that  by 
the  action  of  the  current  the  mo- 
tion of  the  needle  corresponds  to 
the  motion  of  the  handle.  By 
turning  the  handle  to  the  left  the 
current  would  have  the  following 
direction  :  +  pole  x'dffm'TL'p', 
earth  p^Lmcabn^Aq,  conductor 
p'q'^A.'rib'a'y',  —  pole,  and  thus  the 
needle  would  be  deflected  in  the 
opposite  direction. 
Fig.  754-  The  signs  are  given  by  differ- 

ently combined  deflections  of  the 

needle,  as  represented  in  the  alphabet  on  the  dial  (fig.  753).  \  denotes  a 
deflection  of  the  upper  end  of  the  needle  to  the  left,  and  /  a  deflection  to 
the  right ;  I,  for  instance,  is  indicated  by  two  deflections  to  the  left,  and  M 
by  two  to  the  right.  Some  of  the  marks  on  the  alphabet  are  only  half  as 
long  as  the  others  ;  this  indicates  that  the  shortest  of  the  connected  marks 
must  first  be  signalled.  Thus,  D  is  expressed  by  right-left-left,  and  C  by 
right-left-right-left,  etc. 

These  signs  are  somewhat  complicated  and  require  great  practice  ; 
usually  not  more  than  12  to  20  words  can  be  sent  in  a  minute.  The  single 
needle  telegraph  was  formerly  sometimes  replaced  by  the  double  needle  one, 
which  is  constructed  on  the  same  principle,  but  there  are  two  needles  and 
two  wires  instead  of  one. 

885.  Dial  telegraphs. — Of  these  many  kinds  exist.  Figs.  757  and  758 
represent  a  lecture-model  of  one  form,  constructed  by  Froment,  and 
which  well  serves  to  illustrate  the  principle.  It  consists  of  two  parts  :  the 
manipulator  for  transmitting  signals  (fig.  757),  and  the  indicator  (fig.  758) 
for  receiving  them.  The  first  apparatus  is  connected  with  a  battery,  Q,  and 
the  two  apparatus  are  in  communication  by  means  of  metal  wires,  one  of 
which,  AOD  (fig.  757),  goes  from  the  departure  to  the  arrival  station,  and 


-885] 


Dial  Telegraphs. 


789 


the  other,  HKLI  (fig.  758),  from  the  arrival  to  the  departure.     In  practice, 
the  latter  is  replaced  by  the  earth  circuit.    Each  apparatus  is  furnished  with 


Fig-  755- 


a  dial  with  25  of  the  letters  of  the  alphabet,  on  which  a  needle  moves. 
The  needle  at  the  departure  station  is  moved  by  hand,  that  of  the  arrival 
by  electricity. 

The  path  of  the  current  and  its  effects  are  as  follows  :  from  the  battery 
it  passes  through  a  copper  wire,  A  (fig.  757),  into  a  brass  spring,  N, 
which  presses  against  a  metal  wheel,  R,  then  by  a 
second  spring,  M,  into  the  wire  O,  which  joins  the 
other  station.  Thence  the  current  passes  into  the 
bobbin  of  an  electromagnet,  ^,  not  fully  shown  in 
fig.  758,  but  of  which  fig.  756  represents  a  section, 
showing  the  front  of  the  apparatus.  This  electro- 
magnet is  fixed  horizontally  at  one  end,  and  at  the 
other  it  attracts  an  armature  of  soft  iron,  a,  which 
forms  part  of  a  bent  lever,  movable  about  its  axis, 
^,  while  a  spring,  r,  attracts  the  lever  in  the  oppo- 
site direction. 

When  the  current  passes,  the  electromagnet 
attracts  the  lever,  «C,  which  by  a  rod,  /,  acts  on  a 
second  lever,  d,  fixed  to  a  horizontal  axis,  itself  con- 


Fig.  756. 


nected  with  a  fork,  F.  When  the  current  is  broken  the  spring  r  draws  the 
lever  <zC,  and  therewith  all  the  connected  pieces  ;  a  backward  and  forward 
motion  is  produced,  which  is  communicated  to  the  fork  F  ;  this  transmits 
it  to  a  toothed  wheel,  G,  on  the  axis  of  which  is  the  needle.  From  the 


790 


Dynamical  Electricity. 


[885- 


arrangement  of  its  teeth,  the  wheel  G  is  always  moved  in  the  same  direction 
by  the  fork. 


To  explain  the  intermittent  action  of  the  magnet,  we  must  refer  to  rig. 
757-  The  toothed  wheel,  R,  has  26  teeth,  of  which  25  correspond  to  letters 
of  the  alphabet,  and  the  last  to  the  interval  reserved  between  the  letters  Z 


-886]  Morses  Telegraph.  791 

and  A.  When  holding  the  knob  P  in  the  hand  the  wheel  R  is  turned,  the  end 
of  the  plate  N  from  its  curvature  is  always  in  contact  with  the  teeth  ;  the 
plate  M,  on  the  contrary,  terminates  in  a  catch  cut  so  that  contact  is  alter- 
nately made  and  broken.  Hence,  the  connections  with  the  battery  having 
been  made,  if  the  needle  P  is  advanced  through  four  letters,  for  example,  the 
current  passes  four  times  in  N  and  M,  and  is  four  times  broken.  The  electro- 
magnet of  the  arrival  station  will  then  have  attracted  four  times,  and  have 
ceased  to  do  so  four  times.  Lastly,  the  wheel  G  will  have  turned  by  four 
teeth,  and  as  each  tooth  corresponds  to  a  letter,  the  needle  of  the  arrival 
station  will  have  passed  through  exactly  the  same  number  of  letters  as  that 
of  the  departure  station.  The  piece  S,  represented  in  the  two  figures,  is  a 
copper  plate,  movable  on  a  hinge,  which  serves  to  make  or  to  break  the 
current  at  will. 

From  this  explanation  it  will  be  readily  intelligible  how  communications 
are  made  between  different  places.  Suppose,  for  example,  that  the  first  ap- 
paratus being  at  London  and  the  second  at  Brighton,  there  being  metallic 
connection  between  the  two  towns,  it  is  desired  to  send  the  word  signal  to 
the  latter  town  :  as  the  needles  correspond  on  each  apparatus  to  the  interval 
retained  between  Z  and  A,  the  person  sending  the  dispatch  moves  the 
needle  P  to  the  letter  S,  where  it  stops  for  a  very  short  time  ;  as  the  needle 
in  Brighton  accurately  reproduces  the  motion  of  the  London  needle,  it  stops 
at  the  same  letter,  and  the  person  who  receives  the  despatch  notes  this  letter. 
The  one  at  London,  always  continuing  to  turn  in  the  same  direction,  stops 
.at  the  letter  I,  the  second  needle  immediately  stops  at  the  same  letter;  and 
continuing  in  the  same  manner  with  the  letters  G,  N,  A,  L,  all  the  \vord  is 
soon  transmitted  to  Brighton.  The  attention  of  the  observer  at  the  arrival 
station  is  attracted  by  means  of  an  electric  alarum.  Each  station  must 
further  be  provided  with  the  two  apparatus  (figs.  757  and  758),  without  which 
it  would  be  impossible  to  answer. 

886.  Morse's  telegraph. — The  telegraphs  hitherto  described  leave  no 
trace  of  the  despatches  sent,  and  if  any  errors  have  been  made  in  copying 
the  signals  there  is  no  means  of  remedying  them.  These  inconveniences 
are  not  met  with  in  the  case  of  the  writing  telegraphs,  in  which  the  signs 
themselves  are  printed  on  a  strip  of  paper  at  the  time  at  which  they  are 
transmitted. 

Of  the  numerous  printing  and  writing  telegraphs  which  have  been  devised 
that  of  Morse,  first  brought  into  use  in  North  America,  is  best  known.  It 
has  been  almost  universally  adopted  on  the  Continent.  In  this  instrument 
there  are  three  distinct  parts  :  the  indicator,  the  communicator,  and  the 
relay,  figs.  759,  760,  and  761  represent  these  apparatus. 

Indicator.  We  will  first  describe  the  indicator  (fig.  759),  leaving  out  of 
sight  for  the  moment  the  accessory  pieces,  G  and  T,  placed  on  the  right  ot 
the  figure.  The  current  which  enters  the  indicator  by  the  wire,  C,  passes  into 
an  electromagnet  E,  which,  when  the  current  is  closed,  attracts  an  armature 
of  soft  iron,  A,  fixed  at  the  end  of  a  horizontal  lever  movable  about  an  axis,  x  • 
when  the  current  is  open  the  lever  is  raised  by  a  spring,  r.  By  means  of  two 
screws,  m  and  v,  the  amplitude  of  the  oscillations  is  regulated.  At  the 
other  end  of  the  lever  there  is  a  pencil,  o,  which  writes  the  signals.  For  this 
purpose  a  long  band  of  strong  paper,  pp,  rolled  round  a  drum,  R,  passes 


792  Dynamical  Electricity  [886- 

between  two  copper  rollers  with  a  rough  surface,  */,  and  turning  in  contrary 
directions.  Drawn  in  the  direction  of  the  arrows,  the  band  of  paper  be- 
comes rolled  on  a  second  drum,  Q,  which  is  turned  by  hand.  A  clockwork 
motion  placed  in  the  box,  BD,  works  the  rollers,  between  which  the  band  of 
paper  passes. 

The  paper  being  thus  set  in  motion,  whenever  the  electromagnet  works, 
the  point  o  strikes  the  paper,  and,  without  perforating  it,  produces  an  inden- 
tation, the  shape  of  which  depends  on  the  time  during  which  the  point  is  in 
contact  with  the  paper.  If  it  only  strikes  it  instantaneously,  it  makes  &dot 
(-)  or  short  stroke ;  but  if  the  contact  has  any  duration,  a  dash  ( — )  of  corre- 
sponding length  is  produced.  Hence,  by  varying  the  length  of  contact  of 


Fig.  759- 

the  transmitting  key  at  one  station,  a  combination  of  dots  and  dashes  may 
be  produced  at  another  station,  and  it  is  only  necessary  to  give  a  definite 
meaning  to  these  combinations. 

The  same  telegraphic  alphabet  is  now  universally  used  wherever  tele- 
graphic communication  exists  ;  and  the  signals  for  the  single  needle  instru- 
ment (fig.  759)  as  well  as  those  used  for  printing  have  been  modified,  so  that 
they  now  correspond  to  each  other.  Thus  a  beat  of  the  top  of  the  needle  to 
the  left  \  is  equivalent  to  a  dot :  and  a  beat  to  the  right  /  to  a  dash.  The 
following  figure  gives  the  alphabet. 

The  flag  signals  used  in  military  operations  are  similarly  used.  A  swing 
of  the  flag  from  its  upright  vertical  position  to  the  right  or  left  has  the  same 
meaning  as  the  corresponding  motion  of  the  top  end  of  the  needle.  So  too 
long  or  short  obscurations  of  the  lime  light  used  in  signalling  by  night,  or  of 
the  heliograph  (523)  correspond  to  dashes  and  dots. 


-886] 


Morses  Telegraph. 


793 


SC;CLE 

S1XGKE 

PRINTING. 

XJXDLE. 

PRINTING. 

NEEDLE. 

A      

y 

N       

A 

B      

Axv 

0      

III 

C      

AA 

P      

Jk 

D      — 

Ax 

Q       

IIJ 

E      - 

\ 

R 

vA 

F      

xxA 

S 

NXS 

G     

/A 

T        — 

/ 

H     

XNXX 

U       

xx/ 

I      -- 

^ 

V        

xxx/ 

j    

X/// 

y       

Jl 

K      

u 

X       

Ax/ 

L      

J« 

Y       

A// 

M     

// 

Z       

/Av 

Communicator  or  key.  This  consists  of  a  small  mahogany  base,  which 
acts  as  support  for  a  metallic  lever  ab  (fig,  760),  movable  in  its  middle  on  a 
horizontal  axis.  The  extremity  a  of  this  lever  is  always  pressed  upwards  by 
a  spring  beneath,  so  that  it  is  only  by  pressing  with  the  finger  on  the  key  B 
that  the  lever  sinks  and 
strikes  the  button  or. 
Round  the  base  there 
are  three  binding  screws; 
one  connected  with  the 
wire  P,  which  comes 
from  the  positive  pole  of 
the  battery  ;  the  second 
connected  with  L,  the 
line  wire  ;  and  the  third 
with  the  wire  A,  which 
passes  to  the  indicator, 
for  of  course  two  places  in  communication  are  each  provided  wfth  an  indi- 
cator and  communicator. 

These  details  known,  there  are  two  cases  to  be  considered,  i.  The  com- 
municator is  arranged  so  as  to  receive  a  message  from  a  distant  station  ; 
the  end  b  is  then  depressed,  as  represented  in  the  drawing,  so  that  the 
current  which  arrives  by  the  line  wire  L,  and  ascends  in  the  metallic  piece 
m,  redescends  in  the  wire  A,  which  leads  it  to  the  indicator  of  the  post 
at  which  the  apparatus  is  placed.  2.  A  message  is  to  be  transmitted  ;  in 
this  case  the  key  B  is  pressed  so  that  the  lever  comes  in  contact  with  the 

M    M 


Fig.  760. 


794  Dynamical  Electricity.  [886- 

button  x.  The  current  of  the  local  battery,  which  comes  by  the  wire  P^ 
ascending  then  in  the  lever,  redescends  by  m  and  joins  the  wire  L,  which 
conducts  it  to  the  station  to  which  the  despatch  is  addressed.  According  to 
the  length  of  time  during  which  B  is  pressed,  a  dot  or  a  line  is  produced  in 
the  receiver  to  which  the  current  proceeds. 

Relay.  In  describing  the  receiver  we  have  assumed  that  the  current  of 
the  line  coming  by  the  wire  C  (fig.  759)  entered  directly  into  the  electro- 
magnet, and  worked  the  armature  A,  producing  a  despatch  ;  but  when  the 
current  has  traversed  a  distance  of  a  few  miles  its  intensity  has  diminished 
so  greatly  that  it  cannot  act  upon  the  electromagnet  with  sufficient  force  to 
print  a  despatch.  Hence  it  is  necessary  to  have  recourse  to  a  relay — that  is, 
to  an  auxiliary  electromagnet  which  is  still  traversed  by  the  current  of  the 
line,  but  which  serves  to  introduce  into  the  communicator  the  current  of  a 
local  battery  of  4  or  5  elements  placed  at  the  station,  and  which  is  only  used 
to  print  the  signals  transmitted  by  the  wire. 

For  this  purpose  the  current  entering  the  relay  by  the  binding  screw,  L 
(fig.  761),  passes  into  an  electromagnet,  E,  whence  it  passes  into  the  earth 
by  the  binding  screw  T.  Now,  each  time  that  the  current  of  the  line  passes 

into  the  relay,  the 
electromagnet  at- 
tracts an  armature, 
A,  fixed  at  the  bot- 
tom of  a  vertical 
lever,  /,  which  os- 
cillates about  a 
horizontal  axis. 

At  each  oscil- 
lation the  top  of 
the  lever  p  strikes 
against  a  button  «, 
and  at  this  moment 
the  current  of  the 

Fig.  76i.  local  battery  which 

enters  by  the  bind- 
ing screw,  r,  ascends  the  column  ;;/,  passes  into  the  lever/,  descends  by  the  rod 
0,  which  transmits  it  to  the  screw  Z  :  thence  it  enters  the  electromagnet  of  the 
indicator,  whence  it  emerges  by  the  wire  Z,  to  return  to  the  local  battery  from 
which  it  started.  Then,  when  the  current  of  the  line  is  open,  the  electro- 
magnet of  the  relay  does  not  act,  and  the  lever/,  drawn  by  a  spring  r,  leaves 
the  button  «,  as  shown  in  the  drawing,  and  the  local  current  no  longer 
passes.  Thus  the  relay  transmits  to  the  indicator  exactly  the  same  phases  of 
passage  and  intermittence  as  those  effected  by  the  manipulator  in  the  post 
which  sends  the  despatch. 

With  a  general  battery  of  25  Daniell's  elements  the  current  is  strong 
enough  at  upwards  of  90  miles  from  its  starting-point  to  work  a  relay.  For 
a  longer  distance  a  new  current  must  be  taken,  as  will  be  seen  in  the  para- 
graph on  the  change  of  current  (vide  infra}. 

•  Working  of  the  three  apparatus.  The  three  principal  pieces  of  Morse's 
apparatus  being  thus  known,  the  following  is  the  actual  path  of  the  current. 


-  887]  CowpeSs  Writing  Telegraph.  795 

The  current  of  the  line  coming  by  the  wire  L  (fig.  759)  passes  at  first  to 
the  piece  T  intended  to  serve  as  lightning  conductor,  when,  from  the  influence 
of  atmospheric  electricity,  in  time  of  storm  the  conducting  wires  become 
charged  with  so  much  electricity  as  to  give  dangerous  sparks.  This  appara- 
tus consists  of  two  copper  discs,  d  and  /  provided  with  teeth  on  the  sides 
opposite  each  other,  but  not  touching.  The  disc  d  is  connected  with  the 
earth  by  a  metal  plate  at  the  back  of  the  stand  which  supports  this  light- 
ning conductor,  while  the  disc/ is  in  the  current.  The  latter  coming  by  the 
line  L  enters  the  lightning  conductor  by  the  binding  screw  fixed  at  the  lower 
part  of  the  stand  on  the  left ;  then  rises  to  a  commutator,  «,  which  conducts 
it  to  a  button,  <:,  whence  it  reaches  the  disc /by  a  metal  plate  at  the  back  of 
the  stand  ;  in  case  a  lightning  discharge  should  pass  along  the  wire,  it  would 
now  act  inductively  on  the  disc  d,  and  emerge  by  the  points  without  danger 
to  those  about  the  apparatus.  Moreover,  from  the  disc/  the  current  passes 
into  a  very  fine  iron  wire  insulated  on  a  tube  e.  As  the  wire  is  melted,  when 
the  discharge  is  too  intense,  the  electricity  does  not  pass  into  the  apparatus, 
which  still  further  removes  any  danger. 

Lastly,  the  current  proceeds  from  the  foot  of  the  support  to  a  screw  on 
the  right,  which  conducts  it  to  a  small  galvanometer,  G,  serving  to  indicate 
by  the  deflection  of  the  needle  whether  the  current  passes.  From  this  gal- 
vanometer the  current  proceeds  to  a  commutator  (fig.  760),  which  it  enters 
at  L,  whence  it  emerges  at  A  to  go  to  the  relay  (fig.  761).  Entering  this  at 
L,  it  works  the  electromagnet,  and  establishes  the  communication  necessary 
for  the  passage  of  the  current  of  the  local  battery,  as  has  been  said  in 
speaking  of  the  relay. 

L'hange  of  current.  To  complete  this  description  of  Morse's  apparatus  it 
must  be  observed  that  in  general  the  current  which  arrives  at  L  after  having 
traversed  several  miles,  has  not  sufficient  force  to  register  the  despatch,  nor 
to  proceed  to  a  new  distant  point.  Hence  in  each  telegraphic  station  a 
new  current  must  be  taken,  that  of  the  postal  battery,  which  consists  of  20  to 
30  DanielFs  elements,  and  is  not  identical  with  the  local  battery. 

This  new  current  enters  at  P  (fig.  759),  reaches  a  binding  screw  which 
conducts  it  to  the  column  H,  and  thence  only  proceeds  further  when  the 
armature  A  sinks.  A  small  contact  placed  under  the  lever  touches  then  the 
button  v  ;  the  current  proceeds  from  the  column  H  to  the  metallic  mass 
BD,  whence  by  a  binding  screw  and  a  wire,  not  represented  in  the  figure,  it 
reaches  lastly  the  wire  of  the  line,  which  sends  it  to  the  following  post,  and 
so  on  from  one  point  to  another. 

887.  Cowper'm  Writing  Telegrraph. — This  very  remarkable  invention  is 
a  true  telegraph,  in  that  it  faithfully  reproduces  at  a  distance  an  exact  facsimile 
of  a  person's  handwriting. 

The  following  is  a  general  idea  of  the  principle  of  the  instrument. 

Two  line  wires  are  required  which  are  severally  connected  at  the  re- 
ceiving station  with  two  galvanometers,  whose  coils  are  at  right  angles  to 
each  other.  At  the  sending  station  is  a  vertical  pencil  with  two  light  rods, 
jointed  tQ  it  at  right  angles  to  each  other.  One  of  these  contact  rods  guides 
a  contact  piece  which  is  connected  by  a  wire  with  one  pole  of  a  battery,  the 
other  pole  of  which  is  to  earth.  This  contact  piece  slides  over  the  edges  of 
a  series  of  contact  plates  insulated  from  each  other,  between  each  of  which 

M  M  2 


796  Dynamical  Electricity.  [887- 

a  special  resistance  is  interposed,  and  the  last  of  the  contact  plates  is 
connected  with  one  line  wire.  The  other  contact  piece  slides  over  a  second 
series  of  such  plates  connected  with  the  other  line  wire. 

Let  us  consider  one  contact  alone  ;  as  it  moves  over  the  contact  plates  in 
one  direction  or  the  other,  it  brings  less  or  more  resistance  into  the  circuit, 
and  thereby  alters  the  strength  of  the  current.  The  effect  of  this  is  that  the 
needle  of  the  corresponding  galvanometer  is  less  or  more  deflected.  Now  the 
end  of  this  needle  is  connected  by  a  light  thread  with  a  receiving  pen,  which 
is  a  capillary  tube  full  of  ink.  An  oscillation  of  the  needle  would  produce  an 
up  and  down  motion  of  the  pen,  and  if  simultaneously  a  band  of  paper  passed 
under  the  pen,  being  moved  regularly  by  clockwork,  there  would  be  produced 
on  it  a  series  of  up  and  down  strokes.  A  corresponding  effect  would  be  pro- 
duced by  the  action  of  the  needle  of  the  other  galvanometer,  except  that  its 
strokes  would  be  backwards  and  forwards  instead  of  up  and  down. 

Now  the  action  of  the  writing  pen  is  that  it  varies  simultaneously  the 
strengths  of  the  two  currents,  and  they  produce  a  motion  of  the  receiving 
pen  which  is  compounded  of  the  two  movements  described  above,  and 
which  is  an  exact  reproduction,  on  a  smaller  scale,  of  the  original  motion. 
The  following  line  is  a  facsimile. 

— 

Both  the  paper  written  in  pencil  at  the  sending  station  and  that  written 
in  ink  at  the  receiving  station  move  along  as  the  writing  proceeds,  and  the 
messages  have  only  to  be  cut  off  from  time  to  time. 

Experiments  made  with  this  instrument  show  that  it  will  write  through 
resistances  of  36  miles. 

888.  Induction  in  telegraph  cables. — In  the  earliest  experiments  on  the 
use  of  insulated  subterranean  wires  for  telegraphic  communication  it  was 
iound  that  difficulties  occurred  in  their  use  which  were  not  experienced  with 
overland  wires.  This  did  not  arise  from  defective  insulation,  for  the  better 
the  insulation  the  greater  the  difficulty.  It  was  suspected  by  Siemens  and 
others  that  the  retardation  was  due  to  statical  induction,  taking  place  be- 
tween the  inner  wire  through  the  insulator  and  the  external  moisture  ;  and  that 
this  was  the  case  Faraday  proved  by  the  following  experiments  among  others. 
A  length  of  about  100  miles  of  gutta-percha-covered  copper  wire  was  im- 
mersed in  water,  the  ends  being  led  into  the  chamber  of  observation.  When 
the  pole  of  a  battery  containing  a  large  number  of  cells  was  momentarily 
connected  with  one  end  of  the  wire,  the  other  end  being  insulated,  and  a 
person  simultaneously  touched  the  wire  and  the  earth  contact,  he  obtained  a 
violent  shock. 

When  the  wire,  after  being  in  momentary  contact  with  the  battery,  was 
placed  in  connection  with  a  galvanometer,  a  considerable  deflection  was 
observed  ;  there  was  a  feebler  one  3  or  4  minutes  after,  and  even  as  long  as 
20  or  30  minutes  afterwards. 

When  the  insulated  galvanometer  was  permanently  connected  with  one 
end  of  the  wire,  and  then  the  free  end  of  the  galvanometer  wire  joined  to  the 
pole  of  the  battery,  a  rush  of  electricity  through  the  galvanometer  into  the 
wire  was  perceived.  This  speedily  diminished  and  the  needle  ultimately 


-889]  Syphon  Recorder.  797 

came  to  rest.  When  the  galvanometer  was  detached  from  the  battery  and 
put  to  earth,  the  electricity  flowed  as  rapidly  out  of  the  wire,  and  the  needle 
was  momentarily  deflected  in  the  opposite  direction. 

These  phenomena  are  not  difficult  to  explain.  The  wire  with  its  thin 
insulating  coating  of  gutta-percha  becomes  statically  charged  with  electricity 
from  the  battery.  The  coating  of  gutta-percha  through  which  the  inductive 
action  takes  place  is  only  ±  °f  an  mcn  m  thickness,  and  the  extent  of  the 
coatings  is  very  great.  The  surface  of  the  copper  wire  amounts  to  8,300 
square  feet,  and  that  of  the  outside  coating  is  four  times  as  much.  The 
potential  can  only  be  as  great  as  that  of  the  battery,  but  from  the  enormous 
surface  the  capacity,  and  therefore  the  quantity,  is  very  great.  Thus  the 
wires,  after  being  detached  from  the  battery,  showed  all  the  actions  of  a 
powerful  electric  battery.  These  effects  take  place  to  a  far  less  extent  with 
wires  in  air,  for  the  external  coating  is  wanting,  or  at  all  events  is  so  distant 
that  induction  and  charge  are  very  small. 

Hence  the  difficulty  in  submarine  telegraphy.  The  electricity  which 
enters  the  insulating  wire  must  first  be  used  in  charging  the  large  Leyden 
jar  which  it  constitutes,  and  only  after  this  has  happened  can  the  current 
reach  the  distant  end  of  the  circuit.  The  current  begins  later  at  the  distant 
end,  and  ceases  sooner.  If  the  electrical  currents  follow  too  rapidly,  an 
uninterrupted  current  will  appear  at  the  other  end,  which  indicates  small 
differences  in  strength,  but  not  with  sufficient  clearness,  differences  in  dura- 
tion or  direction.  Hence  in  submarine  wires  the  signals  must  be  slower 
than  in  air  wires  to  obtain  clear  indications.  By  the  use  of  alternating 
currents — that  is,  of  currents  which  are  alternately  positive  and  negative — 
their  disturbing  influences  may  be  materially  lessened,  and  communication 
be  accelerated  and  made  more  certain,  but  they  can  never  be  entirely 
obviated. 

In  the  Atlantic  Cable,  instruments  on  the  principle  of  Thomson's  reflect- 
ing galvanometer  (822),  are  used  for  the  reception  of  signals  ;  the  motions 
of  the  spot  of  light  to  the  right  and  left  forming  the  basis  of  the  alphabet. 

889.  Sypbon  Recorder. — Sir  W.  Thomson  has  invented  an  extremely 
ingenious  instrument  called  the  syphon  recorder,  by  which  the  very  feeble 
signals  transmitted  through  long  lengths  of  submarine  cables  are  observed 
and  also  recorded. 

Its  construction  is  somewhat  complicated,  but  the  essential  features  are 
as  follows.  A  light  flat  coil  of  insulated  wire,  which  is  connected  with  the 
line  wire,  is  suspended  by  a  bifilar  suspension  between  the 
two  poles  of  a  powerful  horseshoe  magnet.  When  no  current 
passes  its  plane  is  in  the  right  line  joining  the  poles.  When 
a  current  is  passed,  this  coil,  becoming  thereby  a  magnet,  is 
deflected  either  to  the  right  or  the  left,  according  to  the  direction 
of  the  current.  It  is,  in  short,  the  reverse  of  the  arrangement 
in  (822),  for  here  the  coil  is  movable  and  the  magnets  fixed  ; 
there  the  magnet  is  movable,  and  the  coil  fixed. 

A  very  light  capillary  glass  tube,  shaped  as  represented  in 
fig.  762,  dips  with  its  short  end  in  a  reservoir  of  ink,  while  the  other  end  is 
in  front  of  a  paper  ribbon,  which  is  moved  along  at  a  uniform  rate,  like  a 
ribbon  in  a  Morse's  recorder.     When  this  ink  is  electrified,  it  spurts  out  in  a 


Dynamical  Electricity. 


[889- 


continuous  series  of  fine  drops  against  the  paper,  and  marks  on  it  a  straight 
line  so  long  as  no  current  passes  in  the  coil.  This  syphon  is,  however,  con- 
nected by  a  system  of  silk  threads  with  the  coil,  and  according  as  this  is 
deflected  either  to  the  right  or  the  left  the  end  of  the  syphon  is  deflected 
too,  and  accordingly  traces  a  wavy  line  on  the  paper  which  represents 
deflections  right  or  left  of  the  central  line,  and  are  in  short  the  Morse  signals. 

The  electrification  of  the  ink  is  effected  by  a  small  electrostatic  in- 
duction machine  ;  this  is  worked  by  clockwork,  which  ;at  the  same  time  pays 
out  the  paper  ribbon. 

890.  Duplex  telegraphy. — By  this  is  meant  a  system  of  telegraphy  by 
which  messages  may  be  simultaneously  sent  in  opposite  directions  on  one  and 
the  same  wire,  whereby  the  working  capacity  of  a  line  is  practically  doubled. 

Several  plans  have  been  devised  for  accomplishing  this  very  important 
improvement ;  no  more  can  here  be  attempted  than  to  give  a  general  account 
of  the  principle  of  the  method  in  one  case. 

Let  m,  fig.  763,  represent  the  electromagnet  of  a  Morse's  instrument 
which  is  wound  round  with  two  equal  coils  in  opposite  directions  ;  these  coils 


Fig.  763. 

are  represented  by  the  full  and  dotted  lines,  and  one  of  them,  which  may  be 
called  the  line  coil,  is  joined  to  the  line  LL',  which  connects  the  two  stations. 
The  other  coil,  that  represented  by  the  dotted  line,  which  may  be  called  the 
equating  coil,  is  in  connection  with  the  earth  at  E  by  means  of  an  adjustable 
resistance,  or  artificial  line  R.  By  this  means  the  resistance  of  the  branch 
aRE  may  be  made  equal  to  that  of  the  branch  aLL'a'.  The  battery  b 
has  one  pole  to  earth  at  E,  and  the  other  pole,  by  means  of  a  make-and- 
break  key  c,  can  be  connected  at  a,  where  the  two  oppositely  wound  coils 
bifurcate.  The  back  contact  of  the  key  is  also  connected  with  earth. 

The  station  at  B  is  arranged  in  a  similar  manner,  as  is  represented  by 
corresponding  letters  with  affixes. 

Now  when  B  depresses  his  key  and  sends  a  current  into  the  line,  inasmuch 
as  the  electromagnet  of  his  instrument  is  wound  with  equal  coils  in  opposite 
directions,  the  armature  is  not  attracted,  for  the  core  is  not  magnetised 
because  the  currents  in  the  two  coils  counteract  one  another.  Thus,  although 


-892]  Bains  Electro-diemical  Telegraph.  799 

a  current  passes  from  B,  there  is  no  indication  of  it  in  his  own  instrument— 
a  condition  essential  in  all  systems  of  duplex  telegraphy. 

But  with  regard  to  the  effect  on  A,  there  are  two  cases  according  as  he  is 
or  is  not  sending  a  message  at  the  same  time.  If  A's  key  is  not  down,  then 
the  current  will  circulate  round  the  core  of  the  electromagnet  and  will 
reach  the  earth  by  the  path  L  ac  E  ;  the  core  will  therefore  become  magnet- 
ised, the  armature  attracted,  and  a  signal  be  produced  in  the  ordinary  way. 

If,  however,  at  the  moment  at  which  B  has  his  key  down,  A  also  depresses 
his,  then  it  will  be  seen  that,  as  currents  are  sent  in  opposite  directions  from 
both  A  and  B,  they  neutralise  one  another,  no  current  passes  in  the  line 
a  LL'  a' ;  it  is,  as  it  were,  blocked.  But  though  no  current  passes  in  the  line 
coil,  a  current  does  pass  at  each  station  to  earth,  through  the  equating  coil, 
which  being  no  longer  counterbalanced  by  any  opposite  current  in  the  line 
coil,  magnetises  the  core  of  the  electromagnet,  which  thus  attracts  the  arma- 
ture and  produces  a  signal. 

We  have  here  supposed  that  A  and  B  both  send,  for  instance,  the  same 
currents  to  line  ;  the  final  effect  is  not  different  if  they  send  opposite  currents 
at  the  same  time.  For  then,  as  they  neutralise  each  other  in  the  line  LL', 
the  effect  is  the  same  as  if  the  resistance  of  the  line  were  diminished. 
More  electricity  flows  at  line  from  each  station  through  the  line  coil  being 
no  longer  balanced  by  the  equating  coil ;  the  current  of  the  line  coil  prepon- 
derates and  then  works  the  electromagnet. 

Hence  in  both  these  cases,  each  station,  so  to  speak,  produces  the  signal 
which  the  other  one  wishes  to  send. 

Other  methods  of  duplex  telegraphy  are  based  on  Wheatstone's  Bridge, 
and  on  the  principle  of  leakage,  but  for  these,  as  well  as  for  quadruple* 
telegraphy,  special  manuals  must  be  consulted. 

891.  Earth  current. — In  long  telegraph   circuits  more  or  less  powerful 
currents  are  produced,  even  when  the  battery  is  not  at  work.     This  arises 
from  a  difference  of  potential  being  established  in  the  earth  at  the  two  places 
between  which  the  communication  is  established.     These  currents  are  some- 
times in  one  direction  and  sometimes  in  another,  and  are  at  times  so  power- 
ful and  irregular  as  quite  to  interfere  with  the  working  of  the  lines.     Lines 
running    NE    and    SW  are  most    frequently  affected;  lines  running    N\V 
and  SE  are  less  so  and  the  currents  are  far  weaker. 

These  currents  do  not  seem  to  be  due  to  atmospheric  electricity,  for  they 
cease  if  a  wire  be  disconnected  at  one  of  its  ends,  and  they  appear  in  under- 
ground wires. 

892.  Bain's  electro-chemical  telegraph. —  If  a  strip  of  paper  be  soaked 
in  an  aqueous  solution  of  ferrocyanide  of  potassium  and  connected  with  the 
negative  pole  of  a  battery,  and  if  the  other  face  be  touched  with  a  steel 
pointer  connected  with  the  positive  pole,  a  blue  mark  due  to  the  formation 
of  some  Prussian  blue  will  be  formed  about  the  iron,  so  long  as  the  current 
passes.     The  first  telegraph  based  on  this  principle  was  invented  by  Bain. 
The  alphabet  is  the  same  as  Morse's,  but  the  despatch  is  first  composed  at 
the  departure  station  on  a  long  strip  of  ordinary  paper.     It  is  perforated 
successively  by  small    round    elongated   holes,  which    correspond    respec- 
tively to  the  dots  and  marks.     This  strip  of  paper  is  interposed  between  a 
small  metal  wheel  and  a  metal  spring,  both  forming  part  of  the  circuit.     The 


8oo 


Dynamical  Electricity. 


[892- 


wheel,  in  turning,  carries  with  it  the  paper  strip,  all  parts  of  which  pass 
successively  between  the  wheel  and  the  plate.  If  the  strip  were  not  per- 
forated, it  would,  not  being  a  conductor,  constantly  offer  a  resistance  to  the 
passage  of  the  current  ;  but,  in  consequence  of  the  holes,  every  time  one  of 
them  passes,  there  is  contact  between  the  wheel  and  the  plate.  Thus  the 
current  works  the  relay  of  the  station  to  which  it  is  sent,  and  traces  in  blue, 
on  a  paper  disc,  impregnated  with  ferrocyanide  of  potassium,  the  same  series 
of  points  and  marks  as  those  on  the  perforated  paper. 

893.  The  Sounder. — The    sound  produced   when   the   armature  of  the 
electromagnet  in  a  Morse's  instrument  is  attracted  by  the  passage  of  the 
current,  is  so  distinct  and  clear  that  many  telegraph  operators  have  been  in 
the  habit  of  reading  the  messages  by  the  sounds  thus  produced,  and  at  most 
of  checking  their  reading  by  comparison  with  the  signs  produced  on  the  paper. 

Based  on  this  fact  a  form  of  instrument  invented  in  America  has  come 
into  use  for  the  purpose  of  reading  by  sound.  The  sounder^  as  it  is  called, ' 
is  essentially  a  small  electromagnet  on  an  ebonite  base,  resembling  the  relay 
in  fig.  761.  The  armature  is  attached  to  one  end  of  a  lever,  and  is  kept  at 
a  certain  distance  from  the  electromagnet  by  a  spring.  When  the  current 
passes,  the  armature  is  attracted  against  the  electromagnet,  with  a  sharp 
click,  and  when  the  current  ceases  it  is  withdrawn  by  the  spring.  Hence 
the  interval  between  the  sounds  is  of  longer  or  shorter  duration  according 
to  the  will  of  the  sender,  and  thus  in  effect  a  series  of  short  and  long  sounds  can 
be  produced  which  .correspond  to  the  dots  and  dashes  of  the  Morse  alphabet. 

Such  instruments  are  simple,  easily  adjusted,  and  portable,  not  occupy- 
ing more  space  than  an  ordinary  field-glass.  They  are  coming  into  extended 
use,  especially  for  military  telegraph  work. 

894.  Electric  alarum. — One  form  of  these  instruments  is  represented  in 
fig.  764.     On  a  wooden  board  arranged  vertically  is  fixed  an  electromagnet 

E  ;  the  line  wire  is  connected  with  the  bind- 
ing screw  ;;/,  with  which  is  also  connected 
one  end  of  the  wire  of  the  electromagnet  ; 
the  other  end  is  connected  with  a  spring  c, 
to  which  is  attached  the  armature  a  ;  this 
again  is  pressed  against  by  a  spring  C,  which 
in  turn  is  connected  with  the  binding  screw 
n  from  which  the  wire  leads  to  earth. 

Whenever  the  current  passes,  the  arma- 
ture a  is  attracted,  carrying  with  it  a  hammer. 
P,  which  stiikes  against  the  bell  T  and  makes 
it  sound.  The  moment  this  takes  place, 
contact  is  broken  between  the  armature  a  and 
the  spring  C,  and  the  current  being  stopped 
the  electromagnet  does  not  act ;  the  spring 
c,  however,  in  virtue  of  its  elasticity,  brings 
the  armature  in  contact  with  the  spring  C, 
the  current  again  passes,  and  so  on  as  Tong- 
as the  current  continues  to  pass. 

895.    Electrical        clocks.  —  Electrical 
clocks  are  clockwork  machines,  in  which  an 


Fig.  764. 


electromagnet  is  both  the  motor  and  the  regulator,  by  means  of  an  electric 


-896] 


Electromagnetic  Machines. 


80 1 


current  regularly  interrupted,  in  a  manner  resembling  that  described  in  the 
preceding  paragraph.  Fig.  765  represents  the  face  of  such  a  clock,  and  fig. 
766  the  mechanism  which  works  the  needles. 

An  electromagnet,  B,  attracts  an  armature  of  soft  iron,  P,  movable  on  a 
pivot,  a.     The  armature  P  transmits  its  oscillating  motion  to  a  lever,  j,  which 


Fig.  765- 


by  means  of  a  ratchet ;/,  turns  the  wheel  A.  This,  by  the  pinion  D,  turns 
the  wheel  C,  which  by  a  series  of  wheels  and  pinions  moves  the  hands.  The 
small  one  marks  the  hours,  the  large  one  the  minutes  ;  but  as  the  latter  does 
not  move  regularly,  but  by  sudden  starts  from  second  to  second,  it  follows 
that  it  may  also  be  used  to  indicate  the  seconds. 

It  is  obvious  that  the  regularity  of  the  motion  of  the  hands  depends  on 
the  regularity  of  the  oscillations  of  the  piece  P.  For  this  purpose,  the  oscilla- 
tions of  the  current,  before  passing  into  the  electromagnet  B,  are  regulated 
by  a  standard  clock,  which  itself  has  been  previously  regulated  by  a  seconds 
pendulum.  At  each  oscillation  of  the  pendulum  there  is  an  arrangement  by 
which  it  opens  and  closes  the  current,  and  thus  the  armature  P  beats  seconds 
exactly. 

To  illustrate  the  use  of  these  electrical  clocks,  suppose  that  on  the  railway 
from  London  to  Birmingham  each  station  has  an  electric  clock,  and  that  from 
the  London  station  a  conducting  wire  passes  to  all  the  clocks  on  the  line  as 
far  as  Birmingham.  When  the  current  passes  in  this  wire  all  the  clocks  will 
simultaneously'  indicate  the  same  hour,  the  same  minute,  and  the  same 
second  ;  for  electricity  travels  with  such  enormous  velocity,  that  it  takes  an 
inappreciable  time  to  go  from  London  to  Birmingham. 

896.  Electromagnetic  machines. — Numerous  attempts  have  been  made 
to  apply  electromagnetism  as  a  motive  power  in  machinery.  Fig.  767  repre- 
sents an  engine  of  this  kind  constructed  by  Froment.  It  consists  of  four 
powerful  electromagnets,  ABCD,  fixed  on  an  iron  frame,  X.  Between  these 
electromagnets  is  a  system  of  two  iron  wheels  movable  on  the  same  hori- 
zontal axis,  with  eight  soft  iron  armatures,  M,  on  their  circumference. 

M  M  3 

Of 


802 


Dynamical  Electricity. 


[896- 


The  current  arrives  at  K,  ascends  in  the  wire  E,  and  reaches  a  metallic 
arc,  O,  which  serves  to  pass  the  current  successively  into  each  electromagnet, 
so  that  the  attractions  exerted  on  the  armatures  M  shall  always  be  in  the 
same  direction.  Now  this  can  only  be  the  case  provided  the  current  is 
broken  in  each  electromagnet  just  when  an  armature  comes  in  front  of  the 
axis  of  the  bobbijn.  To  produce  this  interruption  the  arc  O  has  three  branches 
e  each  terminating  with  a  steel  spring,  to  which  a  small  sheave  is  attached. 


Fig.  767. 

Two  of  these  establish  the  communication  respectively  with  an  electromagnet, 
and  the  third  with  two.  On  a  central  wheel,  a,  there  are  cogs,  on  which  the 
sheaves  alternately  rest.  Whenever  one  of  them  rests  on  a  cog,  the  current 
passes  into  the  corresponding  electromagnet,  but  ceases  to  pass  when  there 
is  no  longer  contact.  On  emerging  from  the  electromagnets  the  current 
passes  to  the  negative  pole  of  the  battery  by  the  wire  H. 

In  this  manner,  the  armatures  M  being  successively  attracted  by  the  four 
electromagnets,  the  system  of  wheels  which  carries  them  assumes  a  rapid 
rotatory  motion,  which  by  the  wheel  P  and  an  endless  band  is  transmitted  to 
a  sheave,  Q,  which  sends  it  finally  to  any  machine,  a  grinding  mill  for 
example. 


^896]  Electromagnetic  Mac/lines.  803 

In  his  workshops  Froment  had  an  electromotive  engine  of  one-horse 
power.  But,  though  an  interesting  application  of  the  transformation  of  energy, 
there  is  no  expectation  that  these  machines  will  ever  be  practically  applied  in 
manufactures,  for  the  expense  of  the  acids  and  the  zinc  which  they  use  very 
far  exceeds  that  of  the  coal  in  steam-engines  of  the  same  force. 

Thus  a  machine  devised  by  Kravogl  produces  about  17  per  cent,  of  the 
useful  effect  due  to  the  zinc,  and  therefore  in  utilising  this  force  they  are 
about  equal  to  the  best  steam-engines.  But  a  pound  of  coal  yields  7,200 
thermal  units,  and  a  pound  of  zinc  only  1,200  (484)  ;  and  as  zinc  is  ten  times 
as  dear  as  coal,  engines  worked  by  electricity,  independently  of  any  question 
as  to  the  cost  of  construction,  are  sixty  times  as  dear  to  work  as  steam- 
engines.  Until  some  cheaper  source  of  electricity  shall  have  been  discovered 
there  is  no  expectation  that  they  can  be  applied  at  all  advantageously. 

The  energy  of  the  electrical  current  may  be  compared  with  the  vis  viva 
of  a  small  mass  which  moves  with  very  great  velocity.  Hence  it  can  be 
understood  that  the  most  advantageous  employment  of  electricity  is  to  be 
found,  not  so  much  in  the  transformation  of  its  vis  viva  into  the  relatively 
N!O\V  movement  of  large  masses,  as  in  the  rapid  transmission  of  a  small 
power  to  great  distances,  as  in  the  electric  telegraph. 


304 


Dynamical  Electricity, 


[897- 


CHAPTER   VI. 

VOLTAIC   INDUCTION. 

897.  Induction  by  currents. — We  have  already  seen  (744)  that  under 
the  name  induction  is  meant  the  action  which  electrified  bodies  exert  at  a 
distance  on  bodies  in  the  natural  state.  Hitherto  we  have  only  had  to  deal 
with  electrostatical  induction ;  we  shall  now  see  that  dynamical  electricity 
produces  analogous  effects. 

Faraday  discovered  this  class  of  phenomena  in  1832,  and  he  gave  the 
name  of  currents  of  induction  or  induced  currents  to  instantaneous  currents 
developed  in  metallic  conductors  under  the  influence  of  metallic  conductors 
traversed  by  electric  currents,  or  by  the  influence  of  powerful  magnets,  or 
even  by  the  magnetic  action  of  the  earth  ;  and  the  currents  which  give  rise 
to  them  he  called  inducing  currents. 

The  inductive  action  of  a  current  at  the  moment  of  opening  or  closing 
maybe  shown  by  means  of  a  bobbin  with  two  wires.  This  consists  (fig.  768) 


Fig.  768. 

of  a  cylinder  of  wood  or  of  cardboard,  on  which  a  quantity  of  silk-covered 
No.  1 6  copper  wire  is  coiled  ;  on  this  is  coiled  a  considerably  greater  length 
of  fine  copper  wire,  about  No.  35,  also  insulated  by  being  covered  with  silk. 
This  latter  coil,  which  is  called  the  secondary  coil,  is  connected  by  its  ends 
with  two  binding  screws,  a,  b,  from  which  wires  pass  to  a  galvanometer, 
while  the  thicker  wire,  the  primary  coil,  is  connected  by  its  extremities  with 
two  binding  screws,  c  and  d.  One  of  these,  d,  being  connected  with  one  pole 
of  a  battery,  when  a  wire  from  the  other  pole  is  connected  with  c,  the  cur- 
rent passes  in  the  primary  coil,  and  in  this  alone.  The  following  phenomena 
are  then  observed  : — 


-898]     Production  of  Induced  Currents  by  Continuous  ones.     805 

i.  At  the  moment  at  which  the  thick  wire  is  traversed  by  the  current  the 
galvanometer,  by  the  deflection  of  the  needle,  indicates  the  existence  in  the 
secondary  coil  of  a  current  inverse  to  that  in  the  primary  coil,  that  is,  in  the 
contrary  direction  ;  this  is  only  instantaneous,  for  the  needle  immediately 
reverts  to  zero,  and  remains  so  long  as  the  inducing  current  passes  through 
Of. 

ii.  At  the  moment  at  which  the  current  is  opened,  that  is,  when  the  wire 
c  d  ceases  to  be  traversed  by  a  current,  there  is  again  produced  in  the  wire 
a  b  an  induced  current  instantaneous  like  the  first,  but  direct,  that  is  in  the 
same  direction  as  the  inducing  current. 

898.  Production  of  induced  currents  by  continuous  ones. — Induced 
currents  are  also  produced  when  a  primary  coil  traversed  by  a  current  is 
approached  to  or  removed  from  a  secondary  one  ;  this  may  be  shown  by  the 
following  apparatus,  fig.  769,  in  which  B  is  a  hollow  coil  consisting  of  a 


Fig.  769. 

great  length  of  fine  wire,  and  A  a  coil  consisting  of  a  shorter  and  thicker 
wire,  and  of  such  dimensions  that  it  can  be  placed  in  the  secondary  coil. 
The  coil  A  being  traversed  by  a  current,  if  it  is  suddenly  placed  in  the  coil 
B,  a  galvanometer  connected  with  the  latter  indicates  by  the  direction  of  it? 
deflection  the  existence  in  it  of  an  inverse  current ;  this  is  only  instantaneous, 
the  needle  rapidly  returns  to  zero,  and  remains  so  as  long  as  the  small 
bobbin  is  in  the  large  one.  If  it  is  rapidly  withdrawn,  the  galvanometer 
shows  that  the  wire  is  traversed  by  a  direct  current.  If,  instead  of  rapidly 
introducing  or  replacing  the  primary  coil,  this  is  done  slowly,  the  galvano- 
meter only  indicates  a  weak  current,  and  which  is  the  feebler  the  slower  the 
motion. 

If,  instead  of  varying  the  distance  of  the  inducing  current,  its  intensity 
be  varied,  that  is,  either  increased  by  bringing  additional  battery  power  into 


8o6  Dynamical  Electricity.  [898- 

the  circuit,  or  diminished  by  increasing  the  resistance,  an  induced  current 
is  produced  in  the  secondary  wire,  which  is  inverse  if  the  intensity  of  the 
inducing  current  increases,  and  direct  if  it  diminishes. 

899.  Conditions  of  induction.     Xienz's  law. — From  the  experiments 
which  have  been  described  in  the  previous  paragraphs  the  following  prin- 
ciples may  be  deduced  : — 

I.  The  distance  remaining  the  same,  a  continuous  and  constant  current 
does  not  induce  any  current  in  an  adjacent  conductor. 

II.  A  current  at  the  moment  of  being  closed,  produces  in  an  adjacent 
conductor  an  inverse  current. 

III.  A  current  at  the  moment  it  ceases, produces  a  direct  current. 

IV.  A  current  which  is  removed,  or  whose  intensity  diminishes,  gives  rise 
to  a  direct  induced  current. 

V.  A  current  which  is  approached,  or  whose  intensity  increases,  gives  rise 
to  an  inverse  induced  current. 

VI.  On  the  induction  produced  between  a  closed  circuit  and  a  current  in 
activity,  when  their  relative  distance  varies,  Lenz  has  based  the  following 
law.  which  is  known  as  Lens's  Law  : — 

If  the  relative  position  of  two  conductors  A  and  B  be  changed,  of  which 
A  is  traversed  by  a  current,  a  cttrrent  is  induced  in  B  in  such  a  direction  that 
by  its  electrodynamic  action  on  the  current  in  A,  it  would  have  imparted  to 
the  conductors  a  motion  of  the  contrary  kind  to  that  by  which  the  inducing 
action  was  produced. 

Thus,  for  instance,  in  V.,  when  a  current  is  approached  to  a  conductor, 
an  inverse  current  is  produced ;  but  two  conductors  traversed  by  currents  in 
opposite  directions,  repel  one  another  according  to  the  received  laws  of 
electrodynamics  (868).  Conversely  when  a  current  is  moved  away  from  a 
conductor,  a  current  of  the  same  direction  is  produced  ;  now  two  currents  in 
the  same  direction  attract  one  another. 

On  bringing  the  inducing  wire  near  the  induced  as  well  as  in  removing 
it  away,  work  is  required  ;  hence  a  quantity  of  heat  proportional  to  the  work 
consumed  must  result,  as  Edlund's  investigations  have  shown.  On  the 
other  hand,  when  induction  results  from  the  opening  and  closing  of  the  cir- 
cuit (II.  and  III.)  no  work  is  lost,  but  the  inducing  current  loses  as  much 
heat  as  is  produced  in  the  induced  circuit. 

900.  Inductive  action  of  the  leyden  discharge. — Figure  770  represents 
an  apparatus  devised  by  Matteucci,  which  is  very  well  adapted  for  showing 
the  development  of  induced  currents  produced  either  by  the  discharge  of  a 
Leyden  jar  or  by  the  passage  of  a  voltaic  current. 

It  consists  of  two  glass  plates  about  12  inches  in  diameter,  fixed  vertically 
on  the  two  supports  A  and  B.  These  supports  are  on  movable  feet,  and 
can  either  be  approached  or  removed  at  will.  On  the  anterior  face  of  the 
plate  A  are  coiled  about  30  yards  of  copper  wire,  C,  a  millimetre  in  diameter. 
The  two  ends  of  this  wire  pass  through  the  plate,  one  in  the  centre,  the  other 
near  the  edge,  terminating  in  two  binding  screws,  like  those  represented  in 
m  and  n,  on  the  plate  B.  To  these  binding  screws  are  attached  two  copper 
wires,  c  and  d,  through  which  the  inducing  current  is  passed. 

On  the  face  of  the  plate  B,  which  is  towards  A,  is  enrolled  a  spiral  of 
finer  copper  wire  than  the  wire  C.  Its  extremities  terminate  in  the  binding 


-901] 


Inductive  Action  of  the  Ley  den  Discharge. 


807 


screws  ///  and  ;/,  on  which  are  fixed  two  wires,  h  and  /,  intended  to  transmit 
the  induced  current.  The  two  wires  on  the  plates  are  not  only  covered  with 
silk,  but  each  circuit  is  insulated  from  the  next  one  by  a  thick  layer  of  shellac 
varnish. 

In  order  to  show  the  production  of  the  induced  current  by  the  discharge 
of  a  Leyden  jar,  one  end  of  the  wire  C  is  connected  with  the  outer  coating, 
and  the  other  end  with  the  knob  of  the  Leyden  jar,  as  shown  in  the  figure. 
When  the  spark  passes,  the  electricity  traversing  the  wire  C  acts  by  induc- 
tion on  the  neutral  fluid  of  the  wire  on  the  plate  B,  and  produces  an  instan- 
taneous current  in  this  wire.  A  person  holding  two  copper  handles  connected 
with  the  wires  *  and  /r  receives  a  shock,  the  intensity  of  which  is  greater  in 


proportion  as  the  plates  A  and  B  are  nearer.  This  experiment  proves  that 
frictional  electricity  can  give  rise  to  induced  currents  as  well  as  voltaic 
electricity. 

The  experiment  may  also  be  made  by  simply  twisting  together  two 
lengths  of  a  few  feet  of  gutta-percha-covered  copper  wire.  The  ends  of  one 
length  being  held  in  the  hand,  an  electric  discharge  is  passed  through  the 
other  length. 

The  above  apparatus  can  also  be  used  to  show  the  production  of  induced 
currents  by  the  influence  of  voltaic  currents.  For  this  purpose  the  current 
of  a  battery  is  passed  through  the  inducing  wire  C,  while  the  ends  of  the 
other  wire,  h  and  z,  are  connected  with  a  galvanometer.  At  the  moment  at 
which  the  current  commences  or  finishes,  or  when  the  distance  of  the  two 
conductors  is  varied,  the  same  phenomena  are  observed  as  in  the  case  of  the 
apparatus  represented  in  fig.  768. 

901.  induction  by  magnets. — It  has  been  seen  that  the  influence  of  a 
current  magnetises  a  steel  bar  ;  in  like  manner  a  magnet  can  produce  induced 
currents  in  metal  circuits.  Faraday  showed  this  by  means  of  a  coil  with  a 
single  wire  of  200  to  300  yards  in  length.  The  two  ends  of  the  wire  being 
connected  with  a  galvanometer,  as  shown  in  fig.  771,  a  strongly  magnetised 
bar  is  suddenly  inserted  in  the  bobbin,  and  the  following  phenomena  are 
observed  : — 

i.  At  the  moment  at  which  the  magnet  is  introduced,  the  galvanometer 
indicates  in  the  wire  the  existence  of  a  current,  the  direction  of  which  is 


8o8 


Dynamical  Electricity. 


[901- 


opposed  to  that  which  circulates  round  the  magnet,  considering  the  latter  as 
a  solenoid  on  Ampere's  theory  (878). 

ii.  When  the  magnet  is  withdrawn,  the  needle  of  the  galvanometer,  which 
has  returned  to  zero,  indicates  the  existence  of  a  direct  current. 

The  inductive  action  of  magnets  may  also  be  illustrated  by  the  follow- 
ing experiment  :  a  bar  of  soft  iron  is  placed  in  the  above  bobbin  and  a  strong 
magnet  suddenly  brought  in  contact  with  it  ;  the  needle  of  the  galvanometer 
is  deflected,  but  returns  to  zero  when  the  magnet  is  stationary,  and  is  de- 
flected in  the  opposite  direction  when  it  is  removed.  The  induction  is  here 
produced  by  the  magnetisation  of  the  soft  iron  bar  in  the  interior  of  the 
bobbin  under  the  influence  of  the  magnet. 

The  same  inductive  effects  are  produced  in  the  wires  of  an  electromagnet, 
if  a  strong  magnet  be  made  to  rotate  rapidly  in  front  of  the  extremities  of 


the  wire  in  such  a  manner  that  its  poles  act  successively  by  influence  on  the 
two  branches  of  the  electromagnet  :  or  also  by  forming  two  coils  round  a 
horse-shoe  magnet,  and  passing  a  plate  of  soft  iron  rapidly  in  front  of  the 
poles  of  the  magnet  ;  the  soft  iron  becoming  magnetic  reacts  by  influence  on 
the  magnet,  and  induced  currents  are  produced  in  the  wire  alternately  in 
different  directions. 

The  inductive  action  of  magnets  is  a  confirmation  of  Ampere's  theory 
of  magnetism.  For  as,  on  this  theory,  all  magnets  are  solenoids,  all  the 
experiments  which  have  been  mentioned  may  be  explained  by  the  induc- 
tive action  of  currents  which  traverse  the  surface  of  magnets  ;  the  induction 
of  magnets  is  in  short  an  induction  of  currents.  And  it  is  a  useful  exercise 
to  see  how  on  this  view  the  inductive  action  of  magnets  falls  under  Lenz's 
law  (898). 

902.  Inductive  action  of  magnets  on  bodies  in  motion. — Arago  was 
the  first  to  observe,  in  1824,  that  the  number  of  oscillations  which  a  mag- 
netised needle  makes  in  a  given  time,  under  the  influence  of  the  earth's 


-902]  Inductive  Action  of  Magnets.  809 

magnetism,  is  very  much  lessened  by  the  proximity  of  certain  metallic  masses, 
and  especially  of  copper,  which  may  reduce  the  number  in  a  given  time  from 
300  to  4.  This  observation  led  Arago  in  1825  to  the  discovery  of  an  equally 
unexpected  fact ;  that  of  the  rotative  action  which  a  plate  of  copper  in 
motion  exercises  on  a  magnet. 

This  phenomenon  may  be  shown  by  means  of  the  apparatus  represented 
in  fig.  772.  It  consists  of  a  copper  disc,  M,  movable  about  a  vertical  axis. 
On  this  axis  is  a  sheave,  B,  round  which  is  coiled  an  endless  cord,  passing; 


Fig.  772. 

also  round  the  sheave  A.  By  turning  this  with  the  hand,  the  disc  M  may 
be  rotated  with  great  rapidity.  Above  the  disc  is  a  glass  plate,  on  which  is 
a  small  pivot  supporting  a  magnetic  needle,  ab.  If  the  disc  be  now  moved 
with  a  slow  and  uniform  velocity,  the  needle  is  deflected  in  the  direction  of 
the  motion,  and  stops  at  an  angle  of  from  20°  to  30°  with  the  direction  of  the 
magnetic  meridian,  according  to  the  velocity  of  the  rotation  of  the  disc. 
But  if  this  velocity  increases,  the  needle  is  ultimately  deflected  more  than 
90° ;  it  is  then  carried  along,  describes  an  entire  revolution,  and  follows  the 
motion  of  the  disc  until  this  stops. 

Babbage  and  Herschel  modified  Arago's  experiment  by  causing  a  horse- 
shoe magnet  placed  vertically  to  rotate  below  a  copper  disc  suspended  on 
silk  threads  without  torsion  ;  the  disc  rotated  in  the  same  direction  as  the 
magnets.  The  effect  decreases  with  the  distance  of  the  disc,  and  varies  with 
its  nature.  The  maximum  effect  is  produced  with  metals  ;  with  wood,  glass, 
water,  etc.  it  disappears.  Babbage  and  Herschel  have  found  that  repre- 
senting this  action  on  copper  at  100,  the  action  on  other  metals  is  as 
follows  :  zinc  95,  tin  46,  lead  25,  antimony  9,  bismuth  2.  Lastly,  the  effect 
is  enfeebled  if  there  are  non-conducting  breaks  in  the  disc,  especially  in  the 
direction  of  the  radii ;  but  it  is  the  same  if  these  breaks  are  soldered  with 
any  metal. 

Faraday  made  an  experiment  the  reverse  of  Arago's  first  observation  ; 
since  the  presence  of  a  metal  at  rest  stops  the  oscillations  of  a  magnetic 
needle,  the  neighbourhood  of  a  magnet  at  rest  ought  to  stop  the  motion  of  a 
rotating  mass  of  metal.  Faraday  suspended  a  cube  of  copper  to  a  twisted 


8  io  Dynamical  Electricity.  [902  - 

thread,  which  was  placed  between  the  poles  of  a  powerful  electromagnet. 
When  the  thread  was  left  to  itself,  it  began  to  spin  round  with  great  velocity, 
but  stopped  the  moment  a  powerful  current  passed  through  the  electro- 
magnet. 

Faraday  was  the  first  to  give  an  explanation  of  all  these  phenomena  of 
magnetism  by  rotation.  They  depend  on  the  circumstances  that  a  magnet  or 
a  solenoid  can  induce  currents  in  a  solid  mass  of  metal.  In  the  above  case 
the  magnet  induces  currents  in  the  disc  when  the  latter  is  rotated  ;  and  con- 
versely when  the  magnet  is  rotated  while  the  disc  is  primarily  at  rest.  Now 
these  induced  currents  by  their  electrodynamic  action  tend  to  destroy  the 
motion  which  gave  rise  to  them  ;  they  are  simple  illustrations  of  Lenz's  law  ; 
they  act  just  in  the  same  way  as  friction  would  do. 

i.  For  instance,  let  AB  (fig.  773)  be  a  needle  oscillating  over  a  copper 
disc,  and  suppose  that  in  one  of  its  oscillations  it  goes  in  the  direction  of  the 
arrows  from  N  to  M.  In  approaching  the  point  M,  for 
instance,  it  develops  there  a  current  in  the  opposite 
direction,  and  which  therefore  repels  it  ;  in  moving  away 
from  N  it  produces  currents  which  are  of  the  same  kind, 
and  which  therefore  attract,  and  both  these  actions  con- 
cur in  bringing  it  to  rest. 

ii.  Suppose  the  metallic  mass  turns  from  N  towards 
M,  and  that  the  magnet  is  fixed  ;  the  magnet  will  repel 
by  induction  points  such  as  N  which  are  approaching  A, 
and  will  attract  M  which  is  moving  away  ;  hence  the  motion  of  the  metal 
stops  as  in  Faraday's  experiment. 

iii.  If  in  Arago's  experiment  the  disc  is  moving  from  N  to  M,  N  ap- 
proaches A  and  repels  it,  while  M  moving  away  attracts  it ;  hence  the 
needle  moves  in  the  same  direction  as  the  disc. 

If  this  explanation  is  true,  all  circumstances  which  favour  induction  will 
increase  the  dynamic  action  ;  and  those  which  diminish  the  former  will 
also  lessen  the  latter.  We  know  that  induction  is  greater  in  good  conductors 
and  that  it  does  not  take  place  in  insulating  substances  ;  but  we  have  seen 
that  the  needle  is  moved  with  a  force  which  is  less,  the  less  the  conducting 
power  of  the  disc,  and  it  is  not  moved  when  the  disc  is  of  glass.  Dove  has 
found  that  there  is  no  induction  on  a  tube  split  lengthwise  in  which  a  coil  is 
introduced. 

In  order  to  bring  the  oscillations  of  the  needle  of  a  galvanometer  more 
quickly  to  rest,  the  wire  is  coiled  upon  a  copper  frame.  Such  an  arrange- 
ment is  called  a  damper,  and  in  practice  it  is  frequently  used. 

903.  Induction  by  the  action  of  the  earth. — Faraday  discovered  that 
terrestrial  magnetism  can  develop  induced  currents  in  metallic  bodies  in 
motion,  acting  like  a  powerful  magnet  placed  in  the  interior  of  the  earth  in 
the  direction  of  the  dipping  needle,  or,  according  to  the  theory  of  Ampere, 
like  a  series  of  electrical  currents  directed  from  east  to  west  parallel  to  the 
magnetic  equator.  He  first  proved  this  by  placing  a  long  helix  of  copper 
wire  covered  with  silk  (such  as  A,  fig.  769)  in  the  plane  of 'the  magnetic 
meridian  parallel  to  the  dipping  needle  ;  by  turning  this  helix  180°  about  an 
axis  perpendicular  to  its  length  in  its  middle,  he  observed  that  at  each  turn 
a  galvanometer  connected  with  the  two  ends  of  the  helix  was  deflected.  The 


-904] 


Induction  by  the  Action  of  the  Earth. 


811 


apparatus  depicted  in  fig.  774,  and  known  as  Delezennfs  circle,  serves  for 
showing  the  existence  of  terrestrial  induced  currents.  It  consists  of  a  wooden 
ring,  RS,  about  two  feet  in  diameter,  fixed  to  an  axis,  ao,  about  which  it  can 
be  turned  by  means  of  a  handle,  M.  The  axis  oa  is  itself  fixed  in  a  frame 
PQ,  movable  about  a  horizontal  axis.  By  pointers  fixed  to  these  two  axes 
the  inclination  towards  the  horizon  of  the  frame  PQ,  and  therefore  of  the  axis 
oa,  is  indicated  on  a  dial,  Awhile  a  second  dial,  c,  gives  the  angular  displace- 
ment of  the  ring.  This  ring  has  a  groove  in  which  is  coiled  a  large  quantity 
of  insulated  copper  wire.  The  two  ends  of  the  wire  terminate  in  a  commu- 
tator analogous  to  that  in  Clarke's  apparatus  (910),  the  object  of  which  is  to 
pass  the  current  always  in  the  same  sense,  although  its  direction,  SR,  changes 
at  each  semi-revolution  of  the  ring.  On  each  of  the  rings  of  the  commutator 
are  two  brass  plates,  which  successively  transmit  the  current  to  two  wires  in 


Fig-  774- 

contact  with  the  galvanometer.  The  axis  oa  being  in  the  magnetic  meridian, 
and  the  ring  RS  at  right  angles  to  the  direction  XY  of  the  dipping  needle,  if  it 
is  slowly  rotated  the  needle  of  the  galvanometer  is  deflected,  and  by  its  de- 
flection indicates  in  the  wire  coiled  on  the  ring  an  induced  current  whose 
intensity  increases  until  it  has  been  turned  through  90°  ;  the  deviation  then 
decreases,  and  is  zero  when  the  ring  has  made  a  semi-revolution.  If  the 
rotation  continues,  the  current  reappears,  but  in  a  contrary  direction,  and 
attains  a  second  maximum  at  270°,  becoming  null  again  after  a  complete 
turn.  When  the  axis  oa  is  parallel  to  the  dip  there  is  no  current. 

904.  Induction  of  a  current  on  itself.  Extra  current. — If  a  closed 
circuit  traversed  by  a  voltaic  current  be  opened,  a  scarcely  perceptible  spark 
is  obtained,  if  the  wire  joining  the  two  poles  be  short.  Further,  if  the  ob- 
server himself  form  part  of  the  circuit  by  holding  a  pole  in  each  hand,  no 
shock  is  perceived  unless  the  current  is  very  strong.  If,  on  the  contrary', 
the  wire  is  long,  and  especially  if  it  makes  a  great  number  of  turns,  so  as  to 
form  a  bobbin  with  very  close  folds,  the  spark,  which  is  inappreciable  when 
the  current  is  closed,  acquires  a  great  intensity  when  it  is  opened,  and  an 


812 


Dynamical  Electricity. 


'904- 


observer  in  the  circuit  receives  a  shock  which  is  the  stronger  the  greater  the 
number  of  turns. 

Faraday  has  referred  this  strengthening  of  the  current  when  it  is  broken 
to  an  inductive  action  which  the  current  in  each  coil  exerts  upon  the  adjacent 
coils  :  an  action  in  virtue  of  which  there  is  produced  in  the  bobbin  a  direct 
induced  current — that  is,  one  in  the  same  Direction  as  the  principal  one. 
This  is  known  as  the  extra  current. 

To  show  the  existence  of  this  current,  at  the  moment  of  opening,  Fara- 
day arranged  the  experiment  as  seen  in  fig.  775.  Two  wires  from  the  poles 
E  E'  of  a  battery  are  connected  with  two  binding  screws,  D  and  F,  with 
which  are  also  connected  the  two  ends  of  a  bobbin,  B,  with  a  long  fine  wire, 
which  offers  therefore  a  great  resistance.  On  the  path  of  the  wires  at  the 


Fig-  775- 

points  A  and  C  are  two  other  wires,  which  are  connected  with  a  galvano- 
meter, G.  Hence  the  current  from  the  pole  E  branches  at  A  into  two  cur- 
rents, one  which  traverses  the  galvanometer,  the  other  the  bobbin,  and  both 
joining  the  negative  pole  E'. 

The  needle  of  the  galvanometer  being  then  deflected  from  G  to  a'  by  the 
current  which  goes  from  A  to  C,  it  is  brought  back  to  zero,  and  kept  there  by 
an  obstacle  which  prevents  it  from  turning  in  the  direction  Ga',  but  leaves  it 
free  in  the  opposite  direction.  On  breaking  contact  at  E,  it  is  seen  that  the 
moment  the  circuit  is  open  the  needle  is  deflected  in  the  direction  Ga  ; 
showing  a  current  contrary  to  that  which  passed  during  the  existence  of  the 
current — that  is,  showing  the  current  from  C  to  A.  But  the  battery  current 
having  ceased,  the  only  remaining  one  is  the  current  AFBCDA  ;  and  since  in 
the  part  CA  the  current  goes  from  C  to  A,  it  must  traverse  the  entire  circuit 
in  the  direction  AFBDC — that  is,  the  same  as  the  principal  current.  This 
current,  which  thus  appears  when  the  circuit  is  opened,  is  the  extra 
current. 

905.  Extra  current  on  opening-  and  on  closing:. — The  coils  of  the  spiral 
act  inductively  on  each  other,  not  merely  on  opening,  but  also  on  closing  the 
current.  Hence,  in  accordance  with  the  general  law  of  induction,  each 
spiral  acting  on  each  succeeding  one,  induces  a  current  in  the  opposite 


-906]  Extra  Current.  813 

direction  to  its  own — that  is,  an  inverse  current  :  this,  which  is  the  extra 
current  on  dosing,  or  the  inverse  extra  current,  being  of  contrary  direction 
to  the  principal  one,  diminishes  its  intensity,  and  lessens  or  suppresses  the 
spark  on  closing. 

When,  however,  the  current  is  opened,  each  spire  then  acts  inductively 
on  each  succeeding  one,  producing  a  current  in  the  same  direction  as  its  own, 
and  which  therefore  greatly  heightens  the  intensity  of  the  principal  current. 
This  is  the  e.vtra  current  on  opening,  or  direct  extra  current. 

To  observe  the  direct  extra  current,  the  conductor  on  which  its  effect  is 
to  be  traced  may  be  introduced  into  the  circuit,  by  being  connected  in  any 
suitable  manner  with  the  binding  screws  A  and  C  in  the  place  of  the  galvano- 
meter. 

It  can  thus  be  shown  that  the  direct  extra  current  gives  violent  shocks 
and  bright  sparks,  decomposes  water,  melts  platinum  wires,  and  magnetises 
steel  needles.  Abria  found  that  the  strength  of  the  extra  current  is  about 
072  of  the  principal  current.  The  shock  produced  by  the  current  may 
be  tried  by  attaching  the  ends  of  the  wire  to  two  files,  which  are  held  in 
the  hands.  On  moving  the  point  of  one  file  over  the  teeth  of  the  other,  a 
series  of  shocks  is  obtained,  due  to  the  alternate  opening  and  closing  of  the 
current. 

The  above  effects  acquire  greater  intensity  when  a  bar  of  soft  iron  is 
introduced  into  the  bobbin,  or,  what  is  the  same  thing,  when  the  current  is 
passed  through  the  bobbin  of  an  electromagnet ;  and  still  more  is  this  the 
case  if  the  core,  instead  of  being  massive,  consists  of  a  bundle  of  straight 
wires.  Faraday  explained  this  strengthening  action  of  soft  iron  as  follows  : 
If  inside  the  spiral  there  is  an  iron  bar,  on  opening  the  circuit  when  the 
principal  current  disappears,  the  magnetism  which  it  evokes  in  the  bar  dis- 
appears too  ;  but  the  disappearance  of  this  magnetism  acts  like  the  disappear- 
ance of  the  electrical  current,  and  the  disappearing  magnetism  induces  a 
current  in  the  same  direction  as  the  disappearing  principal  current,  the  effect 
of  which  is  thus  heightened. 

In  the  experiments  just  described  the  effects  of  the  two  extra  currents 
accompany  those  of  the  principal  current.  Edhmd  has  devised  an  in- 
genious arrangement  of  apparatus  by  which  the  action  of  the  principal 
current  on  the  measuring  instruments  can  be  completely  avoided,  so  that  only 
that  of  the  extra  current  remains.  In  this  way  he  has  arrived  at  the  follow- 
ing laws  : — 

i.  The  intensity  of  the  currents  used  being  the  same,  the  extra  currents 
obtained  on  opening  and  closing  have  the  same  electromotive  force. 

ii.  The  electromotive  force  of  the  extra  current  is  proportional  to  the 
intensity  of  the  primary  current. 

906.  Induced  currents  of  different  orders. — Spite  of  their  instantaneous 
character,  induced  currents  can  themselves,  by  their  action  on  closed  circuits, 
<;ive  rise  to  new  induced  currents,  these  again  to  others,  and  so  on,  producing 
induced  currents  of  different  orders. 

These  currents,  discovered  by  Henry,  may  be  obtained  by  causing  to 
act  on  each  other  a  series  of  bobbins,  each  formed  of  a  copper  wire  covered 
with  silk,  and  coiled  spirally  in  one  plane,  like  that  represented  in  plate  A, 
in  fig.  770.  The  currents  thus  produced  are  alternately  in  opposite 


814.  Dynamical  Electricity.  [906- 

directions,  and  their  intensity  decreases  in  proportion  as  they  are  of  a  higher 
order. 

907.  Properties  of  induced  currents. — Notwithstanding  their  instan- 
taneous character,  it  appears  from  the  preceding  experiments  that  induced 
currents  have  all  the  properties  of  ordinary  currents.     They  produce  violent 
physiological,  luminous,  calorific,  and  chemical  effects,  and  finally  give  rise 
to  new  induced  currents.     They  also  deflect  the  magnetic  needle  and  mag- 
netise steel  bars  when  they  are  passed  through  a  copper  wire  coiled  in  a 
helix  round  the  bars. 

The  intensity  of  the  shock  produced  by  induced  currents  renders  their 
effects  comparable  to  those  of  electricity  at  high  potential. 

The  direct  induced  current  and  the  inverse  induced  current  have  been 
compared  as  to  three  of  their  actions  :  the  violence  of  the  shock,  the  deflec- 
tion of  the  galvanometer,  and  the  magnetising  action  on  steel  bars.  In  these 
respects  they  differ  greatly  :  they  are  about  equal  in  their  action  on  the  gal- 
vanometer ;  but  while  the  shock  of  the  direct  current  is  very  powerful,  that 
of  the  inverse  current  is  scarcely  perceptible.  The  same  difference  prevails 
with  reference  to  the  magnetising  force.  The  direct  current  magnetises  to 
saturation,  while  the  inverse  current  does  not  magnetise. 

908.  Xiaws  of  induced  currents. — In  his  special  treatise  on  induction, 
Matteucci  has  deduced  from  his  own  researches,  and  from  those  of  Faraday, 
Lenz,  Dove,  Abria,  Weber,  Marianini,  and  Felici,  the  following  laws  in  refer- 
ence to  induced  currents  : — 

i.  The  strength  of  induced  currents  is  proportional  to  that  of  the  inducing 
currents. 

ii.  This  stre?igth  is  proportional  to  the  product  of  the  length  of  the  induc- 
ing and  induced  currents. 

iii.  The  electromotive  force  developed  by  a  given  quantity  of  electri- 
city is  the  same  whatever  be  the  nature,  section,  or  shape  of  the  inducing 
circuit. 

iv.  The  electromotive  force  developed  by  the  induction  of  a  current  on  any 
given  conducting  circttit  is  independent  of  the  nature  of  the  conductor. 

v.  The  development  of  induction  is  independent  of  the  nature  of  the  insu- 
lating body  interposed  between  the  induced  and  inducing  circuit. 


APPARATUS    FOUNDED   ON    INDUCTION. 

909.  Magneto-electrical  apparatus. — After  the  discovery  of  magneto- 
electrical  induction,  several  attempts  were  made  to  produce  an  uninterrupted 
series  of  sparks  by  means  of  a  magnet.  Apparatus  for  this  purpose  were 
devised  by  Pixii  and  Ritchie,  and  subsequently  by  Saxton,  Ettingshausen, 
and  Clarke.  Fig.  776  represents  that  invented  by  Clarke.  It  consists  of 
a  powerful  horse-shoe  magnetic  battery,  A,  fixed  against  a  vertical  wooden 
support.  In  front  of  this  are  two  bobbins,  B  B',  movable  round  a  hori- 
zontal axis.  These  bobbins  are  coiled  on  two  cylinders  of  soft  iron  joined 
at  one  end  by  a  plate  of  soft  iron,  V,  and  at  the  other  by  a  similar  plate 
of  brass.  These  two  plates  are  fixed  on  a  copper  axis,  terminated  at 
one  end  by  a  commutator,  qi,  and  at  the  other  by  a  pulley,  which  is  moved 


-909] 


Magneto-electrical  Apparatus. 


S'5 


by  an  endless  band  passing  round  a  large  wheel,  which  is  turned  by  a 
handle. 

Each  bobbin  consists  of  about  1,500  turns  of  very  fine  copper  wire 
covered  with  silk.  One  end  of  the  wire  of  the  bobbin  B  is  connected  on 
the  axis  of  rotation  with  one  end  of  the  wire  of  the  bobbin  B',  and  the  two 
other  ends  of  these  wires  terminate  in  a  copper  ferrule  or  washer,  q,  which 
is  fixed  to  the  axis,  but  is  insulated  by  a  cylindrical  envelope  of  ivory.  In 


Fig.  776 

order  that  in  each  wire  the  induced  current  may  be  in  the  same  direction,  it 
is  coiled  on  the  two  bobbins  in  different  directions — that  is,  one  is  right- 
handed,  the  other  left-handed. 

When  now  the  electromagnet  turns,  its  two  branches  become  alternately 
magnetised  in  contrary  directions  under  the  influence  of  the  magnet  A,  and 
in  each  wire  an  induced  current  is  produced,  the  direction  of  which  changes 
at  each  half-turn. 

Let  us  follow  one  of  the  bobbins — B,  for  instance — while  it  makes  a  com- 
plete revolution  in  front  of  the  poles  a  and  b  of  the  magnet ;  calling  the 
poles  of  the  electromagnet  successively  a'  and  b'.  Let  us  further  consider 
the  latter  when  it  passes  in  front  of  the  north  pole  of  the  magnetic  battery 
(fig.  778).  The  iron  has  then  a  south  pole  in  which,  as  we  know,  the  Am- 
perian  currents  move  like  the  hands  of  a  watch.  The  contrary  seems  to  be 
represented  in  fig.  778,  but  it  must  be  remembered  that  the  bobbins  are 
seen  here  as  they  are  in  fig.  776 ;  and  hence,  when  viewed  at  the  end  which 


8i6 


Dynamical  Electricity. 


[909- 


grazes  the  magnet,  the  Amperian  currents  seem  to  turn  like  the  hands  of  a 
watch.  These  currents  act  inductively  on  the  wire  of  the  bobbin,  producing 
a  current  in  the  same  direction  (908,  iii.)  for  the  bobbin  moves  away  from 
the  pole  a,  its  soft  iron  is  demagnetised,  and  the  Amperian  currents  cease 
(899).  The  intensity  of  the  induced  current  in  the  bobbin  decreases,  until 
the  right  line  joining  the  axes  of  the  two  bobbins  is  perpendicular  to  that 
which  joins  the  poles  a  and  b  of  the  bar.  There  is  now  no  magnetism  in  the 
bar,  but  quickly  approaching  the  pole  £,  its  soft  iron  is  then  magnetised  in 
the  opposite  direction — that  is,  becomes  a  north  pole  (fig.  779),  The  Am- 
perian currents  are  then  in  the  direction  of  the  arrow  a' ;  and  as  they  are 


Fig.  778. 


Fig.  779. 


Fig.  780. 


Fig.  781- 


commencing,  they  develop  in  the  wire  of  the  bobbin  an  inverse  current  (899) 
which  is  in  the  same  direction  as  that  developed  in  the  first  quarter  of  the 
revolution.  Moreover,  this  second  current  adds  itself  to  the  first ;  for  while 
the  bobbin  moves  away  from  <z,  it  approaches  b.  Hence,  during  the  lower 
half-revolution  from  a  to  £,  the  wire  was  successively  traversed  by  two 
induced  currents  in  the  same  direction,  and  if  the  rotatory  motion  is  suffi- 
ciently rapid,  we  might  admit  during  this  half-revolution  the  existence  of  a 
single  current  of  the  wire. 

The  same  reasoning  applied  to  the  figures  780  and  781  will  show  that 
during  the  upper  half-revolution  the  wire  of  the  bobbin  B  is  still  traversed  by 
a  single  current,  but  in  the  opposite  direction  to  that  of  the  lower  half-revo- 


-910] 


Commutator. 


kit  ion.  What  has  been  said  about  the  bobbin  B  applies  obviously  to  the 
bobbin  B' ;  yet,  as  one  of  these  is  right-handed  and  the  other  left-handed, 
the  currents  are  constantly  in  the  same  direction  in  the  two  bobbins  during 
each  upper  or  lower  half-revolution.  At  each  successive  half-revolution  they 
both  change,  but  are  in  the  same  direction  as  regards  each  other  ;  the  term 
direction  having  here  reference  to  figs.  778-781. 

910.  Commutator. — The  object  of  this  apparatus  (fig.  782),  of  which  fig. 
783  i-s  a  section,  is  to  bring  the  two  alternating  currents  always  in  the  same 


Fig..  782, 

direction.  It  consists  of  an  insulating  cylinder  of  ivory  or  ebony,  J,  in  the 
axis  of  which  is  a  copper  cylinder,  k,  of  smaller  diameter,  fixed  to  the  arma- 
ture V,  and  turning  with  the  bobbins.  On  the  ivory  cylinder  is  first  a  brass 
ferrule,  ^,  and  in  front  of  it 
two  half-ferrules,  o  and  </r 
also  of  brass  and  completely 
insulated  from  one  another. 
The  half-ferrule  o  is  con- 
nected with  the  ferrule  q  by 
a  tongue,  x.  On  the  sides  of 
a  block  of  wood,  M,  there 
are  two  brass  plates,  »/,  », 
on  which  are  screwed  two 
elastic  springs,  b  and  c\  which 
press  successively  on  the 
half-ferrules  o  and  o',  when  y;g-  ?3> 

rotation  takes  place. 

We  have  already  seen  that  the  two  ends  of  the  wire  of  the  bobbin,  those 
in  the  same  direction  with  respect  to  the  currents  passing  through  them  .at 

N   N 


8 1 8  Dynamical  Electricity.  [910- 

any  time,  which  will  be  found  to  be  those  farthest  away  from  the  armature 
V,  terminate  in  the  metallic  axis  k,  and  therefore  on  the  half-ferrule  o'  ; 
while  the  other  two  ends,  both  in  the  same  direction  with  respect  to  the 
current,  are  joined  to  the  ferrule  <?,  and  therefore  to  the  half-ferrule  o. 
It  follows  that  the  pieces  oo'  are  constantly  poles  of  alternating  currents 
which  are  developed  in  the  bobbins  ;  and,  as  these  are  alternately  in  con- 
trary directions,  the  pieces  o  and  o'  are  alternately  positive  and  nega- 
tive. Now,  taking  the  case  in  which  the  half-ferrule  o'  is  positive,  the 
current  descends  by  the  spring  b,  follows  the  plate  ;;z,  arrives  at  n  by  the 
joining  wire/,  ascends  in  <:,  and  is  closed  by  contact  with  the  piece  o  ;  then 
when,  in  consequence  of  rotation,  o  takes  the  place  of  o',  the  current 
retains  the  same  direction  ;  for,  as  it  is  then  reverse.d  in  the  bobbins,  o 
has  become  positive  and  o'  negative,  and  so  forth  as  long  as  the  bobbin  is 
turned. 

With  the  two  springs  b  and  c  alone,  the  opposite  currents  from  the  two 
pieces  o  and  o'  could  not  unite  when  m  and  n  are  not  joined  ;  this  is  effected 
by  means  of  a  third  spring,  a  (fig.  786),  and  of  two  appendices,  z,  only  one  of 
which  is  visible  in  the  figure.  These  two  pieces  are  insulated  from  one 
another  on  an  ivory  cylinder,  but  communicate  respectively  with  the  pieces 
o  and  o'.  As  often  as  the  spring  a  touches  one  of  these  pieces  it  is  connected 
with  the  spring  b,  and  the  current  is  closed,  for  it  passes  from  b  to  «,  and 
then  reaches  the  spring  c  by  the  plate  n.  On  the  contrary,  as  long  as  the 
spring  a  does  not  touch  one  of  these  appendices  the  current  is  broken. 

For  physiological  effects  the  use  of  the  spring  a  greatly  increases  the 
intensity  of  the  shocks.  For  this  purpose  two  long  spirals  of  copper  wire 
with  handles,/  and  p',  are  fixed  at  n  and  m.  Holding  the  handles  in  the 
hands,  so  long  as  the  spring  a  does  not  touch  the  appendices  z',  the  current 
passes  through  the  body  of  the  experimenter,  but  without  appreciable  effect ; 
while  each  time  that  the  plate  a  touches  one  of  the  appendices  z,  the  current, 
as  we  have  seen  above,  is  closed  by  the  pieces  £,  «,  and  c,  and  ceasing  then 
to  pass  through  the  wires  np,  mp',  there  is  produced  in  this  and  through  the 
body  a  direct  extra-current  which  causes  a  violent  shock. 

This  is  renewed  at  each  half-turn  of  the  electromagnet,  and  its  intensity 
increases  with  the  velocity  of  the  rotation.  The  muscles  contract  with  such 
force  that  they  do  not  obey  the  will,  and  the  two  hands  cannot  be  detached. 

With  an  apparatus  of  large  dimen- 
sions a  continuance  of  the  shock 
is  unendurable. 

All  the  effects  of  voltaic  cur- 
rents may  be  produced  by  the  in- 
duced current  of  Clarke's  machine. 
Fig.  777  shows  how  the  apparatus 
is  to  be  arranged  for  the  decom- 
position of  water.  The  spring  a 
is  suppressed,  the  current  being 
Fig.  784.  Fig.  785.  closed  by  the  two  wires  which  re- 

present the  electrodes. 

For  physiological  and  chemical  effects  the  wire  rolled  on  the  bobbins  is 
fine,  and  each  about  500  or  600  yards  in  length.  For  physical  effects,  on  the 


911]  Magneto-electrical  Machine.  8 1 9 

contrary,  the  wire  is  thick,  and  there  are  about  25  to  35  yards  on  each  bobbin. 
Figs.  784  and  785  represent  the  arrangement  of  the  bobbins  and  the  com- 
mutator in  each  case.  The  first  represents  the  inflammation  of  ether,  and 
the  second  the  incandescence  of  a  metallic  wire,  o,  in  which  the  current  from 
the  plate  a,  to  the  plate  c,  always  passes  in  the  same  direction. 

Pixii's  and  Saxton's  electromagnetic  machine  differs  from  Clarke's  in 
having  the  electromagnet  fixed  while  the  magnet  rotates. 

Wheatstone  devised  a  compendious  form  of  the  magneto-electrical 
machine,  for  the  purpose  of  using  the  induced  spark  in  firing  mines  (794). 

Breguet's  apparatus  for  the  same  purpose  consists  of  a  powerful  horse- 
shoe magnetic  battery,  to  the  ends  of  which  are  screwed  soft  iron  cores, 
round  which  are  coils  of  fine  wires  ;  to  these  are  connected  the  wires  leading 
to  the  mine  to  be  fired.  The  ends  of  the  soft  iron  cores  are  connected  by  a 
soft  iron  keeper;  and  when,  by  a  suitable  mechanism,  this  is  suddenly 
detached  from  the  cores,  a  powerful  momentary  induction  current  is  pro- 
duced in  the  bobbins,  which  is  sufficient  to  fire  more  than  one  fuse,  through 
even  a  considerable  length  of  wire. 

911.  Magneto-electrical  machine. — The  principle  of  Clarke's  apparatus 
has  received  in  the  last  few  years  a  remarkable  extension  in  large  magneto- 
electrical  machines,  by  means  of  which  mechanical  work  is  transformed  into 
powerful  electric  currents  by  the  inductive  action  of  magnets  on  bobbins  in 
motion. 

The  first  machine  of  this  kind  was  invented  by  Nollet,  in  Brussels,  in 
1850  ;  fig.  786  represents  an  improved  form.  It  consists  of  a  cast-iron  frame, 
5^  feet  in  height,  on  the  circumference  of  which,  eight  series  of  five  powerful 
horse-shoe  magnetic  batteries,  A,  A,  A,  are  arranged  in  a  parallel  order  on 
wooden  cross-pieces.  These  batteries,  each  of  which  can  support  from  120 
to  130  pounds,  are  so  arranged  that,  if  they  are  considered  either  parallel  to 
the  axis  of  the  frame,  or  in  a  plane  perpendicular  to  this  axis,  opposite  poles 
always  face  one  another.  In  each  series  the  outside  batteries  consist  of  three 
magnetised  plates,  while  the  three  middle  ones  have  six  plates,  because  they 
act  by  both  faces,  while  the  first  only  acts  by  one. 

On  a  horizontal  iron  axis  going  from  one  end  to  the  other  of  the  frame 
four  bronze  wheels  are  fixed,  each  corresponding  to  the  intervals  between 
the  magnetic  batteries  of  two  vertical  series.  There  are  16  bobbins  on  the 
circumference  of  each  of  these — that  is,  as  many  as  there  are  magnetic  poles 
in  each  vertical  series  of  magnets.  These  bobbins,  represented  in  fig.  788, 
differ  from  those  of  Clarke's  apparatus,  in  having,  instead  of  a  single  wire,  12 
wires  each  1 1£  yards  in  length,  by  which  the  resistance  is  diminished.  The 
coils  of  these  bobbins  are  insulated  by  means  of  bitumen  dissolved  in  oil  of 
turpentine.  These  are  not  rolled  upon  solid  cylinders  of  iron,  but  on  two 
iron  tubes,  split  longitudinally ;  this  device  renders  the  magnetisation  and 
demagnetisation  more  rapid  when  the  bobbins  pass  in  front  of  the  poles  of 
the  magnet.  Further,  the  discs  of  copper  which  terminate  the  bobbins  are 
divided  in  the  direction  of  the  radius,  in  order  to  prevent  the  formation 
of  induced  currents  in  these  discs.  The  four  wheels  being  respectively 
provided  with  16  bobbins  each,  there  are  altogether  64  bobbins  arranged  in 
1 6  horizontal  series  of  four,  as  seen  at  D,  on  the  left  of  the  frame.  The 
length  of  the  wire  on  each  bobbin  being  12  times  u^  yards,  or  138  yards, 

N  x  2 


820 


Dynamical  Electricity, 


[911 


the  total  length  in  the  whole  apparatus  is  64  times    138  yards,  or  8,832 
yards. 

The  wires  are  coiled  on  all  the  bobbins  in  the  same  direction,  and  not 
only  on  the  same  wheel,  but  on  all  four,  all  wires  are  connected  with  one 
another.  For  this  purpose  the  bobbins  are  joined,  as  shown  in  fig.  787 :  on 


liliiiii'illliiB 


Fig.  786. 

the  first  wheel  the  twelve  wires  of  the  first  bobbin,  .r,  are  connected  on  a 
piece  of  mahogany  fixed  on  the  front  face  of  the  wheel  with  a  plate  of  copper, 
;«,  connected  by  a  wire,  O,  with  the  centre  of  the  axis  which  supports  the 
wheels.  At  the  other  end,  on  the  other  face  of  the  wheel,  the  same  wires  are 
soldered  to  a  plate  indicated  by  a  dotted  line  which  connects  them  with  the 
bobbing ;  from  this  they  are  connected  with  the  bobbin  2  by  a  plate,  z',  and 


-911] 


Magneto-electrical  Machine. 


821 


so  on,  for  the  bobbins  /,  w,  .  .  .  up  to  the  last,  v.  The  wires  of  this  bobbin 
terminate  in  a  plate,  «,  which  traverses  the  first  wheel,  and  is  soldered  to  the 
wires  of  the  first  bobbin  of  the  next  wheel,  on  which  the  same  series  of  con- 
nections is  repeated  ;  these  wires  pass  to  the  third  wheel,  thence  to  the 
fourth,  and  so  on,  to  the  end  of  the  axis. 

The  bobbins  being  thus  arranged,  one  after  another,  like  the  elements  of 
;«.  battery  connected  in  a  series  (825),  the  electricity  is  of  high  potential.  But 
the  bobbins  may  also  be  arranged  by  connecting  the  plates  alternately,  not 
with  each  other,  but  with  two  metal  rings  in  such  a  manner  that  all  the  ends 
of  the  same  name  are  connected  with  the  same  ring.  Each  of  these  rings  is 
then  a  pole,  and  this  arrangement  may  be  used  where  a  high  degree  of  po- 
tential is  not  required. 

From  these  explanations  it  will  be  easy  to  understand  the  manner  in 
which  electricity  is  produced  and  propagated  in  this  apparatus.  An  endless 
band  receiving  its  motion  from  a  steam-engine,  passes  round  a  pulley  fixed 
at  the  end  of  the  axis  which  supports  the  wheels  and  the  bobbins,  and  moves 
the  whole  system  with  any  desired  rapidity.  Experience  has  shown  that  to 
obtain  the  greatest  degree  of  light,  the  most  suitable  velocity  is  235  revolu- 


Fig  787. 


Fig.  788. 


tions  in  a  minute.  During  this  rotation  if  we  at  first  consider  a  single 
bobbin,  the  tube  of  soft  iron  on  which  it  is  coiled,  in  passing  in  front  of  the 
poles  of  the  magnet,  undergoes  at  its  two  ends  an  opposite  induction,  the 
effects  of  which  are  added,  but  change  from  one  pole  to  another.  As  these 
tubes,  during  one  rotation,  pass  successively  in  front  of  sixteen  poles 
alternately  of  different  names,  they  are  magnetised  eight  times  in  one  di- 
rection, and  eight  times  in  the  opposite  direction.  In  the  same  time  there 
are  thus  produced  in  the  bobbin  eight  direct  induced  currents  and  eight 
inverse  induced  currents  ;  in  all,  sixteen  currents  in  each  revolution.  \Vitli 
a  velocity  of  235  turns  in  a  minute,  the  number  of  currents  in  the  same  time 
is  235x16  =  3,760  alternately  in  opposite  directions.  The  same  phe- 
nomenon is  produced  with  each  of  the  64  bobbins  ;  but  as  they  are  all  coiled 
in  the  same  direction  and  are  connected  with  each  other,  their  effects 
accumulate,  and  there  is  the  same  number  of  currents,  but  they  are  more 
intense. 

To  utilise  these  currents  in  producing  an  intense  electric  light,  the  com- 
munications are  made  as  shown  in  fig.  789.     On  the  posterior  side  the  last 


822 


Dynamical  Electricity. 


[911- 


bobbin,  ,r',  of  the  fourth  wheel  terminates  by  a  wire,  G,  on  the  axis  MN, 
which  supports  the  wheels  :  the  current  is  thus  conducted  to  the  axis,  and 
thence  over  all  the  machine,  so  that  it  can  be  taken  from  any  desired  point. 
In  the  front  the  first  bobbin,  .r,  of  the  first  wheel  communicates  by  the  wire 
O,  not  with  the  axis  itself  but  with  a  steel  cylinder,  c,  fitted  in  the  axis,  from 
which,  however,  it  is  insulated  by  an  ivory  collar.  The  screw  ^,  to  which 
the  wire  O  is  attached,  is  likewise  insulated  by  a  piece  of  ivory.  From  the 
cylinder  c  the  current  passes  to  a  fixed  metallic  piece,  K,  from  which  it 
passes  to  the  wire  H,  which  transmits  it  to  the  binding  screw  a  of  fig.  786. 
The  binding  screw  b  communicates  with  the  framework,  and  therefore  with 
the  wire  of  the  last  bobbin,  -x'  (fig.  789).  From  the  two  binding  screws  a 
and  £the  current  is  conducted  by  means  of  two  copper  wires  to  two  charcoals, 
the  distance  of  which  is  regulated  by  means  of  an  apparatus  analogous  in 
principle  to  that  already  described  (835). 

In  this  machine  the  currents  are  not  rectified  so  as  to  be  in  the  same 
direction  ;  hence  each  carbon  is  alternately  positive  and  negative,  and  in 


¥         ¥ 


Fig.  789 

fact  they  are  consumed  with  equal  rapidity.  Experiment  has  shown  that, 
when  these  currents  are  applied  to  produce  the  electric  light,  it  is  not  neces- 
sary they  should  be  in  the  same  direction  ;  but  when  they  are  to  be  used 
for  electrometallurgy,  or  for  magnetising,  they  must  be  rectified,  which  is 
effected  by  means  of  a  suitable  commutator. 

This  light,  which  requires  no  other  expenditure  than  that 'of  a  single 
horse-power  to  turn  the  coils  when  there  are  not  more  than  four  of  them,  is 
advantageously  used  for  signalling  by  night  on  large  vessels,  and  for  light- 
houses. One  of  these,  constructed  by  Holmes,  is  now  in  use  at  the  South 
Foreland  lighthouse. 

912.  Siemens'  armature. — Siemens  devised  an  armature  or  bobbin  for 
magneto-electrical  machines,  in  which  the  insulated  wire  is  wound  longi- 
tudinally on  the  core,  instead  of  transversely,  as  is  usually  the  case. 

It  consists  of  a  soft  iron  cylinder,  AB  (fig.  790),  from  one  foot  to  three 
feet  in  length,  according  to  circumstances.  A  deep  groove  is  cut  on  the  outer 
length  of  this  core  and  on  the  ends,  in  which  is  coiled  the  insulated  wire  as 
in  a  multiplier.  To  the  two  ends  of  the  cylinder  brass  discs,  E  and  D,  are 
secured.  With  E  is  connected  a  commutator,  C,  consisting  of  two  pieces  of 
steel  insulated  from  each  other  and  connected  respectively  with  the  two  ends 


-913]  .Siemens  ^Armature.  823 

of  the  wire.     On  the  other  disc  is  a  pulley,  round  which  passes  a  cord,  so 
that  the  bobbin  moves  very  rapidly  on  the  two  pivots. 

When  a  voltaic  current  circulates  in  the  wire,  the  two  cylindrical  seg- 
ments, A  and  B,  are  immediately  magnetised,  one  with  one  polarity  and  the 
other  with  the  opposite.  On  the  other  hand,  if,  instead  of  passing  a  voltaic 
current  through  the  wire  of  the  bobbin,  the  bobbin  itself  be  made  to  rotate 
rapidly  between  the  opposite  poles  of  magnetised  masses,  as  the  segments 
A  and  B  become  alternately  magnetised  and  demagnetised,  their  induction 


Fig.  790. 

produces  in  the  wire  a  series  of  currents  alternately  positive  and  negative, 
as  in  Clarke's  apparatus  (910).  When  these  currents  are  collected  in  a  com- 
mutator which  adjusts  them — that  is,  sends  all  the  positive  currents  on  one 
spring  and  all  the  negative  on  another — these  springs  become  electrodes 
from  one  of  which  positive  electricity  starts  and  from  the  other  negative.  If 
these  springs  are  connected  by  a  conductor,  the  same  effects  are  obtained  as 
when  the  two  poles  of  a  battery  are  united. 

This  armature  has  the  great  advantage  that  a  large  number  of  small 
magnets  may  be  used  instead  of  one  large  one.  As,  weight  for  weight,  the 
former  possesses  greater  magnetic  force  than  the  latter,  they  can  be  made 
more  economically.  And  as  the  armature  is  always  very  near  the  magnets, 
it  receives  greater  momentum,  and  is  more  rapidly  charged. 

913.  Wild's  magneto-electrical  machine. — Mr.  Wild  constructed  a 
magneto-electrical  machine,  in  which  Siemens'  armature  is  used  along  with 
a  new  principle — that  of  the  multiplication  of  the  current.  Instead  of  util- 
ising directly  the  current  produced  by  the  induction  of  a  magnet,  Mr.  Wild 
passes  it  into  a  strong  electromagnet,  and  by  the  induction  of  this  latter  a 
more  energetic  current  is  obtained. 

This  machine  consists  first  of  a  battery  of  12  to  16  magnets  P  (fig.  791), 
each  of  which  weighs  about  3  pounds,  and  can  support  about  20  pounds. 
Between  the  poles  of  the  magnets  two  soft  iron  keepers,  CC,  are  arranged, 
separated  by  a  brass  plate,  O.  These  three  pieces  are  joined  by  bolts,  and 
the  whole  compound  keeper  is  perforated  longitudinally  by  a  cylindrical 
cavity,  in  which  works  a  Siemens'  armature,  n,  about  2  inches  in  diameter. 
The  wire  of  this  armature  terminates  in  a  commutator,  \vhich  leads  the 
positive  and  negative  currents  to  two  binding  screws,  a  and  b.  This  com- 
mutator is  represented  on  a  larger  scale  in  fig.  793.  At  the  other  end  is  a 
pulley  by  which  the  armature  can  be  turned  at  the  rate  of  25  turns  in  a  second. 
The  wire  on  the  armature  is  20  yards  long. 

Below  the  support  for  the  magnets  and  their  armatures  are  two  large 
electromagnets,  BB.  Each  consists  of  a  rectangular  soft  iron  plate,  36  inches 
in  length  by  26  in  breadth  and  i]  inch  thick,  on  which  are  coiled  about  1,600 
feet  of  insulated  copper  wire.  The  wires  of  these  electromagnets  are  joined 


Dynamical  Electricity. 


[913 


at  one  end,  so  as  to  form  a  single  circuit  of  3,200  feet.  One  of  the  other 
ends  is  connected  with  the  binding  screw  a  and  the  other  with  /;.  At  the 
top  the  two  plates  are  joined  by  a  transverse  plate  of  iron  so  as  to  form  a 
single  electromagnet. 


Fig.  791. 


At  the  bottom  of  the  electromagnets  BB  are  two  iron  armatures  separated 
by  a  brass  plate,  O,  and  in  the  entire  length  is  a  cylindrical  channel  in  which 
\vorks  a  Siemens'  armature  ;;/  as  above  :  this  armature,  however,  is  above  a 
yard  in  length,  nearly  6  inches  in  diameter,  and  its  wire  is  100  feet  long. 


-914]  Ladd  's  Dynamomag netic  Machine.  825 

The  ends  are  connected  with  a  commutator,  from  which  the  adjusted  cur- 
rents pass  to  two  wires,  r  and  s.  The  armature  m  is  rotated  at  the  rate  of 
1,700  turns  in  a  minute. 

Fig.  792  shows  on  a  larger  scale  a  cross  section  of  the  bobbin  m  of  the 
armatures  CC  and  of  the  plates  AA,  on  which  is  coiled  the  wire  of  the 
electromagnets  BB. 

These  details  being  premised,  the  following  is  the  working  of  the 
machine  :— When  the  armatures  n  and  m  are  rotated  by  means  of  a  steam 
engine  with  the  velocity  mentioned,  the  magnets  produce  in  the  first  arma- 
ture induced  currents,  which,  adjusted  by  the  commutator,  pass  into  the 
electromagnet  BB,  and  magnetise  it.  But  as  these  impart  to  the  lower 
armatures  CC  opposite  polarities,  the  induction  of  these  latter  produces  in 
the  armature  m  a  series  of  positive  and  negative  currents  far  more  powerful 
than  those  of  the  upper  armature  ;  so  that  when  these  are  adjusted  by  a 
commutator  and  directed  by  the  wires  r  and  j,  very  powerful  effects  are 
obtained. 

These  effects  are  still  further  intensified  if,  as  Mr.  Wild  has  done,  the 
adjusted  current  of  the  armature  m  is  passed  into  a  second  electromagnet, 


Fig.  792.  Fig.  793. 

whose  armatures  surround  a  third  and  larger  Siemens' armature  turning  with 
the  two  others.  A  current  is  thus  obtained  which  melts  an  iron  wire  a  foot 
long  and  more  than  0*2  inch  in  diameter. 

914.  Ladd  s  dynamomagnetic  machine. — -Mr.  Ladd  has  invented  a 
very  remarkable  dynamomagnetic  machine.  It  consists  essentially  of  two 
Siemens'  armatures,  rotating  with  great  velocity,  and  of  two  iron  plates  AA 
(fig.  794)  surrounded  by  an  insulated  copper  wire.  Ladd's  machine  differs 
from  that  of  Wild  in  the  following  respects  : — 

i.  There  are  no  permanent  magnets  :  ii.  the  electromagnets  BB  are  not 
joined  so  as  to  form  a  single  electromagnet,  but  are  two  distinct  electro- 
magnets, each  having  at  the  end  two  hollow  cylinders,  CC',  in  which  are 
fitted  two  Siemens'  armatures,  in  and  ;/ ;  the  current  of  the  armature  n  pass- 
ing round  the  electromagnets  reverts  to  itself.  This  reaction  of  the  current 
upon  itself  is  an  essential  feature  of  the  machine  ;  it  is  an  application  of  a 
principle  announced  simultaneously  by  Sir  C.  Wheatstone  and  by  Mr. 

N  N  3 


826 


Dynamical  Electricity. 


[914- 


Siemens,  and  which  may  be  called  the  dynamo-electiical  principle.  We 
have  in  it  an  analogy  with  Holtz's  machine  (759),  in  which  the  electricity  of 
the  plate  and  conductors  mutually  strengthen  each  other.  The  wire  of  the 


Fig.  794. 

armature  m   is  independent,  and   passes  into  the   apparatus  which  is   to 

utilise  the  current — for  instance,  two  carbon  points,  D. 

The  machine  being 
thus  arranged,  if  a  vol- 
taic current  be  momen- 
tarily passed  once  for 
all  through  the  electro- 
magnets BB,  it  magne- 
tises the  plates  AA  and 
their  keepers,  which  by 
their  reciprocal  action 
retain  a  quantity  of  re- 
manent  magnetism  suffi- 
cient to  work  the  ma- 
chine. If,  then,  the  ar- 
matures m  and  n  be 
rotated  by  means  of 
two  bands  passing  round 
a  common  drum,  the 
magnetism  of  the  hollow 


Fig  795- 


cylinders  CC'  acting  upon  the  armature  «,  excites  induction  currents,  which, 
adjusted  by  a  commutator,  pass  round  the  electro-magnets  BB,  and  more 


-915]  Grammes  Magneto-electrical  Machine.  827 

strongly  magnetise  the  cylinders  or  shoes  CC'.  These,  in  their  turn  reacting 
more  powerfully  on  the  armature  ;/,  strengthen  the  current ;  we  thus  see 
that  //  and  B  continually  and  mutually  strengthen  each  other  as  the  velocity 
of  the  rotation  increases.  Hence,  as  the  iron  of  the  armature  m  becomes 
more  and  more  strongly  magnetised  under  the  influence  of  the  electro- 
magnets BB,  a  gradually  more  intense  induced  current  is  developed  in 
this  armature,  which  is  directed,  commutated  or  not,  according  to  the 
use  for  which  it  is  designed.  The  initial  action  of  the  voltaic  battery  is  not 
even  necessary  ;  the  traces  of  magnetisation  present  in  all  iron  is  sufficient 
to  start  it. 

In  a  machine  exhibited  at  the  Paris  Exhibition  of  1867  the  plates  AA 
were  only  24  inches  in  length  by  12  inches  in  width.  With  these  small 
dimensions  the  current  is  equal  to  that  of  25  to  30  Bunsen's  cells.  It  can 
work  the  electric  light  and  keep  incandescent  a  platinum  wire  a  metre  in 
length  and  0-5  mm.  in  diameter. 

The  above  form  of  the  machine  is  worked  by  steam  power.  Mr. 
Ladd  has  devised  a  more  compact  form,  which  may  be  worked  by  hand. 
This  is  represented  in  fig.  795.  The  two  armatures  are  fixed  end  to 
end,  and  the  coils  are  wound  on  it  at  right  angles  to  each  other,  as  shown 
in  the  figure.  The  current  from  this  can  raise  to  white  heat  18  inches  of 
platinum  wire  O'Oi  in.  in  thickness,  and  with  an  inductorium  (916)  containing  3 
miles  of  secondary  wire  2  in.  sparks  can  be  obtained. 

Both  Ladd's  and  \Vild:s  machines  are  liable  to  the  objection  of  requiring 
to  be  rotated  at  a  rapid  rate.  The  armatures  become  heated  by  the  re- 
peated development  of  induction  currents.  This  has  been  remedied  by 
Mr.  Ladd,  who  has  introduced  into  the  shoes  or  hollow  cylinders  several 
apertures  through  which  a  stream  of  cold  water  is  made  to  flow. 

915.  Grammes  magneto- electrical  machine. — The  magneto-electrical 
machines  which  have  hitherto  been  described  are  all  open  to  the  objection 
that  they  only  give  momentary  currents,  alternately  positive  and  negative. 
These  currents  may  indeed  be  used  for  lighting  and  for  physiological  purposes, 
but  for  other  applications,  such  as  for  electro-plating,  they  must  be  rectified '; 
that  is,  by  means  of  a  commutator,  they  must  be  sent  always  in  the  same 
direction.  This,  however,  is  in  all  cases  accompanied  by  a  certain  loss  of 
electricity,  and  sparks  are  produced  which  rapidly  wear  away  the  armatures 
of  the  commutators. 

These  inconveniences  are  not  met  with  in  an  apparatus  invented  by  M. 
( Gramme,  of  which  fig.  796  is  a  representation  in  about  -*-  of  the  real  size. 
On  a  base  is  fixed  vertically  a  powerful  magnetic  battery  A  (fig.  796),  con- 
structed of  24  steel  plates,  each  i  mm.  in  thickness,  then  separately  magne- 
tised to  saturation.  To  the  two  poles  are  affixed  two  soft  iron  armatures  a 
and  ^,  between  which  an  axle  is  rotated  by  means  of  a  wheel  and  rack- 
work.  On  this  axle  is  a  ring  on  which  are  coiled  a  series  of  thirty  bobbins. 
The  ring  itself  is  not  solid,  but  consists  of  a  coil  of  a  number  of  turns  of  soft 
iron  wire  as  seen  in  fig.  797  ;  the  wire  is  continuous,  and  the  two  ends  are 
soldered  together. 

On  this  core  are  coiled  the  bobbins,  BCD;  they  are  united  by  thin  brass 
knee  plates  ;////,  to  each  of  which  are  soldered  the  copper  wires  of  two  suc- 
cessive bobbins,  so  as  to  form  a  continuous  whole.  The  plates  are  insulated 


828 


Dynamical  Electricity. 


[915- 


from  each  other  and  are  fixed  on  a  wooden  block  0,  mounted  on  the  axis 
of  rotation.     The  branches  m  n  of  the  knee  plates  form  a  sheath  about 

this  axis,  and  two  flat 
brushes  of  copper  wire, 
fixed  to  the  binding 
screws  c  and  z,  are  in 
contact  with  the  upper 
and  lower  parts  of  this 
sheath  and  receive  the 
currents  which  originate 
in  the  coils. 

In  order  to  under- 
stand the  formation  of 
these  currents  it  must  be 
observed  that  each  pole, 
a  and  b  of  the  magnet, 
produces  two  magnetic 
poles  in  the  annular 
bundle  on  which  the 
bobbins  are  coiled.  These 
poles  alter  their  position 
In  the  mass  of  the  bundle 
as  it  turns,  but  are  really 
fixed  in  space  in  presence 
of  the  poles  a  and  b  :  so 
that  the  result  is  the 
same  as  if,  the  magnetised 
bundle  being  fixed,  the 
bobbins  moved  along  its  periphery,  receding  from  one  pole  and  approach- 
ing the  other. 

Hence,  if  we  suppose  the  ring  of 
bobbins  to  tiirn  from  a  towards  b  above 
and  taking  into  consideration  on  the 
one  hand  the  Amperian  currents  which 
circulate  round  the  core,  and  on  the 
other  hand  Lenz's  law,  it  will  be  seen 
that  if  the  direct  current  produced 
is  negative  in  the  coils  which  recede 
from  a,  the  inverse  current  developed 
in  the  bobbin  approaching  b  is  also 
negative.  But  as  all  the  coils  are  con- 
nected, these  two  currents  unite  to  form 
a  single  one  which  passes  by  the  upper 
plates  to  the  wire  brush  fixed  to  the 
binding  screw  i.  Two  positive  currents, 
which  originate  in  like  manner  in  the 

lower  half  of  the  coils,  unite  in  the  brush  which  proceeds  from  the  binding 
screw  c  ;  hence  a  negative  current  is  continually  starting  from  the  terminal 
z,  and  a  positive  current  from  the  terminal  •£. 


Fig.  796. 


-916]  Applications  of  Magneto-electrical  Machines.          829 

Gramme's  machine  is  reversible  ;  for  while  by  its  means  motion  is  con- 
verted into  electricity,  it  can  in  like  manner  convert  electricity  into  motion  ; 
this  may  be  seen  by  connecting  the  binding  screws  c  and  i  with  the  poles 
of  a  Grove's  battery.  This  iron  core  then  becomes  magnetised  by  the 
action  of  the  current  passing  through  the  coils ;  the  whole  system  rotates 
rapidly  under  the  influence  of  the  magnetised  bundle. 

This  apparatus  is  very  powerful ;  the  smallest  size  made  can  decompose 
water,  and  heat  to  redness  an  iron  wire  20  centimetres  in  length  and  a 
millimetre  in  diameter.  Mascart  and  Angot  determined  the  electromotive 
force  of  different  Gramme's  machines  by  placing  in  the  circuit  of  the 
machine,  but  in  opposition  to  it,  a  number  of  DanielFs  elements.  The 
velocity  of  rotation  was  then  increased  until  a  galvanometer  in  the  circuit 
was  not  deflected.  When  this  was  the  case,  seeing  that  the  resistance 
traversed  by  the  opposing  currents  was  the  same,  it  is  clear  that  the  electro- 
motive force  due  to  the  machine  rotating  at  a  given  speed  is  exactly  equi- 
valent to  that  of  the  corresponding  number  of  dements.  Thus,  for  instance, 
the  current  from  3  Daniell's  cells  was  found  to  annul  that  of  a  particular 
Gramme's  machine  rotating  with  a  velocity  of  10*2  turns  per  second.  The 
average  electromotive  force  due  to  this  machine  was  found  equal  to  0*27  of 
a  Daniell  for  a  velocity  of  I  turn  per  second.  With  another  the  ratio 
\\as  0-31,  and  with  others  again  as  much  as  0*8  of  a  Daniell. 

916.  Applications  of  magneto-  and  dynamo-electrical  machines. — 
Great  improvements  have  of  late  been  made  in  magneto-electrical  machines, 
both  in  the  economy  and  simplicity  of  their  construction  and  also  in  their 
power  ;  for  details  on  these  matters  we  must  refer  to  special  technical  works. 

All  such  machines  as  the  above  which  are  really  conversions  of  mecha- 
nical force  into  electricity  consist  essentially  of  a  wire  moving  in  a  magnetic 
field  (707).  Experiment  has  confirmed  the  prevision  that  the  electro- 
motive force  of  the  currents  thus  produced  is  proportional  to  the  velocity 
with  which  the  circuit  moves  through  the  field — in  other  words,  to  the  speed 
with  which  the  coil  is  rotated  ;  and  secondly,  to  the  intensity  of  the  field, 
with  a  given  speed  and  a  given  field  ;  but  with  varying  increase  of  resistance 
it  is  found  that  the  electromotive  force  increases  with  an  increase  in  the  ex- 
ternal resistance  to  a  certain  limit,  after  which  it  is  constant. 

The  energy  of  any  electrical  current  is  measured  by  the  product  of  the 
electromotive  force  into  the  strength  of  the  current  itself. 

A  magneto-electrical  machine  maybe  compared  to  a  pump  forcing  water 
through  a  pipe  against  friction  ;  the  electrical  current  corresponds  to  the 
volume  of  water  passing  in  a  second,  and  the  electromotive  force  corresponds 
to  the  difference  in  pressure  on  the  two  sides  of  the  pump.  Just  as  the 
power  of  a  pump  is  measured  by  the  product  of  the  pressure  and  volume  per 
second,  so  the  product  of  the  electromotive  force  and  pressure  is  power,  and 
the  ratio  of  this  power  to  the  power  expended  in  driving  the  magneto-elec- 
trical machine,  is  the  efficiency  of  the  magneto-electrical  machine.  The 
peculiarity  of  the  dynamo-electrical  machine  is  this,  that  the  electromotive 
force,  or  the  element  corresponding  to  difference  of  pressure  in  the  case  of  a 
pump,  depends  directly  on  the  current  passing.  It  does  not  increase  in- 
definitely with  increase  of  current,  but  increases  to  a  certain  limit,  and  then 
remains  constant. 


830  Dynamical  Electricity.  [916- 

Hopkinson  made  a  series  of  experiments  with  a  machine  of  Siemens' 
construction,  where  special  arrangements  were  made  for  determining  the 
speed  at  which  the  machine  was  driven,  the  driving  power,  the  resistances  in 
the  circuit  and  the  current  passing,  or  the  difference  in  potential  between 
the  two  ends  of  a  known  resistance  in  the  circuit.  He  thus  found,  that  to 
drive  the  machine  in  open  circuit  at  a  speed  of  720  vibrations,  required  an 
expenditure  of  0*28  horse  power.  Exclusive  of  friction,  the  efficiency  of  the 
machine  was  about  90  per  cent. 

If  the  relation  between  the  electromotive  force  measured  in  volts  (814), 
and  the  strength  of  the  current  measured  in  webers  (814),  for  a  given  speed 
of  rotation  be  expressed  by  a  curve,  it  is  found  that  this  curve  has  the  form 
of  a  slanting  straight  line  starting  from  the  origin,  and  then  begins  to  bend 
away  approaching  a  horizontal  line.  The  point  at  which  it  begins  to  bend 
away  is  when  the  electromotive  force  is  about  two-thirds  of  its  maximum, 
and  this  is  called  by  Hopkinson  the  critical  citrrent ;  it  has  this  physical 
meaning,  that  below  this  point  any  change  in  the  speed  of  rotation,  with  a 
steady  external  resistance,  or  any  change  in  the  external  resistance  with  a 
constant  speed  of  rotation,  produces  considerable  changes  in  the  current. 

The  principal  application  which  has  been  made  of  the  currents  produced 
by  magneto-electrical  machines,  is  to  the  production  of  the  electrical  light 
(837).  In  this  respect  it  may  be  said  that  the  arrangements  for  producing 
the  electricity  are  more  perfect  than  those  for  producing  the  light  ;  for  while 
90  per  cent,  of  the  power  used  appears  in  the  form  of  current,  only  about 
half  of  that  which  is  transmitted  to  the  machine  appears  in  the  electrical  arc. 

For  electrodes  of  a  definite  material,  kept  at  a  definite  distance  apart, 
and  under  the  ordinary  atmospheric  pressure,  the  difference  of  potential  is 
approximately  constant.  The  product  of  difference  of  potential  into  the 
current  passing,  is  the  work  developed  in  the  arc,  and  this  divided  by  the 
power  of  driving  the  machine,  is  the  efficiency  of  the  electrical  arc. 

Comparing  together  the  relative  costs  of  producing  a  certain  degree  of 
illumination — #,  by  means  of  gas  ;  ^,  by  the  electrical  arc  with  alternating 
currents  ;  <r,  by  one  with  continuous  currents,  the  machines  for  the  production 
of  the  last  two  being  worked  by  a  gas  engine — it  was  found  that  the  ratio  was 
as  116  :  62  :  15  ;  when  the  machine  was  heated  by  coal  instead  of  gas  the 
cost  was  as  116  :  50  :  10,  it  being  assumed  that  four  pounds  of  co'al  produce 
one  horse  power  per  hour.  The  actual  cost  of  lighting  the  British  Museum 
with  a  light  representing  18,800  candles  was  six  shillings  an  hour,  of  which 
the  carbons  cost  nearly  one  half.  The  cheapening  of  the  electrical  light  is 
in  great  measure  a  question  of  cheapening  the  carbons. 

Edison  in  America  and  Swan  in  this  country  have  come  nearest.  The 
essential  features  of  Swan's  lamp  are,  a  carbon  '  wire '  of  extraordinary  den- 
sity, tenacity,  and  elasticity  which  is  made  incandescent  by  passing  the 
current  through  it  in  a  permanently  exhausted  receiver.  Each  of  these 
filaments  is  about  the  T~  of  an  inch  in  diameter,  and  weighs  about  T\  of  a 
grain.  The  light  of  such  a  lamp  varies  from  36  to  50  candles,  and  as  many 
as  thirty-six  such  lights  have  been  produced  by  a  dynamo-electrical  machine 
worked  by  four  horse  power. 

Siemens  made  a  series  of  experiments  on  the  influence  of  the  electrical 
light  on  vegetation.  The  light  was  produced  by  a  dynamo-electrical  machine 


-916]          Applications  of  Magneto-electrical  Machines.  831 

of  his  construction,  and  was  equal  in  illuminating  power  to  1,400  candles.  Of 
a  series  of  four  sets  of  quickly  growing  plants  in  pots,  such  as  mustard,  beans, 
&c.,  one  set  was  left  in  the  dark,  and  two  other  sets  were  exposed  to  the  action 
of  the  daylight  and  of  the  electric  light  separately  ;  while  the  fourth  was  ex- 
posed to  the  joint  action  of  the  two  lights.  The  first  set  sowed,  withered  and 
died  ;  those  exposed  to  the  electric  light  grew  and  flourished,  but  not  so  vigor- 
ously as  those  exposed  to  daylight  alone  ;  there  was,  however,  a  marked  im- 
provement in  the  case  of  those  which  had  been  exposed  to  the  conjoint  action 
of  both  lights  :  they  showed  the  most  vigorous  growth.  Plants  did  not  seem 
to  require  a  period  of  repose,  but  made  increased  and  vigorous  progress  if 
subjected  at  daytime  to  sunlight,  and  by  night  to  the  electric  light. 

The  electric  light  is  beneficial  not  merely  in  such  plants  as  the  above, 
but  also  in  promoting  the  formation  of  aromatic  and  saccharine  substances 
on  which  the  ripening  of  fruits  depends  ;  this  was  well  seen  in  some  experi- 
ments in  which  early  strawberries  were  forced. 

Abney  found  that  the  luminosity  and  also  the  actinic  action  of  the  light 
produced  by  the  electric  arc  increased  more  rapidly  than  in  direct  ratio  to 
the  velocity  of  rotation,  and  the  horse  power  required  to  produce  it.  This 
increase  was  slowest  for  red  light,  more  rapid  with  blue,  and  most  rapid  of 
all  with  the  actinic  action.  With  a  speed  of  565  rotations,  and  an  expendi- 
ture of  nine  horse  power,  the  actinic  action  was  equal  to  that  of  1 1,000  candles. 
Cohn  found  that  the  electrical  light  is  more  favourable  for  the  pure  per- 
ception of  colour  than  any  other  light  of  equal  luminosity. 

It  is  probable  that  the  temperature  which  can  be  produced  by  the  oxy- 
hydrogen  flame  is  limited  and  has  been  already  reached,  and  that  we  must 
look  to  the  electrical  arc  for  the  production  of  higher  temperatures  than 
those  at  which  carbonic  acid  and  water  are  decomposed.  Direct  experi- 
ments by  Siemens  with  the  electrical  arc  show  not  only  that  it  produces  a 
very  high  temperature  within  a  contracted  space,  but  also  that  it  will  con- 
veniently and  economically  produce  such  larger  effects  as  will  render  it 
useful  for  many  purposes  in  the  arts,  like  the  fusion  of  platinum  and  steel. 
He  constructed  an  arrangement  by  which  the  electric  arc  was  formed  within 
a  crucible  made  of  the  most  refractory  materials  ;  the  one  electrode  passed 
through  the  bottom  of  the  crucible  and  the  other  through  the  lid,  and  there 
was  an  arrangement  by  which  the  distance  of  the  electrodes  could  be  auto- 
matically regulated  ;  another  important  point  was  to  constitute  the  posi- 
tive pole  of  the  material  to  be  fused,  as  it  is  at  this  pole  that  the  heat 
is  principally  developed.  A  dynamo-machine  capable  of  producing  a  current 
of  36  webers,  and  which  produces  a  light  equal  to  6,000  candles,  fused  a 
kilogramme  of  steel  within  half  an  hour.  Siemens  calculated  that  the  heat 
in  his  furnace  represented  £  of  the  horse  power  expended  in  working  the 
machine  ;  and  as  a  good  engine  only  utilises  about  £  of  the  combustible 
value  of  the  coal  employed  in  working  them,  it  follows  that  the  electrical 
furnace  utilises  ~  of  the  energy  residing  in  the  fuel  under  the  engine.  The 
electrical  furnace  is  theoretically  more  economical  than  the  ordinary  air 
furnaces. 

The  magneto-electrical  machine  has  also  been  applied  to  propelling 
carriages  along  a  railway.  A  narrow-gauge  railway  was  laid  down,  and 
upon  this  a  train  of  three  or  four  carriages  was  laid,  and  on  the  first  of  these 


832  Dynamical  Electricity.  [916- 

a  medium-sized  dynamo-machine,  so  fixed  and  connected  with  the  axle  of 
one  pair  of  wheels  as  to  give  motion  to  the  same.  The  two  rails,  being  laid 
upon  wooden  sleepers,  were  sufficiently  insulated  to  serve  for  electrical  con- 
ductors. Between  the  two  rails  a  bar  of  iron  was  fixed  on  wooden  supports, 
through  which  the  current  was  conveyed  to  the  train  by  brushes  fixed  to  the 
driving  carriage,  while  the  return  circuit  was  completed  through  the  rails. 
At  the  station  the  centre  bar  and  rails  were  electrically  connected  with  the 
poles  of  a  dynamo-machine  like  that  on  the  carriage,  and  which  was  worked 
from  a  fixed  steam  engine  on  the  ground.  The  magneto-machine  exerted 
five  horse  power,  and  it  travelled  with  a  velocity  of  15  to  20  miles  an  hour. 
There  is  reason  to  expect  that  this  application  of  magneto-electrical 
machines  will  be  of  service  in  mines,  and  in  railway  tunnels  more 
especially,  in  the  cases  in  which  water  power  is  available. 

Hitherto  the  attempts  made  to  subdivide  the  electrical  light  have  not 
been  completely  successful. 

917.  Znductoriuxn.  RuhmkorfTs  coil. — These  are  arrangements  for 
producing  induced  currents,  in  which  a  current  is  induced  by  the  action  of 
an  electric  current,  wiiose  circuit  is  alternately  opened  and  closed  in  rapid 
succession.  These  instruments,  known  as  inductoriums  or 'induction  coils \ 
present  considerable  variety  in  their  construction,  but  all  consist  essentially 
.of  a  hollow  cylinder  in  which  is  a  bar  of  soft  iron,  or  bundle  of  iron  wires, 
with  two  helices  coiled  round  it,  one  connected  with  the  poles  of  a  battery, 
the  current  of  which  is  alternately  opened  and  closed  by  a  self-acting 


Fig.  798. 

arrangement,  and  the  other  serving  for  the  development  of  the  induced 
current.  By  means  of  these  apparatus,  with  a  current  of  three  or  four 
Grove's  cells,  physical,  chemical,  and  physiological  effects  are  produced  equal 
to  and  superior  to  those  obtainable  with  electrical  machines  and  even  the 
most  powerful  Leyden  batteries, 

Of  all  the  forms  those  constructed  by  Ruhmkorff  are  the  most  powerful. 
Fig.  798  is  a  representation  of  one,  the  coil  of  which  is  about  14  inches  in 
length.  The  primary  or  inducing  wire  is  of  copper,  and  is  about  2  mm.  in 
diameter  and  40  or  50  yards  in  length.  It  is  coiled  directly  on  a  cylinder  of 
cardboard,  which  forms  the  nucleus  of  the  apparatus,  and  is  enclosed  in  an 
insulating  cylinder  of  glass,  or  of  caoutchouc.  On  these  is  coiled  \hzsecond- 


-918] 


RuJnnkorff's  Coil. 


833 


tiry  or  induced  \\\re,  which  is  also  of  copper,  and  is  about  \  mm.  in  diameter. 
A  great  point  in  these  apparatus  is  the  insulation.  The  wires  are  not  merely 
insulated,  by  being  in  the  first  case  covered  with  silk,  but  each  individual 
coil  is  separated  from  the  rest  by  a  layer  of  melted  shellac.  The  length  of 
the  secondary  wire  varies  greatly  ;  in  the  largest  size  hitherto  made,  that  of 
Mr.  Spottiswoode,  it  is  as  much  as  280  miles.  With  these  great  lengths  the 
wire  is  thinner,  about  \  mm.  The  thinner  and  longer  the  wire  the  higher 
the  potential  of  the  induced  electricity. 

The  following  is  the  working  of  the  apparatus  :— The  current  arriving  by 
the  wire  P  at  a  binding  screw,  a,  passes  thence  in  the  commutator  C,  to  be 
afterwards  described  (fig.  80 1),  thence  by  the  binding  screw  b  it  enters  the 
primary  wire,  where  it  acts  inductively  on  the  secondary  wire  ;  having  tra- 
versed the  primary  wire,  it  emerges  by  the  wire  s  (fig.  799).  Following  the 
direction  of  the  arrows,  it  will  be  seen  that  the  current  ascends  in  the 
binding  screw  /,  reaches  an  oscillating  piece  of  iron,  /?,  called  the  hammer, 
descends  by  the  anvil  /f,  and  passes  into  a  copper  plate,  K,  which  takes  it 
to  the  commutator  C.  It  goes  from  there  to  the  binding  screw  c,  and 
finally  to  the  negative  pole  of  the 
battery  by  the  wire  X. 

The  current  in  the  primary  wire 
only  acts  inductively  on  the  second- 
ary wire  (898),  when  it  opens  or 
closes,  and  hence  must  be  con- 
stantly interrupted.  This  is  effected 
by  means  of  the  oscillating  hammer 
o  (fig.  799).  In  the  centre  of  the 
bobbin  is  a  bundle  of  soft  iron  wires, 
forming  together  a  cylinder  a  little 
longer  than  the  bobbin  and  thus 
projecting  at  the  end  as  seen  at 
A.  When  the  current  passes  in 
the  primary  wire,  this  hammer  o  is  attracted  ;  but  immediately,  there  being 
no  contact  between  o  and  //,  the  current  is  broken,  the  magnetisation  ceases, 
and  the  hammer  falls  ;  the  current  again  passing,  the  same  series  of  pheno- 
mena recommences,  so  that  the  hammer  oscillates  with  great  rapidity. 

918.  Condenser. — In  proportion  as  the  current  passes  thus  intermittently 
in  the  primary  wire  of  the  bobbin,  at  each  interruption  an  induced  current, 
alternately  direct  and  inverse,  is  produced  in  the  secondary  wire.  But  as  this 
i>  perfectly  insulated,  the  induced  current  requires  such  a  strength  as  to  pro- 
duce very  powerful  effects.  Frzeau  increased  this  strength  still  more  by 
interposing  a  condenser  in  the  primary  circuit. 

This  condenser  (fig.  800)  consists  of  sheets  of  tinfoil  placed  over  each 
other  and  insulated  by  larger  sheets  of  stout  paper,  v,  soaked  in  paraffine  or 
resin.  The  sheets  of  tinfoil  project  at  the  end  of  the  paper,  one  set  at  s  s'  s'', 
and  the  other  at  the  other  end,  at  e  e'  e",  so  that  when  joined  by  a  binding 
screw  the  odd  numbers  form  one  coating  of  a  condenser,  and  the  even 
numbers  the  other  coating.  In  large  condensers,  the  surface  of  each  con- 
denser is  as  much  as  75  square  yards.  The  whole  being  placed  in  a  box 
at  the  base  of  the  apparatus,  one  of  the  coatings,  the  positive,  is  connected 


Fig.  799. 


$34 


Dynamical  Electricity. 


[918- 


Fig.  800. 


with  the   binding   screw  z,  which  receives    the  current  on    emerging  from 
the  bobbin  ;  and  the  other,  the  negative,  is  connected  with   the   binding 

screw  ;«,  which  communi- 
cates by  the  plate  K  with 
the  commutator  C,  and  with 
the  battery. 

To  understand  the 
effect  of  the  condenser,  it 
must  be  observed  that  at 
each  break  of  the  inducing 
current  an  extra  current 
is  produced  in  the  same 
direction,  which,  continuing  in  a  certain  manner,  prolongs  its  duration.  It 
is  this  extra  current  which  produces  the  spark  that  passes  at  each  break 
between  the  hammer  and  the  anvil ;  when  the  current  is  strong  this  spark 
rapidly  alters  the  surface  of  the  hammer  and  anvil,  though  they  are  of 
platinum.  By  interposing  the  condenser  in  the  inducing  circuit,  the  extra 

current,  instead  of  producing  so  strong  a  spark, 
passes  into  the  condenser  ;  the  positive  elec- 
tricity in  the  coating  connected  with  z',  and  the 
negative  in  that  connected  with  m.  But  the 
opposite  electricities  combining  quickly  by  the 
thick  wire  of  the  primary  coil,  by  the  battery 
and  the  circuit  CK;/z,  give  rise  to  a  current 
contrary  to  that  of  the  battery,  which  instanta- 
neously demagnetises  the  bundle  of  soft  iron  : 
the  induced  current  is  thus  shorter  and  more 
intense.  The  binding  screws  m  and  n  on  the 
base  of  the  apparatus  are  for  receiving  this 
extra  current. 

The  commutator  or  key  serves  to  break  contact  or  send  the  current  in 
either  direction.  The  section  in  fig.  Soi  is  entirely  of  brass,  excepting  the 
core  A,  which  is  of  ebonite  :  on  the  two  sides  are  two  brass  plates  CC'. 
Against  these  press  two  elastic  brass  springs,  joined  to  two  binding  screws, 
a  and  c,  with  which  are  also  connected  the  electrodes  of  the  battery.  The 
current  arriving  at  a  ascends  in  C,  thence  by  a  screw  y  it  attains  the  binding 
screw  b  and  the  bobbin  :  then  returning  by  the  plate  K,  which  is  connected 
with  the  hammer,  the  current  goes  to  C'  by  the  screw  .r,  descends  to  c,  and 
rejoins  the  battery  by  the  wire  N.  If,  by  means  of  the  milled  head,  the  key 
is  turned  180  degrees,  it  is  easy  to  see  that  exactly  the  opposite  takes  place  : 
the  current  reaches  the  hammer  by  the  plate  K  and  emerges  at  b.  If,  lastly, 
it  is  only  turned  through  90  degrees,  the  elastic  plates  rest  on  the  ebonite 
A  instead  of  on  the  plates  CC',  and  the  current  is  broken. 

The  two  wires  from  the  bobbin  at  o  and  o'  (fig.  798)  are  the  two  ends  of 
the  secondary  wire.  They  are  connected  with  the  thicker  wires  PP',  so  that 
the  current  can  be  sent  in  any  desired  direction.  With  large  coils  the 
.hammer  cannot  be  used,  for  the  surfaces  become  so  much  heated  as  to  melt. 
But  Foucault  invented  a  mercury  contact-breaker  which  is  free  from  this  in- 
convenience, and  which  is  an  important  improvement. 


Fig.  801. 


-919]  Effects  produced  by  Ruhmkorff's  Coil.  835 

919.  Effects  produced  by  Ruhmkorff's  coil — The  high  degree  of  poten- 
tial which  the  electricity  of  induction  coil  machines  possesses  has  long  been 
known,  and  many  luminous  and  heating  effects  have  been  obtained  by  their 
means.  But  it  is  only  since  the  improvements  which  Ruhmkorff  has  intro- 
duced into  his  coil,  that  it  has  been  possible  to  utilise  all  the  potential  of 
induced  currents,  and  to  show  that  these  currents  possess  powerful  statical 
as  well  as  dynamical  properties. 

Induced  currents  are  produced  in  the  coil  at  each  opening  and  breaking 
of  contact.  But  these  currents  are  not  equal  either  in  duration  or  in  poten- 
tial. The  direct  current,  or  that  on  opening,  is  of  shorter  duration,  but 
higher  potential  ;  that  of  closing  of  longer  duration,  but  lower  potential. 
Hence  if  the  two  ends  P  and  P'  of  the  fine  wire  (figs.  798  and  799)  are  con- 
nected, as  there  are  two  equal  and  contrary  quantities  of  electricity  in  the 
wire  the  two  currents  neutralise  each  other.  If  a  galvanometer  is  placed  in 
the  circuit,  only  a  very  feeble  deflection  is  produced  in  the  direction  of  the 
direct  current.  This  is  not  the  case  if  the  two  ends  P  and  P'  of  the  wire  are 
separated.  As  the  resistance  of  the  air  is  then  opposed  to  the  passage  of  the 
currents,  that  which  has  highest  potential — that  is,  the  direct  one — passes  in 
excess,  and  the  more  so  the  greater  the  distance  of  P  and  P'  up  to  a  certain 
limit  at  which  neither  pass.  There  are  then  at  P  and  P'  nothing  but  poten- 
tials which  are  alternately  contrary. 

The  physiological  effects  of  Ruhmkorff's  coil  are  very  powerful ;  in  fact, 
shocks  are  so  violent  that  many  experimenters  have  been  suddenly  pro- 
strated by  them.  A  rabbit  may  be  killed  with  two  of  Bunsen's  elements, 
and  a  somewhat  larger  number  of  couples  wrould  kill  a  man. 

The  calorific  effects  are  also  easily  observed  ;  it  is  simply  necessary  to 
interpose  a  very  fine  iron  wire  between  the  two  ends  P  and  P'  of  the  induced 
wire  ;  this  iron  wire  is  immediately  melted,  and  burns  with  a  bright  light.  A 
curious  phenomenon  may  here  be  observed,  namely,  that  when  each  of  the 
wires  P  and  P'  terminates  in  a  very  fine  iron  wire,  and  these  two  are  brought 
near  each  other,  the  wire  corresponding  to  the  negative  pole  alone  melts, 
indicating  that  the  tension  is  greater  at  the  negative  than  at  the  positive 
pole. 

The  chemical  effects  are  very  varied  ;  thus,  according  to  the  shape  and 
distance  of  the  platinum  electrodes  immersed  in  water,  and  to  the  degree 
of  acidulation  of  the  water,  either  luminous  effects  may  be  produced  in 
water  without  decomposition,  or  the  water  may  be  decomposed  and  the 
mixed  gases  disengaged  at  the  two  poles,  or  the  decomposition  may  take 
place,  and  the  mixed  gases  separate  either  at  a  single  pole  or  at  both  poles. 

Gases  may  also  be  decomposed  or  combined  by  the  continued  action  of 
the  spark  from  the  coil.  If  the  current  of  a  Ruhmkorff  s  coil  be  passed 
through  a  hermetically  sealed  tube  containing  air,  as  shown  in  fig.  802, 
nitrogen  and  oxygen  combine  to  form  nitrous  acid. 

The  luminous  effects  of  Ruhmkorff's  coil  are  also  very  remarkable,  and 
vary  according  as  they  take  place  in  air,  in  vapour,  or  in  very  rarefied  vapours. 
In  air  the  coil  produces  a  very  bright  loud  spark,  which,  with  the  largest- 
sized  coil  hitherto  made,  that  of  Mr.  Spottiswoode,  has  a  length  of  42 
inches.  In  vacuo  the  effects  are  also  remarkable.  The  experiment  is  made 
by  connecting  the  two  wires  of  the  coil  P  and  P'  with  the  two  rods  of  the 


836 


Dynamical  Electricity. 


[919- 


electrical  egg  (fig.  646)  used  for  producing  in  vacuo  the  luminous  effects  of 
the  electrical  machine.  A  vacuum  having  been  produced  up  to  I  or  2  milli- 
metres, a  beautiful  luminous  trail  is  produced  from  one 
knob  to  the  other,  which  is  virtually  constant,  and  has  the 
same  intensity  as  that  obtained  with  a  powerful  electrical 
machine  when  the  plate  is  rapidly  turned.  This  ex- 
periment is  shown  in  figs.  807  and  808.  Fig.  806  re- 
presents a  remarkable  deviation  which  light  undergoes 
when  the  hand  is  presented  to  the  egg. 

The  positive  pole  of  the  current  shows  the  greatest 
brilliancy  ;  its  light  is  of  a  fiery  red,  while  that  of  the 
negative  pole  is  of  a  feeble  violet  colour  ;  moreover, 
the  latte'r  extends  along  all  the  length  of  the  negative 
rod,  which  is  not  the  case  with  the  positive  pole. 

The  coil  also  produces  mechanical  effects  so  powerful 
tnati  witn  the  largest  apparatus,  glass  plates  two  inches 
thick  have  been  perforated.     This  result,  however,    is 
not  obtained  by  a  single  charge,  but  by  several  successive  charges. 

The  experiment  is  arranged  as  shown  in  fig.  803.  The  two  poles  of  the  • 
induced  current  correspond  to  the  binding  screws  a  and  b  ;  by  means  of  a 
copper  wire,  the  pole  a  is  connected  with  the  lower  part  of  an  apparatus  for 
piercing  glass  like  that  already  described  (fig.  651),  the  other  pole  is  attached 
to  the  other  conductor  by  a  wire  d.  The  latter  is  insulated  in  a  large 


Fig,  802. 


Fig.  803. 


glass  tube  r,  filled  with  shellac,  which  is  run  in  while  in  a  state  of  fusion. 
Between  the  two  conductors  is  the  glass  to  be  perforated,  V.  When  this 
presents  too  great  a  resistance,  there  is  danger  lest  the  spark  pass  in  the  coil 
itself,  perforating  the  insulating  layers  which  separate  the  wires,  and  then  the 
coil  is  destroyed.  To  avoid  this,  two  wires,  e  and  c,  connect  the  poles  of  the 
coil  with  two  metallic  rods  whose  distance  from  each  other  can  be  regulated. 
If  then  the  spark  cannot  penetrate  through  the  glass,  it  strikes  across,  and 
the  coil  is  not  injured. 


-919] 


Effects  .produced  by  Rnhmkorff's  Coil. 


837 


The  coil  can  also  be  used  to  charge  Leyden  jars.  With  a  large  coil, 
giving  sparks  of  6  to  8  inches,  and  using  6  Bunsen's  elements  with  a  large 
surface,  Ruhmkorff  charged  large  batteries  of  6  jars  each,  having  about  3 
square  yards  of  coated  surface. 

The  experiment  with  a  single  Leyden  jar  (fig.  804)  is  made  as  follows  : — 
The  coatings  of  the  latter  are  in  connection  with  the  poles  of  the  coil  by 
the  wires  d  and  /,  and  these  same  poles  are  also  connected,  by  means  of 


Fig.  804. 

the  wires  c  and  <r,  with  the  two  horizontal  rods  of  a  universal  discharger 
ihg.  638).  The  jar  is  then  being  constantly  charged  by  the  wires  /  and  d* 
sometimes  in  one  direction  and  sometimes  in  another,  and  as  constantly 
discharged  by  the  wires  e  and  c ;  the  discharges  from  m  to  //  taking  place  as 


Fig.  805. 

sparks  two  or  three  inches  in  length,  very  luminous,  and  producing  a  deafen- 
ing sound  ;  they  can  scarcely  be  compared  with  the  sparks  of  the  electrical 
machine,  but  are  rather  true  lightning  flashes. 

To  charge  a  battery,  the  form  of  the  experiment  is  somewhat  varied  ;  the 
outer  coating  being  connected  with  one  pole  of  the  coil  by  the  wire  //,  and 


838 


Dynamical  Electricity. 


[919- 


the  inner  coating  with  the  other  by  the  rods  ;«,  «,  and  the  wire  c  (fig.  805). 
The  rods  m  and  n  are  not,  however,  in  contact.  If  they  were — as  the  two 
currents,  the  inverse  and  direct,  pass  .  equally — the  battery  would  not  be 
constantly  charged  and  discharged  ;  while  from  the  distance  between  m  and 
n  the  direct  current,  that  of  opening,  which  has  higher  potential,  passes  alone, 
and  it  is  this  which  charges  the  battery. 

920.  Stratification  of  the  electric  light. — Quet  observed,  in  studying 
the  electric  light  which  Ruhmkorff  s  coil  gives  in  a  vacuum,  that  if  some  of 
the  vapour  of  turpentine,  wood  spirit,  alcohol,  or  bisulphide  of  carbon,  &c., 
be  introduced  into  the  vessel  before  exhaustion,  the  aspect  of  the  light  is 
totally  modified.  It  appears  then  like  a  series  of  alternately  bright  and  dark 
zones,  forming  a  pile  of  electric  light  between  the  two  poles  (fig.  807). 


Fig.  806. 


Fig.  807. 


Fig.  808. 


In  this  experiment  it  follows  from  the  discontinuity  of  the  current  of 
induction,  that  the  light  is  not  continuous,  but  consists  of  a  series  of  dis- 
charges which  are  nearer  each  other  in  proportion  as  the  hammer  o  (fig.  799) 
oscillates  more  rapidly.  The  zones  appear  to  possess  a  rapid  gyratory  and 
undulatory  motion.  Quet  considers  this  as  an  optical  illusion  ;  for  if  the 
hammer  is  slowly  moved  by  the  hand,  the  zones  appear  very  distinct  and 
fixed. 

The  light  of  the  positive  pole  is  most  frequently  red,  and  that  of  the 
negative  pole  violet.  The  tint  varies,  however,  with  the  vapour  or  gas  in  the 
globe. 


-921] 


Geisslers  Tubes. 


839 


921.  Geissler'a  tabes — The  brilliancy  and  beauty  of  the  stratification: 
of  the  electric  light  are  most  remarkable  when  the  discharge  of  the  Ruhm- 
kortf  coil  takes  place  in  glass  tubes  containing  a  highly  rarefied  vapour  or 
gas.  These  phenomena,  which  have  been  investigated,  are  produced  by 
means  of  sealed  glass  tubes  first  constructed  by  Geissler,  of  Bonn,  and  gene- 
rally known  as  Geisslers  tubes.  The  tubes  are  filled  with  different  gases 
or  vapours,*and  are  then  exhausted,  so  that  the  pressure  does  not  exceed  half 
a  millimetre.  At  the  ends  of  the  tubes  two  platinum  wires  are  soldered  into 
the  glass. 

When  the  two  platinum  wires  are  connected  with  the  ends  of  a  Ruhm- 
korff  s  coil,  magnificent  lustrous  striae,  separated  by  dark  bands,  are  produced 


Fig.  809. 

all  through  the  tube.  These  striae  vary  in  shape,  colour,  and  lustre  with  the 
degree  of  the  vacuum,  the  nature  of  the  gas  or  vapour,  and  the  dimensions 
of  the  tube.  The  phenomenon  has  occasionally  a  still  more  brilliant  aspect 
from  the  fluorescence  which  the  electric  discharge  excites  in  the  glass. 

Fig.  809  represents  the  striae  given  by  hydrogen  under  half  a  millimetre 
of  pressure  ;  in  the  bulbs  the  light  is  white,  in  the  capillary  parts  it  is  red. 

Fig.  810  shows  the  striae  in  carbonic  acid  under  a  quarter  of  a  millimetre 
pressure  ;  the  colour  is  greenish,  and  the  striae  have  not  the  same  form  as 
hydrogen.  In  nitrogen  the  light  is  orange  yellow. 


Fig.  810. 

Pliicker  found  that  the  light  in  a  Geissler's  tube  did  not  depend  on 
the  substance  of  the  electrodes,  but  simply  on  the  nature  of  the  gas  or  vapour 
in  the  tube.  He  has  found  that  the  lights  furnished  by  hydrogen,  nitrogen, 
carbonic  oxide,  &c.,  give  different  spectra  when  they  are  decomposed  by 


840  Dynamical  Electricity.  [921- 

a  prism.  The  discharge  of  the  coil  which  passes  through  a  highly  rarefied 
gas  would  not  pass  through  a  perfect  vacuum,  from  which  it  follows  that  the 
presence  of  a  ponderable  substance  is  absolutely  necessary  for  the  passage 
of  electricity. 

By  the  aid  of  a  powerful  magnet  Pliicker  tried  the  action  of  magnetism 
on  the  electric  discharge  in  a  Geissler's  tube,  as  Davy  had  done  with  the 
ordinary  voltaic  arc,  and  obtained  many  curious  results,  one  of  which  may 
be  mentioned.  He  found  that  where  the  dis- 
charge is  perpendicular  to  the  line  of  the  poles,  it  is 
separated  into  two  distinct  parts,  which  can  be 
referred  to  the  different  action  exerted  by  the 
electromagnet  on  the  two  extra  currents  produced 
in  the  discharge. 

The  light  of  Geissler's  tubes  has  been  applied 
to  medical  purposes.  A  long  capillary  tube  is 
soldered  to  two  bulbs  provided  with  platinum 
wires  ;  this  tube  is  bent  in  the  middle,  so  that  the 
two  branches  touch,  and  their  extremities  are 
twisted,  as  shown  at  a  (fig.  811).  This  tube  con- 
tains a  highly  rarefied  gas,  like  those  previously 
described,  and,  when  the  discharge  passes,  a  light 
is  produced  at  a,  bright  enough  to  illuminate  any  cavity  of  the  body  into 
.which  the  tube  is  introduced. 

<)22a.  De  la  Rue  and  IMCiiller's  experiments. — These  physicists  have  ! 
made  a  very  extensive  and  elaborate  series  of  experiments  on  the  stratifica- 
tion of  the  electric  light  by  means  of  the  currents  produced  by  their  battery 
(812).  They  employed  for  some  of  these  experiments  as  many,  as  14,400 
cells,  which  is  by  far  the  most  powerful  battery  ever  put  together.  It  is 
impossible  to  attempt  here  even  a  condensed  account  of  these  experiments  ; 
but  the  following,  which  are  some  of  the  results  obtained,  may  be  men- 
tioned. 

The  discharge  in  a  \racuum  tube  is  essentially  of  the  same  nature  as  that 
which  takes  place   in  gases  under  the  ordinary  atmospheric  pressure.     A 
vacuum  tube  was   interposed  in  the  circuit  of  a  battery  of  2,400  cells,  to-  ; 
gether  with  a  very  long  resistance.    It  was  found  that  the  potentials  at  the  two 
ends  of  the  tube  are  virtually  the  same  ;  now  according  to  Ohm's  law  there  I 
should  be  a  fall  of  potential  along  the  entire  circuit  ;  it  is  accordingly  con-  ; 
eluded  that  the  discharge  is  not  a  current  in  the  ordinary  sense  of  the  term, 
but  is  disruptive,  the  electricity  being  carried  by  the  molecules  of  the  gas. 
At  no  degree  of  exhaustion  is  air  a  conductor. 

All  the  strata  start  from  the  positive  pole.  For  a  definite  pressure  an  I 
aureole  is  formed  at  the  positive  pole  ;  with  a  diminished  pressure  this  de- 1 
taches  itself,  is  succeeded  by  others,  and  so  on. 

One  of  the  most  curious  results  is  the  definite  and  stationary  character  of  I 
the  striae  for  given  conditions  ;  they  are  remarkably  permanent,  and  seem  I 
almost  as  if  they  could  be  manipulated  ;  a  single  stratum  may  be  seen  falling  | 
down  a  tube  like  a  feather  in  a  vacuum,  or  like  a  drop  of  water.     They  are 
not  produced  in  the  same  way  as  drops  falling,  but  each  of  the  little  strata 
•are  so  many  Ley  den  jars. 


-921]  De  la  Rue  and  MilUer's  Experiments.  841 

The  length  of  the  arc  found  between  two  terminals  varies  with  the  square 
of  the  number  of  cells  ;  thus  while  1,000  cells  give  a  spark  of  0-0051  inch 
under  ordinary  atmospheric  pressure,  1 1,000  cells  give  a  spark  of  0-62  in. 

With  an  increase  of  exhaustion  the  potential  necessary  to  cause  a  current 
to  pass  diminishes  to  a  certain  pressure  which  represents  an  exhaustion  of 
least  resistance  ;  from  this  it  again  increases,  and  the  strata  thicken  and 
diminish  in  number  until  a  point  is  reached  at  which  no  discharge  takes 
place,  however  high  be  the  potential. 

A  change  in  the  current  often  produces  an  entire  change  in  the  colour  of 
the  stratification  ;  thus  in  hydrogen  the  change  is  from  blue  to  pink. 

If  the  discharge  is  irregular  and  the  strata  indistinct  an  alteration  in  the 
strength  of  the  current  makes  the  strata  distinct  and  steady.  Even  when 
the  strata  are  apparently  quite  steady  and  permanent,  a  pulsation  may  be 
detected  in  the  current  by  means  of  the  telephone. 

In  the  same  tube,  and  with  the  same  gas,  a  very  great  variety  of  pheno- 
mena can  be  produced  by  varying  the  pressure  and  the  current.  The  pecu- 
liar luminosity  and  form  of  stratification  can  be  reproduced  in  the  same  tube 
or  others  having  similar  dimensions. 

The  colour  of  the  discharge  in  one  and  the  same  gas  greatly  depends  on 
the  degree  of  rarefaction.  The  least  resistance  to  the  discharge  in  hydrogen, 
and  when  its  brilliancy  is  greatest,  is  at  pressure  of  0-642  mm.  or  845  M 
( M  is  a  very  convenient  symbol  for  the  millionth  of  an  atmosphere).  When 
the  rarefaction  has  attained  0*002  mm.  or  3  |\/|,  the  discharge  only  just  passes 
even  with  a  potential  of  1 1,330  volts  ;  while  with  an  exhaustion  of  0-000055 
mm.,  the  nearest  approach  to  a  perfect  vacuum  ever  attained,  not  only  does 
this  fail  to  produce  a  discharge,  but  the  I  inch  spark  of  an  induction  coil 
does  not  pass. 

Air  offers  a  greater  resistance  than  hydrogen  ;  a  spark  which  passes  in 
hydrogen  across  a  distance  of  5-6  mm.  will  only  strike  across  a  distance  of 
3  mm.  in  air. 

In  air  at  a  pressure  of  62  mm.,  which  corresponds  to  an  atmospheric 
height  of  12*4  miles,  the  electric  discharge  has  the  carmine  tint  so  often  seen 
in  the  display  of  the  aurora  borealis  (991) ;  at  a  pressure  of  1-5  mm.,  corre- 
sponding to  a  height  of  30-96  miles,  it  is  salmon  coloured,  and  at  a  pressure 
of  0-8  mm.,  representing  a  height  of  33*96  miles,  it  is  of  a  pale  white.  Under 
a  pressure  of  0-379  mm.  the  discharge  has  the  greatest  brilliancy.  This 
represents  a  height  of  37-67  miles,  and  would  be  visible  at  a  distance  of  585 
miles  ;  it  is  probably  the  upper  limit  of  the  height,  though  on  the  other  hand 
it  is  possible  that  the  discharge  may  sometimes  take  place  at  a  height  of  a 
few  thousand  feet. 

Crookes's  Experiments.  Crookes  has  made  a  remarkable  series  of  ex- 
periments on  the  phenomena  produced  when  the  electrical  discharge  is 
produced  in  tubes  very  highly  exhausted  ;  that  is,  beyond  the  point  at  which 
the  best  effects  of  the  stratification  are  produced.  This  condition  is  re- 
garded by  him  as  an  ultra-gaseous  state  of  matter,  in  which  the  molecules 
traverse  relatively  great  spaces  without  impinging  on  each  other,  and  thus 
each  individual  molecule  is  more  influenced  by  the  action  of  external  forces 
(294).  The  mean  wave  length  is  no  longer  infinitely  small  in  comparison 
with  the  dimensions  of  the  vessel.  Any  adequate  account  of  these  experi- 

o  O 


842 


Dynamical  Electricity. 


[921- 


ments  would  require  an  amount  of  space  and  of  illustration  inconsistent 
with  the  design  of  this  work  ;  and  it  must  be  added  that  the  theoretical  views, 
to  which  Crookes  has  been  led  by  his  experiments,  have  met  with  a  con- 
siderable degree  of  criticism. 

922.  Rotation  of  induced  currents  by  magnets. — De  la  Rive  de- 
vised an  experi- 
ment that  shows  in 
a  most  ingenious 
manner  that  mag- 
nets act  on  the 
light  in  Geissler's 
tubes  in  accord- 
ance with  the  laws 
with  which  they  act 
on  any  other  mov- 
able conductor. 

This  apparatus 
consists  of  a  glass 
globe  or  electrical 
egg  (fig.  812),  pro- 
vided at  one  end 
with  two  stopcocks, 
one  of  which  can  be 
screwed  on  the  air- 
pump  ;  and  the 
other,  which  is  a 
stopcock  like  that 
of  Gay  Lussac 
(383),  serves  to  in- 
troduce a  few  drops 
of  the  liquid  into 
the  globe.  At  the 
other  end  a  tubu- 
lure  is  cemented, 


Fig.  812. 


through  which  passes  a  rod  of  soft  iron  about  \  of  an  inch  in  diameter,  the 
top  of  which  is  about  the  centre  of  the  globe.  Except  at  the  two  ends,  this 
rod  is  entirely  covered  with  a  very  thick  insulating  layer  of  shellac,  then  with 
a  glass  tube  also  coated  with  shellac,  and  finally  with  another  glass  tube 
uniformly  coated  with  a  layer  of  wax.  This  insulating  layer  must  be  at 
least  |  of  an  inch  thick.  Inside  the  globe,  the  insulating  layer  is  surrounded 
at  x  with  a  copper  ring  connected  by  means  of  a  copper  wire  with  a  binding 
screw,  c. 

The  vessel  having  been  exhausted  as  completely  as  possible,  a  few  drops 
of  ether  or  of  turpentine  are  introduced  by  means  of  the  stopcock  a  ;  it  is 
again  exhausted,  so  that  the  vapour  remaining  is  highly  rarefied. 

A  thick  disc  of  soft  iron,  <?,  provided  with  a  binding  screw,  is  then  placed 
on  one  of  the  branches  of  a  powerful  electromagnet,  and  the  end  m  of  the 
rod  mn  is  placed  on  this  disc,  while  at  the  same  time  one  of  the  ends  of  the 
secondary  wire  of  Ruhmkorft's  coil  is  connected  with  the  binding  screw,  CA 
and  the  other  with  the  knob  o.  If  then  the  coil  is  worked  without  setting  in 


-923]  Development  of  He^t  by  Magnetic  Induction.         843 

action  the  electromagnet,  the  electricity  of  the  wire  s  passes  to  the  top  ;/  of 
the  soft  iron  rod,  and  that  of  the  second  wire  to  the  ring  x,  and  a  more  or 
less  irregular  luminous  sheaf  appears  on  the  inside  of  the  globe  round  the 
rod,  as  in  the  experiment  of  the  electric  egg. 

But  if  a  voltaic  current  passes  into  the  electromagnet,  the  phenomenon  is 
different  ;  instead  of  starting  from  different  points  of  the  upper  surface  #, 
and  the  ring  .r,  the  light  is  condensed  and  emits  a  single  luminous  arc  from 
n  to  .r.  Further,  and  this  is  the  most  remarkable  part  of  the  experiment, 
this  arc  turns  slowly  round  the  magnetised  cylinder  mn,  sometimes  in 
one  direction,  and  sometimes  in  another,  according  to  the  direction  of  the 
induced  current,  or  the  direction  of  the  magnetism.  As  soon  as  the  mag- 
netism ceases  the  luminous  phenomenon  reverts  to  its  original  appearance. 

This  experiment  is  remarkable  as  having  been  devised  a  priori  by  De  la 
Rive  to  explain,  by  the  influence  of  terrestrial  magnetism,  a  kind  of  rotatory 
motion  from  east  to  west,  observed  in  the  aurora  borealis.  The  rotation  of 
the  luminous  arc  in  the  above  experiment  can  evidently  be  referred  to  the 
rotation  of  currents  by  magnets. 

Geissler  has  constructed  a  very  useful  form  of  the  above  experiment,  in 
which  the  globe  is  exhausted  once  for  all.  Apart  from  the  purpose  for  which 
it  was  originally  devised,  it  is  a  very  convenient  arrangement  for  demon- 
strating the  action  of  magnets  on  movable  currents. 

923.  Beat  developed  by  the  induction  of  powerful  mag-nets  on  bodies 
in  motion. — We  have  already  seen  in  Arago's  experiments  (912)  that  a  rota- 
ting copper  disc  acts  at  a  distance  on  a  magnetic  needle,  communicating  to  it 
a  rotatory  motion.  We  shall  presently  see  that  a  cube  of  copper,  rotating 
with  great  velocity,  is  suddenly  stopped  by  the  influence  of  the  poles  of  two 
strong  magnets  (932).  It  is  clear  that  in  order  to  prevent  the  rotation  of  the 
needle  or  of  the  copper,  a  certain  mechanical  force  must  be  consumed  in 
overcoming  the  resistance  which  arises  from  the  inductive  action  of  the  mag- 
net. Reasoning  upon  the  theory  of  the  transformation  of  mechanical  work 
into  heat  (497),  it  has  been  attempted  to  ascertain  what  quantity  of  heat 
is  developed  by  the  action  of  induced  currents  under  the  influence  of  power- 
ful magnets.  Joule,  with  a  view  of  determining  the  mechanical  equivalent 
of  heat,  coiled  a  quantity  of  copper  wire  round  a  cylinder  of  soft  iron,  and, 
having  enclosed  the  whole  in  a  glass  tube  full  of  water,  he  imparted  to 
the  system  a  rapid  rotation  between  the  branches  of  an  electromagnet.  A 
thermometer  placed  in  the  liquid  served  to  measure  the  quantity  of  heat 
produced  by  the  induced  currents  in  the  soft  iron  and  the  wire  round  it.  It 
was  thus  found  that  the  heat  developed  was  proportional  to  the  square 
of  the  magnetism  evoked,  and  was  equivalent  to  the  work  used  in  the  rota- 
tion. 

Foucault  made  a  remarkable  experiment  by  means  of  the  apparatus 
represented  in  fig.  813.  It  consists  of  a  powerful  electromagnet  fixed 
horizontally  on  a  table.  Two  pieces  of  soft  iron,  A  and  R,  are  in  contact 
with  the  poles  of  the  magnet,  and,  becoming  magnetised  by  induction, 
they  concentrate  their  magnetic  inductive  action  on  the  two  faces  of  a 
copper  disc,  D,  3  inches  in  diameter,  and  a  quarter  of  an  inch  thick  ; 
this  disc  partly  projects  'between  the  pieces  A  and  B,  and  can  be  moved  by 
means  of  a  handle  and  a  series  of  toothed  wheels  with  a  velocity  of  150  to 
200  turns  in  a  second. 

002 


844  Dynamical  Electricity.  [923- 

So  long  as  the  current  does  not  pass  through  the  wire  of  the  electro- 
magnet, very  little  resistance  is  experienced  in  turning  the  handle;  and 
when  once  it  has  begun  to  rotate  rapidly,  and  is  left  to  itself,  the  rotation 
continues  in  virtue  of  the  acquired  velocity.  But  if  the  current  passes,  the 


Fig.  813. 

disc  and  other  pieces  stop  almost  instantaneously  ;  and  if  the  handle  is 
turned  considerable  resistance  is  felt.  If,  in  spite  of  this,  the  rotation  be 
continued,  the  force  used  is  transformed  into  heat,  and  the  disc  becomes 
heated  to  a  remarkable  extent.  In  an  experiment  made  by  Foucault  the 
temperature  of  the  disc  rose  from  10°  to  61°,  the  current  being  formed  by 
three  of  Bunsen's  elements  ;  with  six  the  resistance  was  such  that  the 
rotation  could  not  long  be  continued. 

924.  The  Telephone. — To  the  number  of  instruments  depending  on  in- 
duction, may  be  added  this  discovery,  which  is  equally  remarkable  for  the 
surprising  character  of  the  results  which  it  produces,  and  for  the  sim- 
plicity of  the  means  by  which  they  are  produced.  Figure  814  represents 
a  perspective,  and  figure  815  a  section,  of  the  telephone  as  improved  by  its 
inventor,  Mr.  Graham  Bell. 

It  consists  essentially  of  a  steel  magnet  of  about  4  inches  in  length  by 
half  an  inch  in  diameter,  enclosed  in  a  wooden  case.  Round  one  end  of  this 
magnet  is  fitted  a  thin  flat  bobbin  B  B  of  fine  insulated  copper  wire.  For  a 
magnet  of  this  size  a  length  of  250  metres  of  No.  38  wire,  offering  a  resist- 
ance of  350  ohms,  is  well  suited. 

The  ends  of  this  coil  pass  through  longitudinal  holes,  L  L,  in  the  case, 
and  are  connected  with  the  binding  screws  C  C.  In  front  of  the  magnet  and 
at  a  distance  which  can  be  regulated  by  a  screw  S,  but  which  is  something 
less  than  a  millimetre,  is  the  essential  feature  of  the  instrument — a  diaphragm 
D  of  soft  iron,  not  much  thicker  than  a  sheet  of  stout  letter  paper.  This 
diaphragm  is  screwed  down,  by  the  mouthpiece  E,  which  is  similar  to, 
though  somewhat  larger  than,  that  of  a  stethoscope. 


-924]  The  Telephone.  845 

The  instruments  are  connected  by  wires,  for  one  of  which  the  earth  may 
be  substituted,  as  in  ordinary  telegraphic  communication  (884).  Each 
instrument  can  be  used  either  as  sender  or  receiver,  though  in  actual 
practice  it  is  more  convenient  for  each  ope- 
rator to  have  two  telephones,  one  of  which 
is  held  to  the  ear,  while  the  other  is  used  for 
speaking  into;  the  latter  being  larger  and 
more  powerful  than  the  receiver. 

The  action  of  the  instrument  depends  on 
the  fact  that  whenever  the  relative  positions 
of  a  magnet  and  of  a  closed  coil  of  wire  are 
altered  there  is  produced  within  the  coil  a 
current  or  currents  of  electricity.  This  may 
be  illustrated  by  reference  to  fig.  770.  When 
the  magnet  is  suddenly  brought  into  the  coil 
a  current  is  produced  in  the  coil  in  a  parti- 
cular direction.  There  is  no  current  so  long, 
as  the  coil  and  the  magnet  are  stationary.  - 
When,  however,  the  magnet  is  suddenly  with- 
drawn, a  current  is  produced  in  the  oppo- 
site direction.  Similar  effects  are  produced. 
if,  while  the  m?gnet  is  in  the  coil,  its  mag- 
netism is  by  any  means  increased  or  dimi- 
nished. 

Now  in  the  telephone  the  magnet  and  the 
coil,  when  once  properly  adjusted,  remain 
fixed.  But  the  magnet  M  magnetises  by  in- 
duction the  soft  iron  membrane  D  in  front  of 
it  ;  that  is,  converts  it  into  a  magnet.  When, 
by  the  mouthpiece  being  spoken  into,  this 
iron  membrane  vibrates  backwards  and  forwards,  these  vibrations  give  rise 
to  an  alteration  in  the  magnetism  of  the  permanent  magnet,  the  effect  of 


Fig.  814. 


Fig.  815. 

which  is  that  currents  are  produced  in  alternate  directions  in  the  coil 
surrounding  the  pole.  Moreover,  the  alteration  in  the  relative  positions  of 
the  magnetised  diaphragm,  thus  magnetised  by  induction,  and  of  the  coil, 
give  rise  to  currents  in  the  same  direction  as  the  above.  These  alternating 


846  Dynamical  Electricity.  [924- 

currents  being  transmitted  through  the  circuit  to  the  distant  coil,  alternately 
attract,  and  cease  to  attract,  the  corresponding  diaphragm.  They  thereby 
put  this  in  vibration  ;  and,  when  the  mouthpiece  of  this  telephone  is  held  to 
the  ear,  these  vibrations  are  perceived  as  sound  corresponding  to  that  which 
is  transmitted.  Hence,  whatever  sound  produces  the  vibration  of  the  dia- 
phragm of  the  sending  instrument  is  repeated  by  that  of  the  receiver. 

The  reproduction  of  the  sound  in  the  receiving  instrument  is  perfect  as 
far  as  articulation  is  concerned,  but  it  is  considerably  enfeebled,  as  might  be 
expected.  The  sound  has  something  of  a  metallic  character,  appearing  as 
if  heard  through  a  long  length  of  tubing,  while  it  faithfully  reproduces  the 
characteristics  of  the  person  speaking.  It  does  not  result  from  a  series  of 
sharp  and  distinct  makes  and  breaks  ;  but  in  each  of  the  momentary  currents 
there  is  a  continuous  rise  and  fall,  corresponding,  in  every  gradation  and 
inflexion,  to  the  motion  of  the  air  agitated  by  the  speaker.  No  telephone 
can  produce  the  letter  S. 

The  amplitude  of  the  vibration  of  the  disc  is  extremely  small.  According 
to  Bosscha  a  unit  current  produced  a  displacement  of  0-034  of  a  mm.  ;  and,  as 
currents  of  a~^  of  this  are  perceptible,  it  follows  that  the  amount  of  displace- 
ment must  be  about  the  ^  of  the  wave-length  of  yellow  light  (637). 

The  current  in  a  telephone  is  estimated  by  De  la  Rue  as  not  exceeding 
that  which  would  be  produced  by  one  DanielPs  cell  in  a  circuit  of  copper 
wire  4  mm.  in  diameter  of  a  length  sufficient  to  go  290  times  round  the  earth. 
This  current  would  have  to  pass  19  years  through  a  voltameter,  to  produce 
i  c.  c.  of  detonating  gas.  This  is  about  1,000  million  times  less  than  the  cur- 
rents in  ordinary  use.  Such  currents  are,  however,  sufficient  to  cause  the 
contraction  of  a  frog's  leg. 

Siemens  estimates  that  not  more  than  y^o  of  the  mass  of  sound  which 
the  sender  receives  is  reproduced.  That  it  is  possible  to  perceive  this,  is  due 
to  the  great  sensitiveness  and  range  of  the  ear,  which  can  endure  the  sound 
of  a  cannon  at  a  distance  of  5  yards,  and  still  perceives  it  at  a  distance 
10,000  times  as  great.  This  represents  a  ratio  of  intensities  of  one  to  one 
hundred  millions. 

From  some  experiments  on  the  transmission  of  the  sound  of  a  high  pitched 
tuning-fork  (251)  Rontgen  concludes  that  no  less  than  24,000  currents  are 
transmitted  in  one  second. 

This  extreme  delicacy  of  the  telephone  is  its  drawback  to  speaking 
through  ordinary  telegraph  circuits.  The  currents  in  the  adjacent  wires,  and 
the  vibration  of  the  posts  and  of  the  insulators,  the  passage  of  a  cart  over 
the  streets,  acts  by  induction  on  the  telephone  circuit,  and  destroys  its  indi- 
cations. When  a  telephone  circuit  was  placed  at  a  distance  of  20  metres 
from  a  well  insulated  line,  through  which  signals  were  sent  by  means  of  a 
battery  of  a  few  elements,  sounds  were  distinctly  heard  in  the  telephone. 
Speaking  under  such  circumstances  is  like  speaking  in  a  storm. 

Telephones  have  been  constructed  in  which  the  thin  iron  plate  is  re- 
placed by  a  thicker  one,  or  by  an  unmagnetic  one  ;  or  if  the  telephone  is 
held  close  to  the  ear,  the  plate  can  be  dispensed  with  altogether.  In  the 
latter  two  cases  the  sounds  are  only  perceived  when  the  spiral  surrounding 
the  magnet  can  vibrate  with  it. 

A  telephone  may  be  constructed  with  a  rod  of  soft  iron  instead  of  a 


-925] 


T/ie  Microphone. 


847 


magnet  ;  when  the  rod  is  held  in  the  line  of  dip,  and  the  mouthpiece  is  sung 
into,  the  sounds  are  reproduced. 

From  its  extreme  sensitiveness — being,  perhaps,  the  most  delicate  galva- 
noscope  we  possess — the  telephone  has  become  of  great  service  in  scientific 
research.  It  may  be  used  instead  of  a  galvanometer  in  a  Wheatstone's 
bridge.  If  inserted  in  either  of  the  circuits  of  an  induction  coil,  the 
number  of  breaks  can  be  determined  from  the  height  of  the  tone  which  is 
produced.  When  inserted  in  the  current  of  a  Holtz's  machine,  the  disc  of 
which  is  rotating  with  a  uniform  velocity,  the  height  of  the  tone  varies  with 
the  icsistance  of  the  circuit,  and  with  the  capacity  of  the  condensers.  It 
can  be  shown  also  that  the  circumstances  most  favourable  for  the  production 
of  a  most  distinct  stratification  in  a  Geissler's  tube  correspond  to  a  definite 
pitch  in  the  telephone. 

The  telephone  has  been  used  to  test  hardness  of  hearing.  If  the  magnet- 
ism of  a  telephone  be  excited  by  galvanic  currents  which  are  made  inter- 
mittent by  a  vibrating  tuning-fork,  and  if  a  telephone  is  inserted  in  a  branch 
circuit  (954),  then  by  varying  the  strength  of  the  principal  current,  by  the 
insertion  of  resistances,  the  strength  of  the  sounds  in  the  telephone  may 
be  varied  at  will. 

\Yhen  a  telephone  is  held  to  the  ear  during  a  thunderstorm,  every  light- 
ning flash  in  the  sky  is  heard  to  be  accompanied  by  a  sharp  crack. 

If  a  telephone  is  inserted  in  the  circuit  of  a  Morse's  instrument,  the 
sound  of  the  working  is  heard,  and  the  messages  can  be  read  ;  this  is  the 
case  also  of  the  telephone  in  the  branch  circuit  of  a  Morse.  If  the  tele- 
phone is  joined  up  with  the  primary,  and  another  with  the  secondary,  wire 
of  an  induction  coil  communication  is  almost  as  good  as  if  the  two  apparatus 
were  directly  united. 

925.  Tlie  Microphone. — When  the  wires  of  an  electrical  circuit,  in  which 
is  interposed  a  telephone,  are  broken,  and  rest  loosely  on  each  other,  sounds 
produced  near  .the  point  of  contact 
are  reproduced  and  magnified  in 
the  telephone.  The  microphone,  in- 
vented by  Mr.  Hughes,  depends  on 
this  fact;  its  arrangement  may  be 
greatly  varied  ;  one  of  the  simplest 
and  most  convenient  forms  is  that 
represented  in  figure  816.  A  piece 
of  thin  wood  is  fitted  vertically  on  a 
base  of  the  same  material  ;  two 
small  rods  of  gas  carbon  C  C,  about 
£  of  an  inch  thick,  are  fixed  hori- 
zontally in  the  upright ;  by  means  of 
binding  screws,  they  are  in  metallic  < 
connection  with  the  wires  of  a  cir- 
cuit in  which  is  a  small  battery  and 
a  telephone ;  and  in  each  of  them 
is  a  cavity.  A  third  piece  D  of  the  same  material,  and  about  one  inch  long, 
is  pointed  at  each  end,  one  of  which  rests  in  the  lower  cavity,  while  the  other 
pivots  loosely  in  the  upper  one.  When  a  watch  is  placed  on  the  base  B,  its 


8i5. 


848  Dynamical  Electricity.  [925- 

ticking  is  heard  in  the  telephone  with  surprising  loudness  ;  the  walking  of 
a  fly  on  the  base  suggests  the  stamping  of  a  horse  ;  the  scratching  of  a 
quill,  the  rustling  of  silk,  the  beating  of  the  pulse,  are  perceived  in  the 
telephone  at  a  distance  of  a  hundred  miles  from  the  source  of  sound  ; 
while  a  drop  of  water  falling  on  the  base  has  a  loud  crashing  sound.  To 
obtain  the  best  results  with  a  particular  instrument,  the  position  of  the 
carbon  must  be  carefully  adjusted  by  trial ;  and  indeed  the  form  of  the  in- 
strument itself  must  be  variously  modified  for  the  special  object  in  view  :  in 
some  cases  great  sensitiveness  is  required  ;  in  others  great  range.  In  order 
to  eliminate  as  far  as  possible  the  effect  of  accidental  vibrations  due  to 
the  supports,  the  base  should  rest  on  pieces  of  vulcanised  tubing,  or  on 
wadding. 

It  is  known  that  the  compression  of  a  semi-conductor,  such  as  car- 
bon, diminishes  its  resistance,  while  a  diminution  in  the  compression 
increases  the  resistance.  The  action  of  the  microphone  is  to  be  ascribed  to 
this  ;  in  consequence  of  the  minute  alterations  in  the  pressure  and  in  the 
degree  of  contact  at  the  break,  the  electrical  resistance  in  the  circuit  varies 
in  accordance  with  the  sound-waves,  and  consequently  the  strength  of  the 
currents  varies  too.  The  result  of  this  is,  that  what  we  may  call  undulating 
currents  of  electricity  are  produced,  whose  amplitude,  height,  and  form 
are  in  exact  correspondence  with  the  sound  waves.  The  effect  of  the  micro- 
phone is  to  draw  supplies  of  energy  from  the  battery,  which  then  appear  in 
the  telephone. 

926.  Hughes  s  induction  balance. — The  principle  of  this  apparatus  may 
be  thus  stated  : — Suppose  we  have  two  exactly  equal  primary  induction  coils 
A  and  A/5  and  near  them  two  secondary  coils  B  and  B,  also  exactly  equal, 
and  connected  up  with  a  galvanometer,  so  that  the  coils  act  upon  it  in 
opposite  directions.  If  now  the  current  of  a  battery  be  sent  through  the 
primary  coils,  joined  in  series,  the  inductive  effects  on  each  of  the  secondary 
coils  will  be  the  same,  and,  as  their  action  on  the  galvanometer  is  opposed, 
no  deflection  of  the  needle  will  be  produced.  If,  however,  a  piece  of  iron  be 
introduced  into  the  core  of  one  of  the  secondary  coils,  the  equality  in  the 
induction  effects  will  be  destroyed,  and  the  needle  of  the  galvanometer  at 
once  deflected. 

This  principle  was  first  applied  by  Babbage,  Herschell,  and  in  a  special 
apparatus  by  Dove  ;  but  the  microphone  and  the  telephone  have  led  the 
inventor  of  the  former  to  the  invention  of  an  apparatus  which  has  opened 
out  new  possibilities,  and  has  placed  in  the  hands  of  the  physicist  an 
elegant  and  powerful  engine  of  research,  which  in  certain  departments  of 
investigation  promises  to  be  of  great  service. 

The  form  of  instrument  as  devised  by  Professor  Hughes  is  represented 
in  fig.  817,  where  the  essential  parts  are  drawn  to  scale,  though  the  relative 
distances  of  the  parts  are  not  so ;  a  and  a'  are  the  two  primary  coils,  each 
of  which  consists  of  100  metres  of  No.  32  silk-covered  copper  wire  (0-009  m 
diameter)  wound  on  a  flat  boxwood  spool  10  inches  in  depth  ;  b  and  b'  are 
two  secondary  coils,  all  four  coils  being,  in  intention  at  least,  exactly  alike. 
The  two  primary  coils  are  joined  in  series  with  a  battery  of  three  or 
four  small  DanielFs  cells,  in  which  circuit  a  microphone  m  is  also  nserted  ; 
the  ticking  of  a  small  clock  on  the  table  acts  as  make  and  break. 


foiriVB&siTT) 

-926]  Hughes  s  Induction  Balance.  849 

The  secondary  coils  are  joined  up  with  a  telephone  in  such  a  manner 
that  their  action  upon  it  is  opposed. 

Now,  whatever  care  be  taken  in  winding  the  wire  on  the  coils,  it  is  not 
possible  to  get  at  the  outset  an  exact  balance.  Hence,  while  one  of  the 
secondary  coils  b  is  at  a 
fixed  distance  from  a,  the 
corresponding  one  b'  is 
not  so  ;  its  distance  from 
a'  can  be  slightly  modi- 
fied by  means  of  a  micro- 
metric  screw,  and  thus, 
connection  with  the  bat- 
tery circuit  having  been 
made,  a  balance  is  ob- 
tained by  slightly  varying 
the  adjustment,  and  the 
accomplishment  of  this  is 
known  by  there  being 
.silence  in  the  telephone. 
But  if  now  any  metal 
whatever  be  introduced 
in  one  of  the  secondary 
coils,  a  sound  is  at  once 
heard. 

This  arrangement  is  so 
far  a  simple  differential 
one,  and  furnishes  as  yet 
no  means  of  measuring 
the  forces  brought  into 
play,  and  for  this  purpose 
Hughes  uses  what  is  call- 
ed a  sonometer  or  audio- 
meter. This  consists  of  three  similar  coils,  c  d  and  e,  placed  vertically  on  a 
horizontal  graduated  rule  along  which  d  can  be  moved.  By  means  of  a 
switching  key,  or  commutator,  the  primary  coils  c  and  e  can  be  put  in  com- 
munication with  the  battery  and  microphone  circuit  quite  independently  of 
the  balance,  and  it  is  so  arranged  that  the  ends  of  the  coils  c  and  e  facing 
each  other  are  of  the  same  polarity;  the  third  coil  d,  the  secondary  one,  is 
connected  with  the  telephone  circuit. 

If  these  primary  coils  c  and  e  were  quite  equal,  then,  when  connected  up 
with  the  battery  circuit,  no  sound  would  be  heard  in  the  telephone,  when  the 
secondary  d  is  exactly  midway  between  them.  But  as  the  coil  is  moved 
from  this  position  either  towards  c  or  e  a  sound  is  heard,  due  to  the  prepon- 
derance of  one  or  the  other.  In  practice  the  coils  are  so  arranged  that  a 
balance  is  obtained  when  the  secondary  circuit  is  near  one  of  the  coils,  c  for 
instance  ;  this  represents  a  zero  of  sound,  and  as  the  coil  d  is  moved  nearer 
to  e  a  sound  of  gradually  increasing  intensity  is  heard  ;  distances  measured 
off  along  this  scale  represent  values  of  sound  on  an  arbitrary  scale. 

Suppose  now  that  a  balance  has  been  obtained  in  the  induction  balance, 

003 


Fig.  817. 


850  Dynamical  Electricity.  [9 26  - 

and  that  the  coil  d  in  the  sonometer  is  at  zero  ;  no  sound  is  then  heard 
in  the  telephone  when  the  current  is  switched  either  in  one  or  the  other 
circuit.  But  if  the  balance  is  disturbed  by  placing  a  piece  of  metal  in  the 
core  of  b,  a  definite  continuous  sound  is  heard.  The  current  is  then  switched 
into  the  sonometer,  and  the  secondary  coil  e  is  moved  until  the  ear  perceives 
the  same  sound  in  both  circuits.  The  distance  then  along  which  the  coil  d 
has  been  moved  is  thus  an  arbitrary  measure  of  the  effect  produced. 

Although  by  the  switching  key  the  transition  from  one  circuit  to  the 
other  can  be  effected  with  great  rapidity,  and  the  ear  can  appreciate  minute 
differences,  this  has  not  the  value  of  a  null  method.  Hughes  has  still 
further  improved  the  balance  by  the  following  device,  in  which  the  sono- 
meter is  dispensed  with  : — A  graduated  strip  of  zinc  about  200  mm.  in  length 
by  25  mm.  wide,  and  tapering  from  a  thickness  of  4  mm.  at  one  end  to  a  fine 
edge  at  the  other,  is  made  use  of.  The  metal  to  be  tested  is  placed  in  a 
plane  between  a  and  b  on  the  left  of  the  plate,  and  the  strip  is  moved  along 
the  top  of  b'  until  a  balance  is  obtained. 

The  instrument  is  of  surprising  delicacy  ;  a  milligramme  of  copper  or  a 
fine  iron  wire  introduced  into  one  of  the  coils  which  has  been  balanced,  can 
be  loudly  heard,  and  appreciated  by  direct  measurement.  If  two  shillings 
fresh  from  the  Mint  be  balanced,  rubbing  one  of  them  or  breathing  on  it 
at  once  disturbs  the  balance.  A  false  coin  balanced  against  a  genuine  one 
is  at  once  detected.  The  instrument  furnishes  a  means  of  testing  deli- 
cacy of  hearing  •  such  a  piece  of  wire  as  the  above,  or  a  fine  spiral  of  copper, 
furnishes  a  kind  of  test  object  for  this  purpose. 

927.  Tasimeter. — This  instrument,  invented  by  Edison,  consists  essen- 
tially of  an  arrangement  by  which  a  disc  of  carbon  forming  part  of  a  voltaic 
circuit  is  exposed  to  varying  pressure.  It  depends  on  the  fact  that  the  re- 
sistance of  carbon  varies  very  greatly  with  the  pressure  to  which  it  is  ex- 


Fig  81 


posed.  It  consists  of  an  iron  base,  on  which  are  two  rigid  supports  (fig. 
8 1 8),  one  of  which,  «,  is  connected  with  the  galvanometer  g  by  means  of 
a  wire.  An  ebonite  disc  d  is  screwed  into  a,  and  in  a  circular  cavity  in 
this  ebonite  is  a  small  carbon  disc,  not  shown  in  the  figure,  in  the  outer 
surface  of  which  is  a  strip  of  platinum  in  metallic  connection  with  one  pole 
of  an  element  /.  The  disc  of  carbon  is  closed  in  the  cavity  by  a  metal 


-928]  Edison's  Loud-speaking  Telephone.  851 

plug  Cy  in  which  is  a  cavity.  There  is  a  similar  plug  ^,  with  a  correspond- 
ing cavity  at  the  end  of  a  screw  ^,  which  works  in  the  upright  support ;  in 
the  two  cavities  is  placed  the  strip  of  substance/,  with  which  the  experiment 
is  made. 

A  gentle  pressure  being  applied  by  the  screw,  the  needle  is  deflected 
through  a  few  degrees,  and  its  position,  when  it  comes  to  rest,  is  noted.  The 
slightest  subsequent  contraction  or  expansion  is  indicated  by  a  deflection  of 
the  needle  of  the  galvanometer. 

The  sensitiveness  of  the  instrument  is  very  great  ;  a  thin  strip  of  ebonite 
is  expanded  by  the  heat  of  the  hand  held  near  it,  so  as  to  affect  a  not  very 
delicate  galvanometer.  A  strip  of  gelatine,  inserted  instead  of  the  ebonite, 
is  expanded  by  the  moisture  of  a  damp  strip  of  paper  held  two  or  three 
inches  away. 

The  apparatus  seems  well  adapted  for  the  qualitative  observation  of 
minute  changes  in  length  ;  it  has  been  used,  for  instance,  to  show  the  very 
small  elongation  of  an  iron  rod  when  it  is  magnetised  (880).  Great  care  is 
required  in  the  preparation  of  the  carbon  disc  ;  the  best  kind  seems  to  be 
made  from  lampblack  prepared  at  a  low  temperature,  and.  then,  powerfully 
compressed  into  a  button. 

928.  Edison's  loud-speaking:  telephone. — Although  depending  on  a 
different  principle,  we  may  give  a  description  here  of  this  instrument. 

An  adjustable  metal  spring  passes  on  the  surface  of  a  small  cylinder, 
made  of  chalk,  moistened  with  solutions  'of  caustic  potash  and  acetate  of 
mercury  ;  both  the  spring  and  the  cylinder  form  part  of  a  circuit  in  which 
is  a  batter}^  and  a  Reis's  transmitter  (882).  The  spring  is  connected  in  a 
suitable  manner  with  a  mica  disc  which  is  the  vibrating  part  of  a  mouth- 
piece like  that  of  an  ordinary  telephone.  The  cylinder  can  be  turned  at  a 
uniform  rate,  either  by  hand,  or  by  an  automatic  clockwork  arrangement. 

Now  while  the  spring  is  pressing  on  the  cylinder,  if  the  latter  be  rotated 
in  a  direction  away  from  the  mouthpiece,  in  consequence  of  the  friction 
between  the  spring  and  the  surface  of  the  cylinder,  a  certain   pull  will  be 
exerted  on  the  disc,  which  will  tend  to  drag  it  outwards.     If  the  direction  of 
rotation  were  the  opposite,  the  disc  would  be  pushed  inwards.     Now  the 
amount  of  pull  or  push  will  depend  on  the  friction  between  the  point  and  the 
surface.     If  a  momentary  current  be  passed,  there  will  be  a  momentary  de- 
composition at  the  surface  of  the  cylinder,  its  friction  will  be  altered  in  con- 
sequence of  this  momentary  decomposition,  the  effect  of  which  is  that  the 
disc  moves  inwards,  and  a  series  of  such  intermissions  of  the  current  produces 
a  corresponding  series  of  pulsations  of  the  disc,  which,  if  sufficiently  rapid, 
produce  a  sound.     The  friction  of  the  surfaces  in  contact  is  in  fact  modified 
by  means  of  electrical  decomposition,  a  lubricator  is  liberated  in  correspond- 
ence with  the  sound  waves,  and  thus  the  sound  which  they  represent  is 
reproduced.     The  reproduction  is  so  loud  as  to  be  heard  throughout  a  room, 
the  sounding  instrument  being  at  a  distance.     Although  ordinary  speech 
and  music  can  thus  be  transmitted,  yet  the  sounds  have  a  harsh  metallic 
character  which  is  not  pleasing,  but  at  the  same  time  the  individual  character 
of  the  voice  is  preserved. 


852 


Dynamical  Electricity. 


[929- 


CH AFTER  VII. 

OPTICAL  EFFECTS   OF  POWERFUL  MAGNETS.      DIAMAGNETISM. 

929.  Optical  effects  of  powerful  mag-nets. — Faraday  observed,  in  1845, 
that  a  powerful  electromagnet  exercises  an  action  on  many  substances,  such 
that  if  a  polarised  ray  traverses  them  in  the  direction  of  the  line  of  the  mag- 
netic poles,  the  plane  of  polarisation  is  deviated  either  to  the  right  or  to  the 
left,  according  to  the  direction  of  the  magnetisation. 

Figure  819  represents  Faraday's  apparatus,  as  constructed  by  Ruhmkorft. 
It  consists  of  two  very  powerful  electromagnets,  M  and  N,  fixed  on  two  iron 


Fig.  819. 


supports,  OO',  which  can  be  moved  on  a  support,  K.  The  current  from  a 
battery  of  10  or  u  Bunsen's  elements  passes  by  the  wire  A  to  the  commu- 
tator H,  the  bobbin  M,  and  then  to  the  bobbin  N,  by  the  wire  g,  descends  in 
the  wire  z,  passes  again  to  the  commutator,  and  emerges  at  B.  The  two 
cylinders  of  soft  iron,  which  are  in  the  axis  of  the  bobbins,  are  perforated  by 
cylindrical  holes,  to  allow  the  luminous  rays  to  pass.  At  b  and  a  there  are 
two  Nicol's  prisms,  b  serving  as  polariser  and  a  as  analyser.  By  means  of 
a  limb  this  latter  is  turned  round  the  centre  of  a  graduated  circle,  P. 

The  two  prisms  being  then  placed  so  that  their  principal  sections  are 
perpendicular  to  each  other,  the  prism  a  completely  extinguishes  the  light 
transmitted  through  the  prism  b.  If  at  c,  on  the  axis  of  the  two  coils,  a  plate 
be  placed  with  parallel  faces,  either  of  ordinary  or  flint  glass,  light  is  still 


-930]  Phofophone.  853 

extinguished  so  long  as  the  current  does  not  pass  ;  but  when  the  communi- 
cations are  established,  the  light  reappears.  It  is  now  coloured  ;  and  if  the 
analyser  be  turned  froml  eft  or  right,  according  to  the  direction  of  the  current, 
the  light  passes  through  the  different  tints  of  the  spectrum,  as  is  the  case 
with  plates  of  quartz  cut  perpendicularly  to  the  axis  (674).  Becquerel  showed 
that  a  large  number  of  substances  can  also  rotate  the  plane  of  polarisation 
under  the  influence  of  powerful  magnets.  Faraday  assumed  that  in  these 
experiments  the  rotation  of  the  plane  of  polarisation  was  due  to  an  action  of 
the  magnets  on  the  luminous  rays,  while  Biot  and  Becquerel  ascribed  the 
phenomena  to  a.  molecular  action  of  the  magnet  on  the  transparent  bodies 
submitted  to  its  influence. 

930.  Photophone. — Graham  Bell,  the  inventor  of  the  telephone,  has  quite 
recently  invented  an  apparatus  by  which  articulate  speech  can  be  trans- 
mitted to  a  considerable  distance  by  the  simple  agency  of  a  ray  of  light. 

The  essential  features  of  the  apparatus  are  represented  in  fig.  820,  in 
which  m  is  the  transmitter.  This  consists  of  a  wooden  box  closed  by  a 
thin  plate  of  microscope  glass  silvered  in  front,  which  acts  as  mirror  ;  in  the 
back  of  the  box  is  an  aperture  provided  with  a  flexible  tube  and  mouth-piece. 


Fig.  820, 

A  powerful  beam  of  solar  or  of  the  electrical  light  falls  against  a  large 
mirror  //,  and  is  reflected  by  it  on  a  lens/ by  which  the  rays  are  concentrated 
on  the  mirror  b  of  the  transmitter.  An  alum  cell  a  is  sometimes  interposed  to 
cut  off  the  influence  of  the  heating  rays. 

From  the  mirror  m  the  reflected  rays  pass  through  a  lens  /by  which  they 
are  rendered  parallel,  and  fall  on  a  parabolic  mirror^  at  the  distant  station. 
Here  they  are  concentrated  on  what  may  be  called  a  selenium  rheostate, 
.?,  which  is  interposed  in  a  circuit  consisting  of  a  few  Leclanche  cells  and  a 
telephone  /. 

The  action  depends  on  the  alterations  in  the  resistance  of  selenium 
produced  by  the  action  of  light.  The  construction  of  the  rheostate  is  as 
follows  : — A  number  of  discs  of  thin  sheet  brass  are  taken,  separated  from 
each  other  by  thin  discs  of  mica  of  somewhat  smaller  diameter,  and,  the  whole 
having  been  tightly  screwed  together,  the  interstitial  spaces  are  filled  with 


854  Dynamical  Electricity.  [930- 

melted  selenium.  All  the  odd  numbers  of  brass  discs  are  in  metallic  con- 
nection with  each  other  and  with  one  pole  of  the  circuit,  and  all  the  even 
ones  are  also  in  metallic  connection  with  each  other  and  with  the  other  pole. 
In  this  way  two  conditions  are  realised  ;  namely,  that  the  surface  of  selenium 
exposed  to  the  action  of  light  is  as  large,  and  its  resistance  as  small, 
as  possible. 

This  being  premised,  when  light  falls  on  the  plane  mirror  at  rest,  its  rays 
are  reflected  parallel  against  the  parabolic  mirror  by  which  they  are  con- 
centrated on  the  cell,  the  cylindrical  shape  being  well  adapted  for  this. 
But  if,  by  being  spoken  against,  the  transmitting  mirror  m  i-s  put  in  vibration, 
it  bulges  in  and  out — that  is,  becomes  convex  and  concave — and  the  rays  no 
longer  fall  parallel  on  the  parabolic  mirror ;  they  diverge  or  converge — in 
other  words,  the  whole  of  the  light  is  no  longer  concentrated  on  the  selenium 
cell  ;  its  intensity  changes  at  every  instant,  and  these  variations  in  the  action 
of  the  light  produce  corresponding  variations  in  the  resistance  of  the  sele- 
nium, which  again  produce  corresponding  variations  in  the  strength  of  the 
current,  and  these  are  revealed  by  the  articulate  sounds  of  the  telephone. 

Mr.  Bell  has  found  that  a  great  number  of  substances  are  thrown  into 
vibration  by  the  intermittent  action  of  light.  If  a  ray  of  light  reflected  from 
a  mirror  M  be  brought  to  a  focus,  and  at  the  focus  there  is  a  disc/  per- 
forated by  holes  near  the  edge,  rotated  in  a  vertical  plane  with  great  velocity, 
this  gives  rise  to  what  Mr.  Bell  calls  a  vibratory  ray.  After  traversing  the 
disc  h  (fig.  821),  they  are  caught  upon  another  lens  a,  which  makes  them 


Fig.   821. 

parallel,  and  they  are  again  concentrated  by  a  second  lens  c  on  a  point.  If 
now  a  thin  plate  of  ebonite  be  placed  at  this  point,  a  distinct  musical  note 
will  be  heard  ;  or  if  almost  any  opaque  substance  be  placed  at  the  open  end 
of  a  tube,  the  other  end  being  in  the  ear,  a  note  is  also  heard.  The  same 
result  follows  even  if  the  tube  be  suppressed,  and  the  reflected  ray  is  directly 
received  in  the  ear.  Lord  Rayleigh's  calculations  show  that  there  is  no 
reason  for  discarding  the  explanation  that  the  sounds  in  question  are  due 
to  the  bending  of  the  plates  in  consequence  of  unequal  heating. 

931.  Xerr's  electro-optical  experiments. — Kerr  has  discovered  a  re- 
markable relationship  between  electricity  and  light.  He  finds  that  when  certain 
dielectrics  are  subjected  to  a  state  of  electrical  strain,  they  develope  doubly 
refringent  properties  (639).  The  general  arrangement  of  the  experiments  is 
as  follows  :  a  cell,  P  (fig.  821),  is  suitably  constructed  of  stout  glass  plates, 
in  which  is  placed  the  liquid  under  examination  ;  its  dimensions  are  4 


-931]  Kerr's  Electro-optical  Experiments,  855 

inches  in  length  by  I  inch  in  width,  and  about  \  of  an  inch  in  thickness. 
Two  copper  plates  placed  horizontally,  and  kept  at  a  distance  of  about  ^ 
of  an  inch,  can  be  connected  with  the  poles  of  a  Holtz's  machine  (fig.  615), 
or,  what  is  more  convenient,  with  the  opposite  coatings  of  a  Leyden  jar, 
which  in  turn  is  worked  by  such  a  machine.  B  is  the  mirror  of  a  heliostat, 
by  which  a  beam  of  light  may  be  sent  in  any  direction.  M  and  N  are  two 
Nicol's  prisms  (660) ;  C  is  a  compensator,  while  D  is  a  condensing  lens. 


L 

3? 


Fig.  822. 


Of  the  two  Xicol's  prisms,  M  serves  as  polariser,  and  N  as  analyser  (656)  ; 
at  the  outset  they  are  arranged  so  that  their  principal  sections  are  at  right 
angles  to  each  other,  and  make  an  angle  of  45°  with  the  vertical.  Thus  the 
light  polarised  by  the  prism  M  is  extinguished  by  the  analyser  N,  so  that 
the  field  between  them  is  quite  dark,  and  remains  so  even  when  the  cell  is 
filled  with  liquid  ;  the  cell  is  so  arranged  that  the  observer  looks  fairly  through 
the  slit  of  dielectric  which  is  between  the  conductors  in  the  cell. 

If  now  the  plates  are  placed  in  opposite  electrical  conditions,  the  field  at 
once  becomes  clear.  Of  all  dielectrics  hitherto  examined,  carbon  bisulphide 
is  that  which  best  exhibits  the  phenomenon.  A  fraction  of  a  turn  of  a  Holtz's 
machine  is  at  once  sufficient  to  produce  light  in  the  field,  which  disappears 
immediately  the  plates  are  discharged.  As  the  machine  is  worked  and  the 
potential  rises,  the  light  between  the  conductors  gradually  increases  in  bright- 
ness until  a  pure  and  brilliant  white  is  obtained  ;  with  increase  of  potential 
a  fine  progression  of  chromatic  effects  is  obtained  ;  the  luminous  band 
between  the  conductors  issue,  first  from  white  to  a  straw-colour,  which 
deepens  gradually  to  a  rich  yellow  ;  it  then  passes  through  orange  to  a  deep 
brown,  next  to  a  pure  and  dense  red,  through  purple  and  violet  to  a  rich  and 
full  blue,  and  then  to  green.  All  the  colours  are  beautifully  dense  and  pure, 
and  as  fine  as  anything  seen  in  experiments  with  crystals  in  the  polariscope. 
The  phenomenon  generally  ceases  at  the  green  of  the  second  order  with  a 
discharge  of  electric  sparks.  The  action  of  bisulphide  of  carbon  under 
electrical  strain  is  similar  to  that  of  glass  stretched  in  a  direction  parallel  to 
the  lines  of  force  ;  it  is  an  action  of  the  same  kind  as  that  of  a  uniaxial  bire- 
fringent  crystal  (631)  ;  in  this  respect  carbon  bisulphide  occupies  a  place 
among  dielectrics  similar  to  that  of  Iceland  spar  among  crystals. 

In  order  to  measure  the  effect  produced,  a  compensator,  C,  is  placed 
behind  the  cell  ;  the  plates  are  connected  with  a  Thomson's  electrometer 
in  such  a  manner  that  the  potential  can  be  directly  measured,  and  then 
compared  simultaneously  with  the  difference  of  the  path  of  the  extraordinary 
and  ordinary  ray  in  the  dielectric.  Kerr  arrived  thus  at  the  law  :  *  the  strength 
of  the  electro-optical  action  of  a  given  dielectric  —  that  is,  the  difference  in  the 
path  of  the  ordinary  and  extraordinary-  rays,  for  unit  thickness  of  the 
dielectric—  varies  directly  as  the  square  of  the  resultant  electrical  force.' 


856 


Dynamical  Electricity. 


[932- 


932.  Diamagnetism. — Coulomb  observed,  in  1802,  that  magnets  act  upon 
all  bodies  in  a  more  or  less  marked  degree  ;  this  action  was  at  first  attributed 
to  the  presence  of  ferruginous  particles.  Brugmann  also  found  that  certain 
bodies,  for  instance,  bars  of  bismuth,  when  suspended  between  the  poles  of 
a  powerful  magnet,  do  not  set  axially  between  the  poles — that  is,  in  the  line 
joining  the  poles — but  equatorially,  or  at  right  angles  to  that  line.  This 


Fig.  823. 


Fig.  824. 


phenomenon  was  explained  by  the  assumption  that  the  bodies  were 
transversely  magnetic.  Faraday  made  the  important  discovery  in  1843 
that  all  solids  and  liquids  which  he  examined  are  either  attracted  or  repelled 
by  a  powerful  electromagnet.  The  bodies  which  are  attracted  are  called 
magnetic  or  paramagnetic  substances,  and  those  which  are  repelled  are 
diamagnetic  bodies.  Among  the  metals,  iron,  nickel,  cobalt,  manganese, 
platinum,  cerium,  osmium,  and  palladium  are  magnetic  ;  while  bismuth, 
antimony,  zinc,  tin,  mercury,  lead,  silver,  copper,  gold,  and  arsenic  are 
diamagnetic,  bismuth  being  the  most  so  and  arsenic  the  least.  The  diamag- 
netic effects  can  only  be  produced  by  means  of  very  powerful  magnets,  and 
it  is  by  means  of  Faraday's  apparatus  that  they  have  been  discovered  and 
studied.  In  experimenting  on  the  diamagnetic  effects — solids,  liquids,  and 
gases — armatures  of  soft  iron,  S  and  Q  (figs.  823-825),  of  different  shapes 
are  screwed  on  the  magnets. 

i.  Diamagnetism  of  solids.  If  a  small  cube  of  copper  suspended  by  a 
fine  silk  thread  between  the  poles  of  the  magnet  (fig.  824),  be  in  rapid  rota- 
tion between  the  poles  of  an  electromagnet,  it  stops,  the  moment  the  current 
passes  through  the  bobbins.  If  the  moveable  piece  have  the  form  of  a  small 
rectangular  bar  it  sets  equatorially,  or  at  right  angles  to  the  axis  of  the  bob- 
bins, if  it  is  a  diamagnetic  substance,  such  as  bismuth,  antimony,  or  copper ; 
but  axially,  or  in  the  direction  of  the  axis,  if  it  is  a  magnetic  substance,  such 
as  iron,  nickel,  or  cobalt.  Besides  the  substances  enumerated  above, 
the  following  are  diamagnetic  :  rock  crystal,  alum,  glass,  phosphorus,  iodine, 
sulphur,  sugar,  bread ;  and  the  following  are  magnetic  :  many  kinds  of  paper 
and  sealing-wax,  fluorspar,  graphite,  charcoal,  &c. 

ii.  Diamagnetism  of  liquids.  To  experiment  with  liquids,  very  thin  glass 
tubes  filled  with  them  are  suspended  between  the  poles  instead  of  the  cube 
m  in  the  figure  824.  If  the  liquids  are  magnetic,  such  as  solutions 
of  iron  or  cobalt,  the  tubes  set  axially ;  if  diamagnetic,  like  water,  blood, 
milk,  alcohol,  ether,  oil  of  turpentine,  and  most  saline  solutions,  the  tubes  set 


-932]  Diamagnetism.  857 

equatorially.  Very  remarkable  changes  take  place  in  the  direction  of  mag- 
netic and  diamagnetic  substances  when  they  are  suspended  in  liquids.  A 
magnetic  substance  is  indifferent  in  an  equally  strong  magnetic  liquid  ;  it  sets 
equatorially  in  a  stronger  magnetic  substance,  and  axially  in  a  substance 
which  is  less  strongly  magnetic  ;  it  sets  axially  in  all  diamagnetic  liquids. 

A  diamagnetic  substance  surrounded  by  a  magnetic  or  diamagnetic  sub- 
stance sets  equatorially.  According  to  its  composition,  glass  is  sometimes 
magnetic  and  sometimes  diamagnetic,  and,  as  in  these  investigations  glass 
tubes  are  used  for  containing  the  liquids,  its  deportment  must  first  be  deter- 
mined, and  then  taken  into  account  in  the  experiment. 

The  action  of  powerful  magnets  on  liquids  may  also  be  observed  in  the 
following  experiment  devised  by  Pliicker  : — A  solution  of  a  magnetic  liquid 
is  placed  on  a  watch  glass  between  the  two  poles,  S  and  O,  of  a  powerful 
electromagnet.  When  the  current  passes,  the  solution  forms  the  enlarge- 
ment represented  in  fig.  824 ;  this  continues  as  long  as  the  current  passes, 
and  is  produced  to  different  extents  with  all  magnetic  liquids.  The  changes 
in  the  aspects  of  the  liquids  are,  however,  so  small  as  to  require  careful 
scrutiny  to  detect  their  existence.  A  method  of  magnifying  these  changes 
so  as  to  render  them  visible  to  large  audiences,  was  devised  by  Prof. 
Barrett.  A  source  of  light  is  placed  above  the  watch  glass  containing  a  drop 
of  the  solution  to  be  tried.  Below  the  watch  glass,  and  between  the  legs  of 
the  magnet,  is  placed  a  mirror  at  the  angle  of  45°.  By  this  means  the  beam 
of  light  passing  through  the  watch  glass  is  reflected  at  right  angles  on  to  a 
screen,  where  an  image  of  the  drop  is  focussed  by  a  lens.  If  now  a  drop  of 
diamagnetic  liquid — such  as  water,  or,  better,  sulphuric  acid — be  placed  on  the 
watch  glass,  as  soon  as  the  current  passes,  the  flattened  drop  retreats  from 
the  two  poles,  and  gathers  itself  up  into  a  little  heap,  as  at  A  (fig.  825).  So 
doing,  it  forms  a  double  convex  lens,  by  which  the  light  is  brought  to  a  short 
focus  below  the  drop,  an  effect  instantly  seen  on  the  screen.  When  the  current 
is  interrupted  the  drop  falls,  and  the  light  returns  to  its  former  appearance. 
A  magnetic  liquid,  such  as  a  solution  of  perchloride  of  iron,  has  exactly  the 
opposite  effect.  The  drop  attracted  to  the  two  poles  becomes  flattened,  and 
instead  of  a  plano-convex  shape,  at  which  it  rests,  it  becomes  nearly  concavo- 
convex  as  at  B.  The  light  is  dispersed,  and  the  effect  manifest  on  the  screen. 
Instead  of  a  mirror  and  lens,  a  sheet  of  white  paper  may  be  placed  in  an  in- 
clined position  under  the  watch  glass,  and  the  effects  are  somewhat  varied, 
but  equally  well  pronounced. 

iii.  Diamagnetism  of  gases.  Bancalari  observed  that  the  flame  of  a  candle 
placed  between  the  two  poles  in  Faraday's  apparatus  was  strongly  repelled 
(fig.  823).  All  flames  present  the  same  phenomenon  to  different  extents, 
resinous  flames  or  smoke  being  most  powerfully  affected. 

The  magnetic  deportment  of  gases  may  be  exhibited  for  lecture  purposes 
by  inflating  soap  bubbles  with  them  between  the  poles  of  the  electromagnet, 
and  projecting  on  them  either  the  lime  or  the  electric  light. 

Faraday  experimented  on  the  magnetic  or  diamagnetic  nature  of  gases. 
He  allowed  gas  mixed  with  a  small  quantity  of  a  visible  gas  or  vapour,  so 
as  to  render  it  perceptible,  to  ascend  between  the  two  poles  of  a  magnet,  and 
observed  their  deflections  from  the  vertical  line  in  the  axial  or  equatorial 
direction ;  in  this  way  he  found  that  oxygen  was  least,  and  nitrogen  more 


858  Dynamical  Electricity.  [932- 

and  hydrogen  most  diamagnetic.  With  iodine  vapour,  produced  by  placing 
a  little  iodine  on  a  hot  plate  between  the  two  poles,  the  repulsion  is  strongly 
marked.  Becquerel  found  that  oxygen  is  the  most  strongly  magnetic  of  all 
gases,  and  that  a  cubic  yard  of  this  gas  condensed  would  act  on  a  magnetic 
needle  like  5-5  grains  of  iron.  Faraday  found  that  oxygen,  although  magnetic 
under  ordinary  circumstances,  became  diamagnetic  when  the  temperature 
was  much  raised,  and  that  the  magnetism  or  diamagnetism  of  a  substance 
depends  on  the  medium  in  which  it  is  placed.  A  substance,  for  instance, 
which  is  magnetic  in  vacuo,  may  be  diamagnetic  in  air. 

In  the  crystallised  bodies  which  do  not  belong  to  the  regular  system,  the 
directions  in  which  the  magnetism  or  diamagnetism  of  a  body  is  most  easily 
excited  are  generally  related  to  the  crystallographic  axis  of  the  substance. 
The  optic  axis  of  the  uniaxial  crystals  sets  either  axially  or  equatorially  when 
a  crystal  is  suspended  between  the  poles  of  an  electromagnet.  Faraday  has 
assumed  from  this  the  existence  of  a  magneto-crystalline  force  ;  but  it  appears 
probable,  from  Knoblauch's  researches,  that  the  action  arises  from  an  unequal 
density  in  different  directions,  inasmuch  as  unequal  pressure  in  different 
directions  produces  the  same  result. 

According  to  Pliicker,  for  a  given  unit  ot  magnetising  force,  the  specific 
magnetisms  developed  in  equal  weights  of  the  undermentioned  substances 
are  represented  by  the  following  numbers,  those  bodies  with  the  minus  signs 
prefixed  being  diamagnetic  : — 

Iron  ....  1,000,000  Nickel  oxide     .         .         .     287 

Cobalt        .        .         .  1,009,000  Water      .         .         .         .    —  25 

Nickel        .         .         .  465,800  Bismuth  ....    -23-6 

Iron  oxide         .         .  759  Phosphorus      .         .         .--13-1 

iv.  Detonation  produced  by  the  rupture  of  a  current  under  the  influence  of 
a  powerful  electromagnet.  The  following  experiment  by  Ruhmkorff  is  a 
remarkable  effect  of  Faraday's  apparatus  : — When  the  two  ends  of  a  stout  wire 
in  which  the  current  of  the  electromagnet  passes  are  placed  between  the 
two  poles,  S  and  Q,  of  figure  823,  that  is  to  say,  when  the  current  is  closed 
between  S  and  Q,  this  closing  takes  place  without  a  spark  and  without  noise, 
or  merely  a  feeble  noise  and  a  spark.  But  when  the  two  ends  are  sepa- 
rated, and  the  current  is  hence  broken,  a  violent  noise  is  heard  almost  as 
strong  as  the  report  of  a  pistol.  This  appears  to  be  the  extra  current,  the 
intensity  of  which  is  greatly  increased  by  the  influence  of  two  poles. 

The  repulsion  produced  in  a  diamagnetic  body  under  the  influence  of  a 
powerful  magnet  is  due  to  the  fact  that  the  magnet  developes  in  the  end 
nearest  to  it  like  polarity,  and  in  the  end  furthest  away  unlike  polarity  ;  a 
phenomenon  the  exact  opposite  of  that  of  iron. 

The  following  experiment,  which  is  due  to  Weber,  is  considered  to  prove 
that  diamagnetism  is  a  polar  force  : — A  coil  was  placed  near  the  end  of  an 
electromagnet,  its  axis  being  in  the  prolongation  of  the  axis  of  the  magnet, 
and  its  ends  being  connected  with  a  sensitive  galvanometer.  When  a  bar  of 
bismuth  was  suddenly  introduced  and  removed  from  the  coil,  induction 
currents  were  produced  in  the  circuit,  the  direction  of  which,  as  shown  by 
the  galvanometer,  was  the  exact  opposite  of  those  which  iron  would  have 
produced  under  the  same  circumstances. 


-934] 


Thermo-electricity. 


859 


CHAPTER  VIII. 

THERMO-ELECTRIC  CURRENT. 

933.  Thermo-electricity. —  In  1821,  Professor  Seebeck,  of  Berlin,  found 
that  by  heating  one  of  the  junctions  of  a  metallic  circuit,  consisting  of  two 
metals  soldered  together,  an  electric  current  was  produced.  This  pheno- 
menon may  be  shown  by  means  of  the  apparatus  represented  in  fig.  826, 
which  consists  of  a  plate 
of  copper,  mn,  the  ends 
of  which  are  bent  and 
soldered  to  a  place  of  bis- 
muth, op.  In  the  interior 
of  the  circuit  is  a  magnetic 
needle  moving  on  a  pivot. 
When  the  apparatus  is 
placed  in  the  magnetic 
meridian,  and  one  of  the 
solderings  gently  heated, 
as  shown  in  the  figure, 
the  needle  is  deflected  in 


Fig.  826. 


a  manner  wrhich  indicates 
the  passage  of  a  current 
from  n  to  m  ;  that  is,  from  the  heated  to  the  cool  junction  in  the  copper.  If 
instead  of  heating  the  junction,  «,  it  is  cooled  by  ice,  or  by  placing  upon  it 
cotton  wool  moistened  with  ether,  the  other  junction  remaining  at  the  ordi- 
nary temperature,  a  current  is  produced,  but  in  the  opposite  direction — that 
is  to  say,  from  m  to  n  ;  in  both  cases  the  current  is  more  energetic  in  pro- 
portion as  the  difference  in  temperature  of  the  solderings  is  greater. 

Seebeck  gave  the  name  thermo-electric  to  this  current,  and  to  the  couple 
which  produces  it,  to  distinguish  it  from  the  hydro-electric  or  ordinary  voltaic 
current  and  couple. 

934.  Thermo-electric  series. — If  small  bars  of  two  different  metals  are 
soldered  together  at  one  end  while  the  free  ends  are  connected  with  the 
•wires  of  a  galvanometer,  and  if  now  the  point  of  junction  of  the  two  metals 
be  heated,  a  current  is  produced,  the  direction  of  which  is  indicated  by  the 
deflection  of  the  needle  of  the  galvanometer.  Moreover,  the  strength  of  the 
current,  calculated  from  the  deflection  of  the  galvanometer,  is  proportional  to 
the  electromotive  force  of  the  thermo-element.  By  experimenting  in  this 
way  with  different  metals,  they  may  be  formed  in  a  list  such  that  each  metal 
gives  rise  to  positive  electricity  when  associated  with  one  of  the  following, 
and  negative  electricity  with  one  of  those  that  precede  : — that  is,  that,  in 
heating  the  soldering,  the  positive  current  goes  from  the  positive  to  thenega- 


860  Dynamical  Electricity.  [934- 

tive  metal  across  the  soldering,  just  as  if  the  soldering  represented  the  liquid.] 
in  a  hydro-electrical  element ;  hence  out  of  the  element,  in  the  connecting 
wire  in  the  galvanometer  for  instance,  the  current  goes  from  the  negative  to] 
the  positive  metal. 

Thus  a  couple,  bismuth-antimony,  heated  at  the  junction  would  corre-  i 
spond  to  a  couple,  zinc-copper,  immersed  in  sulphuric  acid.  The  following 
is  a  list  drawn  up  from  Matthiessen's  researches,  which  also  gives  compara- 
tive numerical  values  for  the  electromotive  force  : — 

Bismuth  .         .         .          +  25  Gas  coke       .         .         .  -o.  i 

Cobalt      ....      9  Zinc      ...  c-2 

Potassium        .         .              5-5  Cadmium      ...  0-3 

Nickel      ....      5  Strontium      ...  2*0 

Sodium    ....     3  Arsenic          ...  3-8 

Lead        .         .         .         .     1-03  Iron       ....  5-2 

Tin i  Red  phosphorus    .         .  9-6 

Copper     ....     i  Antimony       .         .         .  9*8 

Platinum.         .         .         .07  Tellurium       .         .         .  179*9 

Silver       .         .         .              ro  Selenium       .         .         .—290*0 

The  meaning  of  the  numbers  in  this  list  is  that,  taking  the  electromotive 
force  of  the  copper-silver  couple  as  unity,  the  electromotive  force  of  any  pair 
of  metals  is  expressed  by  the  difference  of  the  numbers  where  the  signs  are 
the  same  and  by  the  sum  where  the  signs  are  different.  Thus  the  electro- 
motive force  of  a  bismuth-nickel  couple  would  be  25-5  =  20;  of  a  cobalt- 
iron  9  —  ( +  5*2)  =  14*2,  and  of  an  iron-antimony—  5*2  -  9*8  =  —4*6.  Where 
the  positive  sign  is  fixed,  the  current  is  from  the  other  metal  to  silver  across 
the  soldering  ;  and  where  the  negative,  from  silver  to  that  metal. 

Hence,  of  these  bodies,  bismuth  and  selenium  produce  the  greatest 
electromotive  force  ;  but  from  the  expense  of  this  latter  element,  and  on 
account  of  its  low  conducting  power,  and  the  difficulty  of  making  good  joints, 
antimony  is  generally  substituted.  The  antimony  is  the  negative  metal  but 
the  positive  pole,  and  the  bismuth  the  positive  metal  but  the  negative  pole, 
and  the  current  goes  from  bismuth  to  antimony  across  the  junction. 

If  copper  wires  connected  with  the  ends  of  a  galvanometer  are  soldered 
together  to  the  ends  of  an  antimony  rod,  and  if  one  of  the  junctions  is  heated 
to  50°,  the  other  being  mantained  at  o°,  a  certain  deflection  is  observed,  in 
the  galvanometer.  If  similarly  a  compound  bar,  consisting  of  antimony  and 
tin  soldered  together,  be  connected  with  the  ends  of  the  galvanometer,  and  if 
the  junction  copper-tin  and  the  junction  tin-antimony,  be  heated  to  50°, 
while  the  junction  antimony-copper  is  kept  at  o°,  the  deflection  is  the  same 
as  in  the  previous  case.  Hence  the  electromotive  force  produced  by  heating 
the  two  junctions,  copper-tin  and  tin-antimony,  is  equal  to  the  electromotive 
force  produced  by  heating  the  copper-antimony. 

Becquerel  found  with  a  number  of  couples,  where  one  end  of  the  junction 
was  heated  to  a  given  temperature  and  the  other  kept  at  o°,  that  the  inten- 
sity of  the  current  was  proportional  to  the  temperature  at  the  heated  junction. 
If  the  two  junctions  are  at  any  given  temperatures,  the  intensity  of  the 
current  is  proportional  to  the  difference  of  the  temperature  of  the  two  places, 
provided  that  this  does  not  exceed  50°. 


-936]  Thermo-electric  Couples.  86 1 

The  direction  of  the  current  frequently  changes  when  the  emperature  of 
the  couple  is  raised  beyond  a  certain  limit.  Thus,  in  a  copper  and  iron  cir- 
cuit, the  current  goes  from  copper  to  iron  through  the  heated  part,  provided 
the  temperature  does  not  exceed  300°  ;  at  a  higher  temperature  the  current 
changes  its  direction,  and  goes  from  iron  to  copper. 

As  compared  with  ordinary  hydro-electric  currents,  the  electromotive 
force  of  thermo-currents  is  very  small  ;  thus  the  electromotive  force  of  a 
bismuth-copper  element  with  a  difference  of  100°  C.  in  the  temperatures  of 
their  junctions  is  according  to  Wheatstone  -9^,  and  according  to  Neumann 
:hat  of  Daniell's  element :  according  to  Kohlrausch  the  electromotive 
force  of  an  iron-argentan  couple  with  10°  to  15°  difference  of  temperatures 
at  their  junctions  is  -^^  that  of  a  Daniell. 

935.  Causes  of  thermo-electric  currents. — The  thermo-electric  currents 
are  probably  to  be  attributed  to  an  electromotive  force  produced  by  the  con- 
tact of  heterogeneous  substances,  a  force  which  varies  with  the  temperature. 
Becquerel  ascribed  them  to  the  unequal  propagation  of  heat  in  the  different 
parts  of  the  circuit.  He  found  that  when  all  the  parts  of  a  circuit  are  homo- 
geneous, no  current  is  produced  on  heating,  because  the  heat  is  equally 
propagated  in  all  directions.  This  is  the  case  if  the  wires  of  the  galvano- 
meter are  connected  by  a  second  copper  wire.  But  if  the  uniformity  of  this 
is  destroyed  by  coiling  it  in  a  spiral,  or  by  knotting  it,  the  needle  indicates 
by  its  deflection  a  current  going  from  the  heated  part  to  that  in  which  the 
homogeneity  has  been  destroyed.  If  the  ends  of  the  galvanometer  wires  be 
coiled  in  a  spiral,  and  one  end  heated  and  touched  with  the  other,  the 
current  goes  from  the  heated  to  the  cooled  end. 

\Yhen  two  plates  of  the  same  metal,  but  at  different  temperatures,  are 
placed  in  a  fused  salt  such  as  borax,  which  conducts  electricity  but  exerts  no 
chemical  action,  a  current  passes  from  the  hotter  metal  through  the  fused 
salt  to  the  colder  one.  Hot  and  cold  water  in  contact  produce  a  current 
which  goes  from  the  warm  water  to  the  cold. 

Svanberg  has  found  that  the  thermo-electromotive  force  is  influenced  by 
the  crystallisation  ;  for  instance,  if  the  cleavage  of  bismuth  is  parallel  to  the 
face  of  contact,  it  is  greater  than  if  both  are 
at  right  angles,  and  that  the  reverse  is  the 
case  with  antimony.  Thermo-electric  ele- 
ments may  be  constructed  of  either  two 
pieces  of  bismuth  or  two  pieces  of  antimony  ; 
if  in  the  one  the  principal  cleavage  is  parallel 
to  the  place  of  contact,  and  in  the  other  is 
at  right  angles.  Hence  the  position  of  metals 
in  thermo-electric  series  is  influenced  by  their 
crystalline  structure. 

936.  Thermo-electric  couples. — From 
what  has  been  said  it  will  be  understood  that 
a  thermo-electric  couple  consists  of  two  metals 
soldered  together,  the  two  ends  of  which  can 
be  joined  by  a  conductor.  Fig.  826  represents 

a  bismuth-copper  couple  ;  fig.  827  represents  a  series  of  couples  used  by 
Pouiilet.  The  former  consists  of  a  bar  of  bismuth  bent  twice  at  right  angles,  at 


862 


Dynamical  Electricity, 


[936- 


the  ends  of  which  are  soldered  two  copper  strips,  c,  d,  which  terminate  in 
two  binding  screws  fixed  on  some  insulating  material. 

When  several  of  these  couples  are  joined  so  that  the  second  copper  of 
the  first  is  soldered  to  the  bismuth  of  the  second,  then  the  second  copper  of 


Fig.  828.   ' 

this  to  the  bismuth  of  the  third,  and  so  on,  this  arrangement  constitutes  a 
thermo-electric  battery,  which  is  worked  by  keeping  the  odd  solderings,  for 
instance,  in  ice,  and  the  even  ones  in  water,  which  is  heated  to  100°. 

937.  Nobili's  thermo-electric  pile. — Nobili  devised  a  form  of  thermo- 
electric battery,  or  pile  as  it   is  usually  termed,  in  which  there  are  a  large 
number  of  elements  in  a  very  small  space.     For  this  purpose  he  joined  the 
couples  of  bismuth  and  antimony  in  such  a  manner,  that  after  having  formed 
a  series  of  five  couples,  as  represented  in  fig.  830,  the  bismuth  from  b  was 
soldered  to  the  antimony  of  a  second  series  arranged  similarly  ;    the  last 
bismuth  of  this  to  the  antimony  of  a  third,  and  so  on  for  four  vertical  series, 

containing  together  20  couples,  com- 
mencing by  antimony,  finishing  by 
bismuth. 

Thus  arranged,  the  couples  are 
insulated  from  one  another  by  means 
of  small  paper  bands-  covered  with 
varnish,  and  are  then  enclosed  in  a 
copper  frame,  P  (fig.  829),  so  that  only 
the  solderings  appear  at  the  two  ends 
of  the  pile.  Two  small  copper  binding 
screws,  m  and  n,  insulated  in  an  ivory 
ring,  communicate  in  the  interior,  one 
with  the  first  antimony,  representing  the  positive  pole,  and  the  other  with 
the  last  bismuth,  representing  the  negative  pole.  These  binding  screws 
communicate  with  the  extremities  of  a  galvanometer  wire  when  the  thermo- 
electric current  is  to  be  observed. 

938.  Becquerel's  tbermo-electric  battery. — Becquerel  has  found  that 
artificial  sulphuret  of  copper  heated  from  200°  to  300°  is  powerfully  positive, 
and  that  a  couple  of  this  substance  and  copper  has  an  electromotive  force 
nearly  ten  times  as  great  as  that  of  the  bismuth  and  copper  couple  in  fig.  826. 


Fig.  829. 


Fig  830. 


-938] 


Becquerel  's  Thermo-electric  Battery. 


Native  sulphuret,  on  the  contrary,  is  powerfully  negative.  As  the  artificial 
sulphuret  only  melts  at  about  1,035°,  it  mav  De  used  at  very  high  tempera- 
tures. The  metal  joined  with  it  is  German  silver  (90  of  copper  and  10  of 
nickel).  Fig.  831  represents  the  arrangement  of  a  battery  of  50  couples 


Fig.  831. 

arranged  in  two  series  of  25.  Fig.  833  gives  on  a  larger  scale  the  view  of  a 
single  couple,  and  fig.  832  that  of  6  couples  in  two  series  of  3.  The  sulphuret 
is  cut  in  the  form  of  rectangular  prisms,  10  centimetres  in  length,  by  i8mm. 
in  breadth,  and  I2inm.  thick.  In  front  is  a  plate  of  German  silver  m  (fig.  833), 
intended  to  protect  the  sulphuret  from  roasting  when  it  is  placed  in  a  gas 
flame.  Below  there  is  a  plate  of  German  silver  MM,  which  is  bent  several 


Fig.  832. 


Fig-  833. 


times  so  as  to  be  joined  to  the  sulphuret  of  the  next,  and  so  on.  The  couples, 
thus  arranged  in  two  series  of  25,  are  fixed  to  a  wooden  frame  supported 
by  two  brass  columns  AB,  on  which  it  can  be  more  or  less  raised.  Below  the 
couples  is  a  brass  trough,  through  which  water  is  constantly  flowing,  arriving 
by  the  tube  b  and  emerging  by  the  stopcock  r.  The  plates  of  German  silver 
are  thus  kept  at  a  constant  temperature.  On  each  side  of  the  trough  are  two 
long  burners  on  the  Argand  principle  fed  by  gas  from  a  caoutchouc  tube,  a. 
The  frame  being  sufficiently  lowered,  the  ends  are  kept  at  a  temperature  of 
200°  or  300°.  For  utilising  the  current,  two  binding  screws  are  placed  onj 


864  Dynamical  Electricity.  [938- 

the  left  of  the  frame,  one  communicating  with  the  first  sulphuret — that  is,  the 
positive  pole — and  the  other  with  the  last  German  silver,  or  the  negative  pole. 
At  the  other  end  of  the  frame  are  two  binding  screws,  which  facilitate  the 
arrangement  of  the  couples  in  different  ways. 

The  current  of  this  battery  may  be  used  for  telegraphing  even  through  a 
great  distance,  and  passed  into  an  electromagnet  can  lift  a  weight  of  200 
pounds.  It  can  raise  a  short  piece  of  fine  iron  wire  to  redness,  and  freely 
decomposes  water.  The  electromotive  force  of  a  Daniell's  cell  is  equal  to 
about  8  or  9  of  these  couples. 

939.  Clamond's  thermo-electric  battery. — Of  the  attempts  which  have 
been  made  to  apply  thermo-electric  currents  to  directly  practical  purposes  the 
most  successful  has  been  Clamond's,  which  is  used  both  for  telegraphic  pur- 
poses and  also  for  electroplating.     Its  characteristic  features  are  the  con- 
struction and  arrangement  of  the  elements,  and  the  manner  in  which  the 
heating  is  effected. 

The  negative  element  consists  of  an  alloy  of  two  parts  of  antimony  and 
one  of  zinc,  forming  a  flat  spindle-shaped  bar  from  2  to  3  inches  in  length,  by 
§  in.  in  thickness  (fig.  835).  The  positive  metal  is  a  thin  strip  or  lug  of  tin 
plate,  stamped  as  represented  at  aa'  in  fig.  834  ;  this  is  then  bent  in  as  shown 
at  c,  and  being  held  in  a  mould,  the  alloy,  which  melts  at  260°  C.,  is  poured  in. 
The  individual  elements  have  then  the  appearance  represented  in  fig.  835, 
and  to  connect  them  together  the  tin  lugs  are  bent  into  shape,  and  joined  in 
a  circle  of  elements  (fig.  836),  being  kept  in  their  position  by  a  paste  of 
asbestos  and  soluble  glass  ;  flat  rings  of  this  composition  are  also  made, 
and  are  placed  between  each  series  of  rings  piled  over  each  other  ;  the  con- 
nection between  the  individual  elements  and  between  the  sets  of  rings  is 
made  by  soldering  together  the  projecting  ends  of  the  tin  lugs.  Thin  plates 
of  mica  are  placed  between  the  alloy  and  the  tin  plate,  excepting  at  the 
place  of  soldering.  Looked  at  from  the  inside 
the  faces  of  the  battery  present  the  appearance 
of  a  perfect  cylinder. 

The  heating  is  effected  by  means  of  coal 
gas,  admitted  through  an  earthenware  tube, 
AB,  fig.  837,  perforated  by  numerous  small 
holes  ;  this  is  surrounded  by  a  somewhat  larger 
Fig  835  iron  tube  CD,  reaching  nearly  to  the  top  of  the 
cylinder,  which  is  closed  by  a  lid,  EF.  Air 
enters  at  the  bottom  of  this  tube,  and  the  heated  gases  passing  up  the  tube, 
curl  over  the  top,  descend  on  the  outside,  and  escape  by  a  chimney  GH.  This 
arrangement  economises  gas  and  prevents  danger  from  overheating,  as  the 
gas-jets  do  not  impinge  directly  on  the  element.  The  supply  of  gas  is 
regulated  by  an  automatic  arrangement,  so  that  the  temperature  is  not 
higher  than  about  200°. 

A  battery  of  60  such  elements  has  an  electromotive  force  of  three  volts, 
and  an  internal  resistance  of  i^  ohm.  The  amount  of  the  gas  consumed 
per  hour  for  this  size  is  three  cubic  feet,  and  such  a  battery  costs  four 
pounds. 

940.  Melloni's  thermomultiplier. — We  have  already  noticed  the  use 
which  Melloni  has  made  of  Nobili's  pile,  in  conjunction  with  the  galvano- 


-940] 


Melloni  's  Tformomultiplier. 


865 


meter,  for  measuring  the   most  feeble   alterations   of  temperature.      The 
arrangement  he  used  for  his  experiments  is  represented  in  fig.  838. 

On  a  wooden  base,  provided  with  levelling  screws,  a  graduated  copper 
rule,  about  a  metre  long,  is  fixed  edgeways.     On  this  rule  the  various  parts 


Fig.  836. 


Fig.  837. 


composing  the  apparatus  are  placed,  and  their  distance  can  be  fixed  by 
means  of  binding  screws,  a  is  a  support  for  a  Locatelli's  lamp,  or  other  source 
of  heat ;  F  and  E  are  screens  :  C  is  a  support  for  the  bodies  under  experi- 
ment, and  m  is  a  thermo-electrical  battery.  Near  the  apparatus  is  a  gal- 
vanometer D  ;  this  has  only  a  comparatively  few  turns  of  a  tolerably  thick 


Fig  838. 

(i  mm.)  copper  wire  ;  for  the  electromotive  force  of  the  thermocurrents  is 
small,  and  as  the  internal  resistance  is  small  too — for  it  only  consists  of  metal 
— it  is  clear  that  no  great  resistance  can  be  introduced  into  the  circuit  if  the 

P  P 


866  Dynamical  Electricity.  [940- 

current  is  not  to  be  completely  stopped.  Such  galvanometers  are  called 
thermomultipliers.  The  delicacy  of  this  apparatus  is  so  great  that  the  heat 
of  the  hand  is  enough  at  a  distance  of  a  yard  from  the  pile  to  deflect  the 
needle  of  the  galvanometer. 

In  using  it  for  measuring  temperature,  the  relation  of  the  deflection  of  the 
needle,  and  therefore  of  the  strength  of  the  current,  to  the  difference  of  the 
temperatures  of  the  two  ends,  must  be  determined.  That  known,  the  tem- 
peratures of  the  ends  not  exposed  to  the  source  of  heat  being  known,  the 
observed  deflection  gives  the  temperature  of  the  other,  and  therewith  the 
intensity  of  the  source  of  heat. 

94  !•  Properties  and  uses  of  thermo-electric  currents — Thermo-elec- 
tric currents  are  of  extremely  low  potential,  but  of  great  constancy  ;  for  their 
opposite  junctions,  by  means  of  melting  ice  and  boiling  water,  can  easily  be 
kept  at  o°  and  100°  C.  On  this  account,  Ohm  used  them  in  the  experimental 
establishment  of  his  law.  They  can  produce  all  the  actions  of  the  ordinary 
battery  in  kind,  though  in  less  degree.  By  means  of  a  thermo-electrical  pile 
consisting  of  769  elements  of  iron  and  German  silver,  the  ends  of  which 
differed  in  temperature  by  about  10°  to  15°,  Kohlrausch  proved  the  presence 
of  free  positive  and  negative  electricity  at  the  two  ends  of  the  open  pile 
respectively.  He  found  that  the  density  of  the  free  electricity  was  nearly 
proportional  to  the  number  of  elements,  and  also  that  the  electromotive  force 
of  a  single  element  under  the  above  circumstances  was  about  -~^  that  of 
a  single  Daniell's  element.  On  account  of  their  feeble  tension,  thermo- 
electric piles  produce  only  feeble  chemical  actions.  Botto,  however,  with 
1 20  platinum  and  iron  wires,  has  decomposed  water. 

Besides  these,  sparks  can  be  obtained  on  breaking  circuit,  and  magnetic 
and  physiological  effects  produced  as  with  other  sources  of  electricity. 

942.  Becquerel  s  electrical  thermometer.— This  consists  of  a  copper 
?nd  iron  wire  of  many  yards  in  length  soldered  at  their  ends,  but  otherwise 
insulated  from  each  other  by  being  covered  with  gutta-percha.  The  copper 
wire  is  cut  twice  and  connected  with  the  binding  screws  of  a  galvanometer 
(fig.  839).  One  of  the  solderings  is  arranged  in  the  place  whose  temperature 
is  to  be  measured.  In  the  figure  it  is  at  B  at  the  top  of  a  pole  A,  and  is 
underneath  a  hood,  which  protects  it  from  rain  and  the  sun,  but  allows  air  to 
circulate  round  it. 

The  other  soldering  is  immersed  in  mercury  contained  in  a  glass  tube, 
and  which  in  turn  is  placed  in  a  large  cylinder  C  containing  ether.  On  one 
side  is  a  very  delicate  thermometer  /,  which  indicates  the  temperature 
of  the  ether.  By  means  of  a  small  bellows  S,  a  caoutchouc  tube  and  a 
glass  tube,  a  current  of  air  can  be  sent  through  the  ether,  which  being  thus 
vaporised  is  cooled.  If,  on  the  contrary,  the  temperature  of  the  ether  is  to 
be  raised,  a  tin-plate  vessel  containing  hot  water  is  brought  near  the  cylin- 
der C. 

These  details  being  known,  when  the  solderings  are  at  the  same  tempera- 
ture no  current  is  produced  in  the  circuit,  and  the  galvanometer  remains  at 
zero  ;  but  when  there  is  the  least  difference  in  temperature,  the  deflection  of 
the  galvanometer  tells  which  of  these  solderings  is  the  hottest.  If  it  is  the 
one  which  is  immersed  in  the  mercury,  the  bellows  is  worked  until,  the  ether 
being  cooled,  the  galvanometer  reverts  to  zero.  The  two  solderings  being 


-943] 


Becquerel  's  Eledtric  Pyrometer. 


867 


then  at  the  same  temperature  the  thermometer  /  at  once  indicates  the  tem- 
perature in  B. 

Becquerel  has  applied  this  instrument  to  investigations  on  the  temperature 


Fig.  839. 

of  the  ground  at  various  depths,  that  of  the  air  at  different  heights,  and  also 
on  the  temperature  of  plants  and  animals. 

943.  Becquerel  s  electric  pyrometer. — This  apparatus  is  an  improved 
form  of  one  originally  devised  by  Pouillet.  It  consists  (fig.  840)  of  two  wires — 
one  of  platinum,  and  the  other  of  palladium — both  two  metres  in  length  and 
a  square  millimetre  in  section.  They  are  not  soldered  at  the  ends,  but  firmly 
tied  for  a  distance  of  a  centimetre  with  fine  platinum  wire.  The  palladium 
wire  is  enclosed  in  a  thin  porcelain  tube  :  the  platinum  wire  is  on  the  outside, 
and  the  whole  is  enclosed  in  a  larger  porcelain  tube  P.  At  the  end  of  this 
is  the  junction,  which  is  adjusted  in  the  place  the  temperature  of  which  is  to 
be  investigated.  At  the  other  end  project  the  platinum  and  palladium  wires 
;;/  and  «,  which  are  soldered  to  two  copper  wires  that  lead  the  current  to  a 
magnetometer  G.  These  wires  at  the  junction  are  placed  in  a  glass  tube 
immersed  in  ice,  so  that,  being  both  at  the  same  temperature,  they  give  rise 
to  no  current. 

The  magnetometer,  which  was  devised  by  Weber,  is  in  effect  a  large 
galvanometer.  It  consists  of  a  magnetised  bar«,  £,  placed  in  the  centre  of 
a  copper  frame  which  deadens  the  oscillations  (902)  and  rests  on  a  stirrup, 
H,  which  in  turn  is  suspended  to  a  long  and  very  fine  platinum  wire.  On 
the  stirrup  is  fixed  a  mirror  M,  which  moves  with  the  magnet,  and  gives 

p  p  2 


868 


Dynamical  Electricity. 


[943- 


by  reflection  the  image  of  divisions  traced  on  a  horizontal  scale  E  at  a 
distance.  These  divisions  are  observed  by  a  telescope.  With  this  view, 
before  the  current  passes,  the  image  of  the  zero  of  the  scale  is  made  to  coincide 
with  the  micrometer  wire  of  the  telescope ;  then  the  slightest  deflection  of 
the  mirror  gives  the  image  of  another  division,  and  therefore  the  angular 
deflection  of  the  bar  (529).  This  angle  is  always  small  and  should  not 
exceed  3  or  4  degrees  :  this  is  effected  by  placing,  if  necessary,  a  rheostat  or 
any  resistance  coil  in  the  circuit.  The  angular  deflection  being  known,  the 


Fig.  840. 

intensity  of  the  current  and  the  temperature  of  the  junction  are  deduced 
from  pyrometic  tables.  These  are  constructed  by  interpolation  when  the 
strengths  are  known,  which  correspond  to  two  temperatures  near  those  to  be 
observed. 

The  indications  of  the  pyrometer  extend  to  the  fusing  point  of  the 
palladium. 

944.  Peltier's  cross. — When  on  a  bar  of  bismuth,  BB',  cut  half-way 
through  at  its  centre  (fig.  841),  is  soldered  a  bar  of  antimony  with  a  similar 
cut,  and  when  the  ends  A  and  B  are  connected  with  a  galvanometer ;  the 
needle  of  the  galvanometer  is  deflected  in  one  direction  when  the  junction 
is  heated,  and  in  the  other  when  it  is  cooled. 


-944]  Peltiers  Cross.  869 

Peltier  found  that  when  A'  was  connected  with  one  pole,  and  B'  with  the 
other  pole,  of  a  voltaic  element,  so  that  a  current  passed  from  A'  through 
the  junction  to  B',  the  needle  was  deflected  in  such  a 
direction  as  to  show  that  the  junction  was  heated  when 
the  positive  current  passed  from  A'  to  B',  while  it  was 
cooled  when  the  current  passed  in  the  opposite  direction, 
This  experiment  may  be  made  by  hermetically  fixing  in 
two  tubulures  in  an  air  thermometer,  a  compound  bar 
consisting  of  bismuth  and  antimony  soldered  together,  B 

in  such  a  manner  that  the  ends  project  on  each  side.  Fig.  84r. 

The  projecting  parts  are  provided  with  binding  screws, 
so  as  to  allow  a  current  to  be  passed  through.  When  the  positive  current 
passes  from  the  antimony  to  the  bismuth,  the  air  in  the  bulh  is  heated,  it 
expands,  and  the  liquid  in  the  stem  sinks  ;  but  if  it  passes  in  the  opposite 
direction  the  air  is  cooled,  it  contracts,  and  the  liquid  rises  in  the  stem. 
For  this  experiment  the  current  must  have  a  certain  definite  strength,  which 
is  found  by  experiment ;  it  is  best  regulated  by  a  rheostat  (945). 

These  experiments  form  an  interesting  illustration  of  the  principle,  that 
whenever  the  effects  of  heat  are  reversed,  heat  is  produced  ;  and  whenever 
the  effects  ordinarily  produced  by  heat  are  otherwise  produced,  cold  is  the 
result. 


8;o 


Dynamical  Electricity. 


[945- 


CHAPTER   IX. 

DETERMINATION   OF   ELECTRICAL   CONSTANTS. 

945.  Rheostat. — The  rheostat  is  an  instrument  by  which  the  resistance 
of  any  given  circuit  can  be  increased  or  diminished  without  opening  the 

circuit.  The  original  form  invented  by 
Wheatstone  consists  of  two  parallel 
cylinders,  one,  A,  of  brass,  the  other, 
B,  of  wood  (fig.  842).  In  the  latter 
there  is  a  spiral  groove,  which  termi- 
nates at  a  in  a  copper  ring,  to  which  is 
fixed  the  end  of  a  fine  brass  wire.  This 
wire,  which  is  about  40  yards  long,  is 
partially  coiled  on  the  groove;  it  passes 
to  the  cylinder  A,  and,  after  a  great 
number  of  turns  on  this  cylinder,  is 
fixed  at  the  extremity  e.  Two  binding 
screws,  n  and  <?,  connected  with  the 
battery,  communicate  by  two  steel 
plates  ;  one  with  the  cylinder  A,  the 
other  with  the  ring  a. 

When    a   current    enters   at   #    it 


Fig.  842. 


simply  traverses  that  portion  of  the  wire  rolled  on  the  cylinder  B,  where  the 
windings  are  insulated  by  the  grooves  ;  passing  thence  to  the  cylinder  A, 
which  is  of  metal,  and  in  contact  with  the  wire,  the  current  passes  directly 
to  7/2,  and  thence  to  n.  Hence,  if  the  length  of  the  current  is  to  be  increased, 
the  handle  d  must  be  turned  from  right  to  left.  If,  on  the  contrary,  it 
is  to  be  diminished,  the  handle  is  to  be  fixed  on  the  axis  r,  and,  turning 
then  from  left  to  right,  the  wire  is  coiled  on  the  cylinder  A.  The  length  of 
the  circuit  is  indicated  in  feet  and  inches,  by  two  needles,  at  the  end  of 
the  apparatus  not  seen  in  the  figure,  which  are  moved  by  the  cylinders  A 
and  B. 

946.  Determination  of  the  resistance  of  a  conductor.  Reduced  length. 
— If  in  the  circuit  of  a  constant  element  a  tangent  galvanometer  be  inter- 
posed, a  certain  deflection  of  the  needle  will  be  produced.  If,  then,  different 
lengths  of  copper  wire  of  the  same  diameter  be  successively  interposed, 
corresponding  deflections  will  in  each  case  be  produced.  Let  us  suppose 
that  in  a  particular  case  the  tangent  of  the  angle  of  deflection  (823)  observed 
with  the  element  and  tangent  galvanometer  alone  was  I  '88,  and  that  when 
5,  40,  70,  and  100  yards  of  copper  wire  were  successively  placed  in  the 
circuit,  the  tangents  of  the  corresponding  deflections  were  0-849,  0-172, 


-947]  Absolute  Measure  of  Electrical  Resistance.  871 

0-105,  a°d  0-074.  Now,  in  this  experiment,  the  total  resistance  consists  of 
two  components  ;  the  resistance  offered  by  the  element  and  the  tangent 
galvanometer,  and  the  resistance  offered  by  the  wire  in  each  case.  The 
former  resistance  may  be  supposed  to  be  equal  to  the  resistance  of  x  yards  of 
copper  wire  of  the  same  diameter  as  that  used,  and  then  we  have  the  follow- 
ing relations  : — 

Length  of  wire.  Tangent  of  angle  of  deflection. 

r  yards 1-88 

.r+5          „       .  .     0-849 

.i-  +  40        „  .         .     0-172 

-r+7o        „ 0-105 

.1-+  100      „ 0-074 

If  the  intensities  of  the  currents  are  inversely  as  the  resistances — that  is, 
as  the  lengths  of  the  circuits — the  proportion  must  prevail, 

x  :  x+  5  =  0-849  :  r886; 

from  which  .i-  =  4'ii.  Combining,  in  like  manner,  the  other  observations,  we 
ijet  a  series  of  numbers,  the  mean  of  which  is  4-08  ;  that  is,  the  resistance 
offered  by  the  element  and  galvanometer  is  equal  to  the  resistance  of  4-08 
yards  of  such  copper  wire,  and  this  is  said  to  be  the  reduced  length  of  the 
element  and  galvanometer  in  terms  of  that  particular  copper  wire. 

It  is  of  great  scientific  and  practical  importance  to  have  a  unit  or  standard 
of  comparison  of  resistance,  and  numerous  such  have  been  proposed.  Jacobi 
proposed  the  resistance  of  a  metre  of  a  special  copper  wire  a  millimetre  in 
diameter.  Copper  is,  however,  ill  adapted  for  the  purpose,  as  it  is  difficult  to 
obtain  pure.  Mathiessen  proposed  an  alloy  of  gold  and  silver,  contain- 
ing two  parts  of  gold  and  one  of  silver  :  its  conducting  power  is  very  little 
affected  by  impurities  in  the  metals,  by  annealing,  or  by  moderate  changes 
of  temperature. 

Siemens'  unit  is  a  metre  of  pure  mercury,  having  a  section  of  a  square 
millimetre.  Its  actual  material  reproduction  for  ordinary  use  is  a  German 
silver  wire  3-8  metres  in  length,  and  0-9  mm.  in  diameter.  It  is  0-9536  of  an 
ohm,  or  BA  unit  (947). 

A  mile  of  No.  16  pure  copper  wire  represents  a  resistance  of  13-67  ohms. 

947.  Absolute  measure  of  electrical  resistance. — When  the  resistance 
of  any  conductor  has  been  measured-  and  expressed  by  reference  to  any  of 
the  standards  of  resistance  mentioned  in  the  preceding  paragraph,  the  num- 
ber denoting  the  result  of  the  measurement  still  does  not  tell  us  what  the 
resistance  of  the  conductor  in  question  really  is  :  it  only  tells  us  what  mul- 
tiple it  is  of  the  resistance  of  the  particular  conductor  with  which  the  com- 
parison has  been  made.  It  gives  us  merely  a  relative,  and  not  an  absolute, 
measure.  Just  in  the  same  way,  if  we  are  told  that  the  pressure  of  the  steam 
in  a  boiler  is  equal  to  (say)  8  atmospheres  (157),  this  statement  does  not  in 
itself  enable  us  to  form  any  estimate  of  what  the  actual  pressure  of  the  steam 
is  :  it  only  tells  us  that,  whatever  the  pressure  of  an  atmosphere  may  be, 
that  of  the  steam  is  8  times  as  great.  In  order  that  we  may  be  able  to  cal- 
culate what  effects  the  pressure  of  the  steam  is  capable  of  producing,  we 
require  to  have  it  stated  in  absolute  measure  ;  that  is,  not  how  much  greater 


872  Dynamical  Electricity.  [947- 

or  less  it  is  than  some  other  pressure,  but  what  actual  force  is  exerted  by  it 
on  each  unit  of  surface.  So,  for  very  many  purposes  we  require  absolute 
measures  of  electrical  resistance,  instead  of  mere  comparisons  of  the  resist- 
ance of  one  conductor  with  that  of  another. 

To  see  how  it  is  possible  to  get  an  absolute  measure  of  resistance,  we 
must  go  back  to  the  fundamental  meaning  expressed  by  the  term.  If,  by 
any  means  whatever,  a  definite  electromotive  force  (difference  of  potential)  is 
maintained  between  any  two  given  cross-sections  of  a  conductor,  a  constant 
electric  current  flows  from  one  cross  section  to  the  other,  and,  for  the  same 
conductor,  the  ratio  of  the  electromotive  force  to  the  strength  of  the  resulting 
current  is  constant.  That  is,  if  Ej,  E2,  E3,  ...  be  various  values  succes- 
sively given  to  the  electromotive  force,  and  C15  C2,  C3,  . .,  .  be  the  corre- 
sponding strengths  of  the  current,  then 

pj«5l«pfi,    .  .  .    - R  (a  constant). 
C:     L2      L3 

This  constant  ratio  of  electromotive  force  to  strength  of  current,  is  charac- 
teristic of  the  individual  conductor  employed,  and  is  called  its  electrical 
resistance.  And,  when  the  resistance  of  a  conductor  is  stated  as  the  value 
of  the  ratio  in  question,  the  statement  gives  us  the  absolute  measure  of  the 
resistance ;  that  is,  it  gives  us  definite  information  about  the  electrical  pro- 
perties of  that  particular  conductor  without  implying  a  comparison  of  it  with 
any  other  conductor. 

Hence  it  appears  that  the  absolute  resistance  of  a  given  conductor  is 
determined  if  we  can  ascertain  the  ratio  of  any  electromotive  force  to  the 
strength  of  the  current  which  it  is  capable  of  producing  in  the  conductor  in 
question.  It  is  not,  however,  needful  to  make  an  independent  measurement 
of  this  ratio  in  the  case  of  every  conductor  whose  resistance  we  require  to 
know  :  it  is  sufficient  to  determine  it  once  for  all  for  some  one  conductor, 
and  then,  taking  this  conductor  as  a  standard,  to  compare  the  resistance  of 
other  conductors  with  that  of  this  one,  by  means  of  Wheatstone's  bridge 
(948),  or  any  other  convenient  method. 

The  methods  available  for  determining  the  ratio  between  electromotive 
force  and  resistance,  required  for  an  absolute  measurement  of  resistance, 
depend  on  the  electromagnetic  phenomena  presented  by  electric  conductors 
and  currents  ;  it  will  be  sufficient  here  to  indicate  the  general  principles 
upon  which  such  methods  can  be  founded.  From  what  has  been  said,  it  will 
be  seen  that  any  method  for  this  purpose  involves  a  measurement  of  electro- 
motive force  and  a  measurement  of  the  strength  of  a  current.  It  will  be 
convenient  to  treat  these  two  parts  of  the  process  separately. 

A.  Absolute  measurement  of  electromotive  force.  When  any  electric 
conductor  is  moved  in  a  magnetic  field  (707) — that  is  to  say,  in  any  region 
where  there  is  magnetic  force — an  electromotive  force  is  in  general  developed 
in  the  conductor  during  its  motion.  The  magnitude  of  this  electromotive 
force  depends  upon  the  intensity  of  the  magnetic  field,  on  the  length  and 
form  of  the  conductor,  and  on  the  velocity  and  direction  of  its  motion.  The 
simplest  case  is  presented  by  a  straight  conductor,  with  its  length  perpendi- 
cular to  the  direction  of  the  force  in  a  uniform  magnetic  field,  and  moving  at 
right  angles  to  its  length  and  to  the  direction  of  the  force.  If  T  be  the  in- 


-947]  Absolute  Measure  of  Electromotive  Force.  873 

tensity  of  the  field,  /  the  length  of  the  conductor,  and  v  the  velocity,  the 
electromotive  force  E  is 


where  k  is  a  constant,  depending  on  the  unit  adopted  for  the  measurement 
of  electromotive  force.  If  we  define  the  unit  of  electromotive  force  as  that 
which  is  developed  in  a  conductor  of  unit  length  moving  (yn.  the  way  specified 
above)  with  unit  velocity  in  a  magnetic  field  of  unit  intensity  -,  the  constant  k 
becomes  «  I,  and  the  value  of  E  is 

E-Tfo, 

If  the  length  and  the  direction  of  motion  of  the  conductor  are  not  at  right 
angles  to  the  direction  of  magnetic  force,  we  must  project  both  on  a  plane 
perpendicular  to  the  direction  of  the  force  :  thus,  if  the  conductor  is  inclined 
at  an  angle  a,  and  moves  in  a  direction  making  an  angle  /3,  both  being 
measured  from  the  direction  of  magnetic  force,  the  electromotive  force 
becomes 

E  =  TV  sin  a.  v  sin  /3. 

If  the  conductor  is  bent  in  any  way,  so  that  a  has  different  values  for  differ- 
ent parts,  and  if  the  direction  or  velocity  of  its  motion  varies  from  one  part  to 
another,  we  may  conceive  of  it  as  divided  into  a  great  number  of  equal  parts, 
each  so  small  that  no  sensible  variation  of  a,  /3,  or  v,  can  occur  within  it  ;  we 
may  calculate  the  electromotive  force  due  to  each  of  these  small  parts  taken 
separately  by  the  last  formula,  and  then,  adding  all  the  results  together,  we 
obtain  the  electromotive  force  developed  in  the  whole  conductor.  A  little 
consideration  will  show  that  the  following  statement  is  equivalent  to  that 
just  given  :  namely,  the  electromotive  force  generated  in  a  conductor  mov- 
ing in  any  manner  in  a  magnetic  field  is  proportional  at  each  instant  to  the 
rate  of  variation  of  the  area  swept  over  by  its  projection  on  a  plane  perpendi- 
cular to  the  direction  of  the  magnetic  force  ;  and  the  average  electromotive 
force  acting  in  the  conductor  during  any  interval  of  time  is  proportional 
directly  to  the  total  area  swept  over  by  its  projection  during  the  interval, 
and  inversely  to  the  length  of  the  interval. 

In  order  to  apply  practically  the  principles  that  have  been  pointed  out, 
it  is  most  convenient  to  take  advantage  of  the  magnetic  field  due  to  the 
magnetism  of  the  earth.  Throughout  any  moderate  space  at  a  distance 
from  magnets  or  masses  of  iron,  the  magnetic  force  due  to  the  earth  is 
uniform  in  intensity  and  direction.  Suppose,  then,  a  circular  conducting 
ring,  placed  so  that  its  plane  is  perpendicular  to  the  direction  of  the  earth  s 
magnetic  force  —  that  is,  to  the  direction  of  the  dipping  needle  —  to  be  turned 
through  half  a  revolution  about  one  of  its  diameters  ;  we  may  regard  its  pro- 
jection on  a  plane  perpendicular  to  the  direction  of  the  earth's  force  to  be 
made  up  of  the  projections  of  the  two  semicircles  into  which  it  is  divided  by 
the  axis  of  rotation.  During  the  half-turn  made  by  the  ring,  the  projection 
of  each  semicircle  sweeps  through  an  area  equal  to  that  of  the  whole  ring  ; 
but  one  projection  passes  over  this  area  in  one  direction,  and  the  other  in 
the  opposite  direction.  Consequently,  equal  electromotive  forces  are  gene- 
rated in  the  two  halves  of  the  ring,  in  opposite  directions  as  regarded  from 
outside,  but  both  in  the  same  direction  if  considered  as  tending  to  produce  a 
current  round  the  ring  :  the  total  electromotive  force  is  therefore  the  sum  of 


874  Dynamical  Electricity.  [947- 

the  forces  in  the  two  halves  ;  and  if  r  be  the  radius  of  the  ring  and  therefore 
7rr~  its  area,  and  n  the  number  of  revolutions  per  second,  so  that  the  time 

occupied  by  each  half-revolution  is  —  ,  the  average  electromotive  force  act- 
ing in  the  ring  as  it  rotates  uniformly  about  a  diameter,  is 

2T  .  7rr*-«-  —  =4T7rrJ« 
2* 

where  T  stands  for  the  whole  intensity  of  the  earth's  magnetic  force.  If, 
instead  of  a  single  ring,  we  have  a  circular  coil  of  wire  of  u  convolutions, 
and  if  the  axis  of  rotation  makes  any  angle  a  with  the  line  of  dip,  the  elec- 
tromotive force  due  to  the  rotation  of  the  coil  is 

E  =  A^-nr^nu  sin  a. 

Consequently,  the  rotation  of  a  coil  of  wire  under  the  circumstances  named 
furnishes  the  means  of  obtaining  an  electromotive  force,  the  absolute  value 
of  which  is  given  by  the  intensity  of  the  magnetic  field,  the  dimensions  and 
speed  of  the  coil,  and  the  position  of  its  axis  of  rotation.  If  we  can  deter- 
mine the  strength  of  current  which  this  electromotive  force  is  capable  of 
producing  in  a  given  conductor,  the  absolute  resistance  of  the  conductor  is 
at  once  known. 

B.  Absolute  measurement  of  the  -strength  of  currents.  —  The  method  of 
measuring  the  strength  of  electric  currents  is  founded  on  the  fact  that  a 
force  is  exerted  between  a  conductor  carrying  a  current  and  any  magnetic 
pole  in  its  neighbourhood.  In  general,  both  the  distance  and  the  direction, 
as  seen  from  a  given  magnetic  pole,  vary  from  point  to  point  of  the  con- 
ductor, so  that  it  is  generally  impossible  to  give  any  simple  statement  of  the 
law  according  to  which  a  given  current  acts  upon  a  magnetic  pole  in  a 
given  position.  But,  if  we  consider  only  a  very  small  length  of  a  current, 
neither  the  distance  of  its  various  points  from  a  given  magnetic  pole,  nor 
their  directions,  can  vary  to  a  sensible  extent  ;  and  when  these  two  condi- 
tions are  constant,  the  law  of  the  force  between  the  current  and  the  pole 
may  be  stated  as  follows  :—  As  to  direction,  the  force  is  perpendicular  to  a 
plane  containing  the  current  and  the  pole,  and  acts  upon  a  north  pole,  to- 
wards the  left  hand  of  an  observer  looking  at  the  pole  from  the  line  of  the 
current,  and  so  placed  that  the  nominal  direction  of  the  current  is  from  his 
feet  to  his  head,  or,  upon  a  south  pole,  towards  the  right  hand  of  an  ob- 
server similarly  placed  ;  as  to  magnitude,  the  force  is  proportional  directly 
to  the  length  (/)  and  to  the  strength  (C)  of  the  current,  to  the  strength  of  the 
magnetic  pole  (m\  and  to  the  sine  of  the  angle  (ff)  made  by  the  direction  ot 
the  current  with  a  straight  line,  drawn  from  it  to  the  pole,  and  inversely  to 
the  square  of  the  distance  (r'}  from  the  current  to  the  pole.  Hence,  if  the 
force  be  denoted  b  we  have 


f    j  .     „ 

f=k  .^-  sin  (9, 

where  k  is  a  constant,  depending  on  the  units  in  which  the  numerical  values 
of  the  various  quantities  are  expressed.  If  we  define  the  unit  strength  of 
current  as  the  strength  of  a  current  of  which  unit  length,  placed  at  unit  dis- 
tance from  a  magnetic  pole  of  unit  strength,  and  making  everywhere  a  right 


-947]  Absolute  Measure  of  ^Strength  of  Currents.  875 

angle  with  a  line  drawn  from  it  to  the  pole,  exerts  unit  force  on  the  pole,  k 
becomes  unity,  and  we  have 


. 

ml  sin  6 

The  most  convenient  way  of  founding  upon  these  principles  a  practical 
measurement  of  the  strength  of  a  current  is  to  cause  the  current  to  go  one 
or  more  times  round  a  vertical  circle  of  known  radius  placed  in  the  plane  of 
the  magnetic  meridian,  with  a  very  short  magnet  suspended  at  the  centre 
This  is  the  arrangement  of  the  tangent  galvanometer  already  described 
(823).  If  H  is  the  intensity  of  the  horizontal  component  of  the  earth's  mag- 
netic force,  the  force  which  must  be  exerted  upon  each  pole  of  a  magnet 
whose  poles  are  of  the  strength  +  m  and  — ;//,  in  a  direction  perpendicular 
to  the  magnetic  meridian,  in  order  to  deflect  the  magnet  through  an  angle 
y  is 

f=  H/;;  tan  y. 

Putting  this  value  of /into  the  expression  given  above  for  the  strength  of 
a  current,  we  have 

~  _  Hm  tan  y  r"1 
ml  sin  6 

But  in  the  case  supposed,  that  of  a  tangent-galvanometer  with  the  current 
going  u'  times  round  the  circle,  we  have  l=u'2na,  if  a  is  the  radius  of  the 
circle  ;  moreover,  the  distance  r'  of  each  part  of  the  current  from  the  magnet 
is  constant  and  equal  to  the  radius,  or  r'  ~  a  and  the  angle  6  is  also  constant, 
being  everywhere  a  right  angle,  so  that  sin  6  =  I  ;  consequently  we  get  for 
the  strength  of  the  current  in  absolute  measure, 

C-   ""^tony-litany. 

mu'l-na  2nu' 

We  have  thus  shown  how  both  electromotive  force  and  strength  of  cur- 
rent can  be  measured  in  absolute  units  ;  and  if  these  two  measurements  be 
combined,  the  ratio  of  the  numerical  value  of  the  electromotive  force,  acting 
in  a  conductor,  to  that  of  the  strength  of  the  resulting  current  is  the  measure 
of  the  resistance  of  the  conductor  in  question.  Using  the  notation  employed 
above,  this  leads  to  the  following  expression  for  the  absolute  measure  of  re- 
sistance, 

R  _  E  =  4  Tnr^un  sin  a  .  2-nii' 
~  C  ~       ~'H^  tan  y 

Various  practical  methods  of  measurement  founded  upon  this  principle  have 
been  devised  ;  and  when  any  of  them  is  employed  the  value  of  the  resistance 
under  investigation  is  obtained  by  putting  in  this  formula  the  values  of  elec- 
tromotive force  and  strength  of  current  that  result  from  the  particular 
arrangement  adopted. 

It  may  be  observed,  with  regard  to  the  above  expression,  that  the  factors 
TT,  «,  u',  sin  a  and  tan  #,  are  all  of  them  simple  numbers,  that  T  and  H  are 
quantities  of  the  same  kind,  so  that  their  ratio  is  also  a  pure  number.  The 
only  factors  which  involve  reference  to  physical  units  are  therefore  r2,  r\  and 
«,  and,  the  two  former  being  both  distances,  the  ratio  ri-*-r/  is  the  first  power 
of  a  distance,  while  «,  the  number  of  revolutions  per  unit  of  time,  is  the  re- 


876  Dynamical  Electricity.  [947— 

ciprocal  of  the  time  occupied  by  a  single  revolution.  Hence  the  expression 
for  the  absolute  resistance  of  a  conductor  is  in  all  cases  reducible  to 

a  distance  x  a  numerical  factor  ; 
a  time 

that  is  to  say,  electrical  resistance  maybe  expressed  in  terms  of  the  units  of 
length  (or  distance)  and  time  in  the  same  manner  as  a  velocity,  and  the 
natural  unit  of  resistance,  like  the  natural  unit  of  velocity,  would  be  repre- 
sented by  a  unit  of  length  per  unit  of  time.  If,  as  is  frequently  done  for 
scientific  purposes  (814).  we  adopt  the  centimetre  as  unit  of  length  and  .the 
second  as  unit  of  time,  the  absolute  unit  of  resistance  becomes  i  centimetre 
per  second ;  such  a  resistance,  however,  is  so  small  that  resistances  com- 
monly occurring  in  practice  would  have  to  be  represented  by  inconveniently 
great  multiples  of  it.  As  a  practical  standard  of  resistance,  it  is  therefore 
more  usual  to  employ  the  '  Ohm,'  which  is  a  resistance  of  one  thousand 
million  centimetres  per  second,  or 

io9  centimetres 
i  second 

948.  Wheatstone  s  bridgre. — The  various  methods  of  determining  the 
electrical  conductivity  of  a  body  consist  essentially  in  ascertaining  the  ratio 
between  the  resistance  of  a  certain  length  of  the  conductor  in  question, 
having  a  given  section,  to  that  of  a  known  length  of  a  known  section  of  some 
substance  taken  as  standard.  The  most  convenient  method  of  ascertaining 
experimentally  the  ratio  between  the  resistance  of  two  conductors  is  by  a 
method  known  as  that  of  WheatstonJs  bridge^  the  general  principle  of  which 
may  be  thus  stated  : — 

The  conductors,  which  may  be  denoted  by  AB  and  BC,  are  connected 
end  to  end,  as  shown  in  fig.  843,  and  one  end  of  each  is  also  connected  with 

B 


Fig  843. 

a  battery,  say  the  end  A  of  AB  with  the  positive  pole,  and  the  end  C  of  BC 
with  the  negative  pole  ;  the  ends  that  are  in  connection  with  the  battery  are 
likewise  connected  together  by  another  conductor  AB'C.  A  current  will 
thus  pass  from  A  to  C  by  each  of  the  two  paths  ABC  and  AB'C,  and  there 
will  be  a  gradual  fall  of  potential  in  passing  from  A  to  C  along  either  path  ; 
so  that  for  every  point  in  the  conductors  AB  and  BC,  there  is  a  point  in  the 
wire  AB'C  which  has  the  same  potential.  If  one  end  of  a  galvanometer 
wire  BGB'  be  connected  with  the  point  of  junction  B,  the  point  of  AB'C 
which  has  the  same  potential  as  the  point  B  can  be  found  by  applying  the 
other  end  of  the  galvanometer  wire  to  AB'C,  and  shifting  the  point  of  contact 
towards  A  or  C  until  the  galvanometer  shows  no  deflection.  Let  B'  be  the 
point  so  found  ;  the  fact  that  when  it  is  connected  with  B  by  the  bridge 
BGB'  no  current  passes  from  one  to  the  other  proves  that  the  potential  at 


-949] 


Equivalent  Conductors. 


877 


B'  is  the  same  as  the  potential  at  B.  From  this  it  follows  that  if  r  and  r' 
are  the  resistances  of  AB  and  BC  respectively,  and  s  and  s'  the  resistances 
of  AH' and  B'C, 

r  .  r'  =  s  :  s'. 

If  the  conductor  AB'C  is  a  wire  of  uniform  material  and  diameter,  the 
ratio  of  the  resistances  s  and  s'  will  be  the  ratio  of  the  lengths  of  the  corre- 
sponding portions  of  wire,  and  can  therefore  be  at  once  really  ascertained. 

To  prove  this,  let  MN,  NO,  MN'  and  N'O'  (fig.  844)  be  taken  in  the 
same  straight  line,  proportional  respectively  to  the  several  resistances 
rr7,  s  s' ',  and  let  MP  be  drawn  at  right  angles  to  O'MO  of  a  length  pro- 
portional to  the  difference  of  potential  between  the  points  A  and  C.  Then  if 
the  straight  lines  PO  and  PO'  be  drawn,  the  potential  at  N  (the  point  of 
junction  of  the  conductors  whose  resistances  r  and  r'  are  to  be  compared — 
i.e.  the  point  corresponding  to  B  in  the  previous  figure)  will  be  given  by  the 


Fig.  844. 

length  of  the  line  NQ,  drawn  from  N  at  right  angles  to  NO  ;  and  the  point 
N'  (corresponding  to  B'  in  the  previous  figure)  where  the  potential  is  the 
same  as  at  N  will  be  found  by  drawing  QO'  parallel  to  OO',  and  letting  fall 
from  Q'  the  perpendicular  Q'N'  upon  O'M.  The  geometry  of  the  figure 
gives  obviously. 


MP 


-- 

s  +  s'      MP  ' 


and  therefore  since 


r  _s 

r'     s' 


The  resistance  of  a  galvanometer  may  be  determined  by  making  it  one 
of  the  four  conductors  of  a  Wheatstone's  bridge  arrangement ;  replacing  it 
in  the  bridge  by  an  ordinary  contact  key.  The  resistances  of  the  other  con- 
ductors are  then  varied  until,  on  making  contact,  the  deflection  of  the  gal- 
vanometer is  constant. 

949.  Equivalent  conductors. — The  resistance  of  a  conductor  depends, 
as  we  have  seen  (825),  on  its  length,  section,  and  conductivity.  Two  con- 
ductors, C  and  C',  whose  length,  conductivity,  and  section  are  respectively 
AX',  KK',  toco',  would  offer  the  same  resistance,  and  might  be  substituted  for 
each  other  in  any  voltaic  circuit,  without  altering  its  intensity,  provided  that 

=   ,   , ;  and  such  conductors  are  said  to  be  equivalent  to  each  other.     An 

Kd)        K  ft) 

example  will  best  illustrate  the  application  of  this  principle. 


878  Dynamical  Electricity.  [949  - 

It  is  required  to  know  what  length  of  a  cylindrical  copper  wire  4  mm.  in 
diameter  would  be  equivalent  to  12  metres  of  copper  wire  i  mm.  in  dia- 
meter. 

Let  X=  12  the  length  of  the  copper  wire  I  mm.  in  diameter,  and  X'  the 
length  of  the  other  wire  ;  then  since  in  this  case  the  material  is  the  same 

the  conductivity  is  the  same,  and  the  equation  becomes  —  =  —  ..     Now  the 

CO          CO 

sections  of  the  wires  are  directly  as  the  squares  of  the  diameters,  and  hence 

12     A' 
we  have    2  =  _2,  or  X'=  12  x  16=  192.     That  is,  192  metres  of  copper  wire  4 

mm.  in  thickness  would  only  offer  the  same  resistance  as  12  metres  of  copper 
wire  i  mm.  in  thickness. 

How  thick  must  an  iron  wire  be  which  for  the  same  length  shall  offer  the 
same  resistance  as  a  copper  wire  2-5  mm.  in  diameter  ? 

Here,  the  length  being  the  same,  the  expression  becomes  KO>  =  *'&/,  or  since 
the  sections  are  as  the  squares  of  the  diameter,  *^2  =  t'df.  The  conductivity 
of  copper  is  unity,  and  that  of  iron  0-138  Hence  we  have  2'52  =  <//2  x  0-138 
or  <//2  =  6-2  5  -0-138  =  45'3  mm.  or  ^'  =  67  mm.;  that  is,  any  length  of  a 
copper  wire  2*5  mm.  in  diameter  might  be  replaced  by  iron  wire  of  the  same 
length,  provided  its  diameter  were  67  mm. 

950.  Determination  of  tbe  internal  resistance  of  an  element.  —  The 
following  is  a  method  of  determining  the  internal  resistance  of  an  element. 
A  circuit  is  formed  consisting  of  one  element,  a  rheostat,  and  a  galvanometer, 
and  the  strength  C  is  noted  on  the  galvanometer.  A  second  element  is  then 
joined  with  the  first,  so  as  to  form  one  of  double  the  size,  and  therefore  half 
the  resistance,  and  then  by  adding  a  length,  /,  of  the  rheostat  wire,  the 
strength  is  brought  to  what  it  originally  was.  Then  if  E  is  the  electromotive 
force,  and  R  the  resistance  of  the  element,  r  the  resistance  of  the  galvano- 
meter and  the  other  parts  of  the  circuit  ;  the  current  strength  C  in  the  one 

case  is  C  =  -  -  ,and  in  the  other  =  .  --  ;  and  since  the  strength  in  both 


cases  is  the  same,  R  =  2/. 

951.  Electrical  conductivity.  —  We  can  regard  conductors  in  two 
aspects,  and  consider  them  as  endowed  with  a  greater  or  less  facility  for  al- 
lowing electricity  to  traverse  them  —  a  property  which  is  termed  conductivity  — 
or  we  may  consider  conductors  interposed  in  a  circuit  as  offering  an  obstacle 
to  the  passage  of  electricity  :  that  is,  a  resistance  which  it  must  over- 
come. A  good  conductor  offers  a  feeble  resistance,  and  a  bad  conductor 
a  great  resistance.  Conductivity  and  resistance  are  the  inverse  of  each 
other. 

The  conductivity  of  metals  has  been  investigated  by  many  physicists  by 
methods  analogous  in  general  to  that  described  in  the  preceding  paragraph, 
and  very  different  results  have  been  obtained.  This  arises  mainly  from  the 
various  degrees  of  purity  of  the  specimens  investigated,  but  their  molecular 
condition  has  also  great  influence.  Matthiessen  found  the  difference  in  con- 
ductivity between  hard-drawn  and  annealed  silver  wire  to  amount  to  85, 
for  copper  2-2,  and  for  gold  1-9  per  cent.  The  following  are  results  of  a 
series  of  careful  experiments  by  Matthiessen  on  the  electrical  conductivity 
of  metals  at  o°  C.  compared  with  silver  as  a  standard  :  — 


-951]  Electrical  Conductivity.  879 

Silver    .  .  .  IOCTO  Platinum  .  .18-0 

Copper .  .  .  99-9  Iron    .  .16-8 

('.old      .  .  .  80-0  Tin     .  13-1 

Sodium.  .  .  37-4  Lead  .  8-3 

Aluminum  .  .  34*0  German  Silver  77 

Zinc       .  .  .  29-0  Antimony  .  .         4'6 

Cadmium  .  .  237  Mercury  .  I* 

Brass     .  .  .  22-0  Bismuth  .  .         1*2 

Potassium  .  .  20*8  Graphite  .  .         0*07 

Silver  and  copper  have  the  smallest  resistance  for  a  given  volume,  while 
aluminum  has  the  smallest  for  a  given  weight. 

The  conductivity  of  metals  is  diminished  by  an  increase  in  temperature, 
The  law  of  this  diminution  is  expressed  by  the  formula 

K  =Ko(i-at  +#•'); 

where  *,  and  KO  are  the  conductivities  at  /  and  o°  respectively,  and  a  and  b 
are  constants,  which  are  probably  the  same  for  all  pure  metals.  For  ten 
metals  investigated  by  Matthiessen  he  found  that  the  conductivity  is  ex- 
pressed by  the  formula 

Kt  -  K0  ( i  -  0-0037647/  +  o-ooooo834/-). 

It  seems  that  this  value  is  about  0*00368  for  each  degree  C.  This  co- 
efficient agrees  in  a  surprising  manner  with  the  co-efficient  of  expansion  of 
gases  which  is  ^=3 

Liquids  are  far  worse  conductors  than  metals.  The  conductivity 
of  a  solution  of  one  part  of  chloride  of  sodium  in  100  parts  of  water  is 
3oooo~ooo  l^at  °f  c°PPer-  In  general,  acids  have  the  highest  and  solutions  of 
alkalies  and  neutral  salts  the  lowest  conductivity.  Yet,  in  solutions,  the 
conductivity  does  not  increase  in  direct  proportion  to  the  quantity  of  salt 
dissolved. 

The  following  is  a  list  of  the  conductivity  of  a  few  liquids  as  compared 
with  that  of  pure  silver  : — 

Pure  silver        .....       100,000,000-00 

Nitrate  of  copper,  saturated  solution  .             .  8*99 

Sulphate  of  copper            ditto             .  5-42 

Chloride  of  sodium            ditto             .             .  3J*52 

Sulphate  of  zinc                 ditto             .             .  577 

Sulphuric  acid,  riosp.gr.       .             .             .  99'°7 

i'24sp.gr.      .             .             .  13275 

„        I -40  sp.gr.      .                         .  9075 

Nitric  acid,  commercial           .             .             .  88'68 

Distilled  water.             ....  o-oi 

Liquids  and  fused  conductors  increase  in  conductivity  by  an  increase  of 
temperature.  This  increase  is  expressed  by  the  formula 

Kt  =  K0(i  +  at\ 

and  the  values  of  a  are  considerable.  Thus,  for  a  saturated  solution  of  sul- 
phate of  copper,  it  is  0-0286. 

The  influence  of  light  upon  electrical-conductivity  in  the  case  of  selenium 


88o  Dynamical  Electricity.  [951- 

has  been  already  alluded  to  (930),  and  is  directly  proved  by  the  following 
experiment  :  A  thin  strip  of  this  metalloid,  about  38  mm.  in  length,  by  13 
in  breadth,  was  provided  at  the  ends  with  conducting  wires  and  placed  in  a 
box  with  a  draw-lid.  The  selenium,  having  been  carefully  balanced  in  a 
Wheatstone's  bridge,  was  exposed  to  diffused  light  by  withdrawing  the  lid, 
when  the  resistance  at  once  fell  in  the  ratio  of  1  1  to  9.  On  exposure  to  the 
various  spectral  colours,  after  having  been  in  the  dark,  it  was  found  to  be 
most  affected  by  the  red  ;  but  the  maximum  action  was  just  outside  the  red, 
where  the  resistance  fell  in  the  ratio  of  3  to  2.  Momentary  exposure  to  the 
light  of  a  gas  lamp  or  even  to  that  of  a  candle  causes  a  diminution  of  resist- 
ance. Exposure  to  full  sunlight  diminished  the  resistance  to  one  half. 

The  effect  produced  on  exposure  to  light  is  immediate,  while  recurrence 
to  the  normal  state  takes  place  more  slowly.  A  vessel  of  hot  water  placed 
near  the  strip  produced  no  effect,  and  hence  the  phenomenon  cannot  be  due 
to  heat,  but  there  appear  to  be  certain  rays  which  have  the  power  of  pro- 
ducing a  molecular  change  in  the  selenium  by  which  its  conductivity  is  in- 
creased. 

952.  Determination  of  electromotive  force.  Wheatstone  s  method. 
—  In  the  circuit  of  the  element  whose  electromotive  force  is  to  be  determined  a 
tangent  galvanometer  and  a  rheostat  are  inserted,  the  latter  being  so  arranged 
that  the  strength,  C,  of  the  current  is  a  definite  amount  ;  for  example,  the 
galvanometer  indicates  45°.  By  increasing  the  amount  of  the  rheostat  wire 
by  the  length,  /,  a  diminished  strength,  c  (for  instance,  40°),  is  obtained. 

A  second  standard  element  is  then  substituted  for  that  under  trial,  and, 
by  arranging  the  rheostat,  the  strength  of  the  current  is  first  made  equal  to 
C,  and  then,  by  addition  of  /  lengths  of  the  rheostat,  is  made  =  c. 

Then  if  E  and  Ej  are  the  two  electromotive  forces,  R  and  Rx  their  resist- 
ances when  they  have  the  intensity  I,  and  /  and  /1  the  lengths  added,  we 
have 

Trial  Element.  Standard  Element. 


=  ^ 


from  which  we  have  E  =  E  ^ 

Hence  the  electromotive  forces  of  the  elements  compared  are  directly  as  the 
lengths  of  the  wire  interposed. 

Another  method  is  described  by  Wiedemann.  The  two  elements  are 
connected  in  the  same  circuit  with  a  tangent  galvanometer,  or  other  appa- 
ratus for  measuring  strength,  first  in  such  a  manner  that  their  currents  go 
in  the  same  direction,  and  secondly  that  they  are  opposed.  Then  if  the 
electromotive  forces  are  E  and  E',  their  resistances  are  R  and  R',  the  other 
resistances  in  the  circuits  being  r,  while  Cg  is  the  intensity  when  the  elements 
are  in  the  same  direction,  and  Cd  the  intensity  when  they  go  in  opposite  direc- 
tions, then  F  +  F'  F  F' 
C8=  ^  and  "- 

T 

whence 


-954]  Divided  or  BraJich  Currents.  88 1 

955.  Siemens'  electrical  resistance  thermometer. — Supposing  in  a 
Wheatstone's  bridge  arrangement,  after  the  ratio  r  :  r^  =  s  :  j,  has  been  estab- 
lished, the  temperature  of  one  of  the  coils,  r,  for  instance,  be  increased,  the 
above  ratio  will  no  longer  prevail,  for  the  resistance  of  r  will  have  been 
altered  by  the  temperature,  and  the  ratio  of  s  and  sl  must  be  altered  so  as  to 
produce  equivalence.  On  this  idea  Siemens  has  based  a  mode  of  observing 
the  temperature  of  places  which  are  difficult  of  direct  access.  He  places  a 
coil  of  known  resistance  in  the  particular  locality  whose  temperature  is  to  be 
observed  :  it  is  connected  by  means  of  long  good  conducting  wires  with  the 
place  of  observation,  where  it  forms  part  of  a  Wheatstone's  bridge  arrange- 
ment. The  resistance  of  the  coil  is  known  in  terms  of  the  rheostat,  and  by 
preliminary  trials  it  has  been  ascertained  how  much  additional  wire  must  be 
introduced  to  balance  a  given  increase  in  the  temperature  of  the  resistance 
coil.  This  being  known,  and  the  apparatus  adjusted  at  the  ordinary  tempera- 
ture, when  the  temperature  of  the  resistance  coil  varies,  this  variation  in  either 
direction  is  at  once  known  by  observing  the  quantity  which  must  be  brought 
in  or  out  of  the  rheostat  to  produce  equivalence. 

This  apparatus  has  been  of  essential  service  in  watching  the  tempera- 
ture of  large  coils  of  telegraph  wire,  which,  stowed  away  in  the  hold  of  vessels, 
are  very  liable  to  become  heated.  It  might  also  be  used  for  the  continuous 
and  convenient  observation  of  underground  and  submarine  temperatures. 
If  a  coil  of  platinum  wire  were  substituted  for  the  copper,  the  apparatus  could 
be  used  for  watching  the  temperature  of  the  interior  of  a  furnace. 

It  has  been  found  that  the  magnetism  of  ships  (715)  excited  so  perturbing 
an  influence  on  the  needle  of  the  galvanometer  as  to  make  its  indications 
untrustworthy.  Hence  for  use  in  such  cases  Siemens  replaces  the  galvano- 
meter, as  an  indicator,  by  a  voltameter  specially  constructed  for  the  purpose. 

954.  Divided  or  branch  currents. — In  fig.  845  the  current  from  Bunsen's 
element  traverses  the  wire  rqpnm  :  let  us  take  the  case  in  which  any  two 
points  of  this  cir- 
cuit, n  and  q,  are 
joined  by  a 
second  wire, 
nxq.  The  cur- 
rent will  then 
divide  at  the 
point  q  into  two 
others,  one  of 
which  goes  in  the 

direction  qpnm,  while  another  takes  the  direction  qxnm.  The  two  points  q 
and  «  from  which  the  second  conductor  starts  and  ends  are  called  \hzpoints 
of  derivation,  the  wire  qpm  and  the  wire  qxn  are  derived  wires.  The  currents 
which  traverse  these  wires  are  called  the  derived  or  partial  currents  ;  the 
current  which  traversed  the  circuit  rqpnm  before  it  branches  is  the  primitive 
current :  and  the  name  principal  current  is  given  to  the  whole  of  the  current 
which  traverses  the  circuit  when  the  derived  wire  has  been  added.  The 
principal  current  is  stronger  than  the  primitive  one,  because  the  interposition 
of  the  wire  qxn  lessens  the  total  resistance  of  the  circuit. 

If  the  two  derived  wires  are  of  the  same  length  and  the  same  section,  their 
action  would  be  the  same  as  if  they  were  juxtaposed  and  they  might  be  re- 


882  Dynamical  Electricity.  [954- 

placed  by  a  single  wire  of  the  same  length  but  of  twice  the  section,  and 
therefore  with  half  the  resistance.  Hence  the  current  would  divide  into  two 
equal  parts  along  the  two  conductors. 

When  the  two  wires  are  of  the  same  length  but  of  different  sections,  the 
current  would  divide  unequally,  and  the  quantity  which  traversed  each  wire 
would  be  proportional  to  its  section  ;  just  as,  when  a  river  divides  into  two 
branches,  the  quantity  of  water  which  passes  in  each  branch  is  proportional 
to  its  dimensions.  Hence  the  resistance  of  the  two  conductors  joined  would 
be  the  same  as  that  of  a  single  wire  of  the  same  length,  the  section  of  which 
would  be  the  sum  of  the  two  sections. 

If  the  two  conductors  qpn  and  qocn  are  different,  both  in  kind,  length, 
and  section,  they  could  always  be  replaced  by  two  wires  of  the  same  kind 
and  length,  with  such  sections  that  their  resistances  would  be  equal  to  the 
two  conductors  ;  in  short,  they  might  be  replaced  by  equivalent  conductors. 
These  two  wires  would  produce  in  the  circuit  the  same  effect  as  a  single 
wire,  which  had  this  common  length,  and  whose  section  would  be  the  sum 
of  the  sections  thus  calculated.  The  current  divides  at  the  junction  into  two 
parts  proportional  to  these  sections,  or  inversely  as  the  resistances  of  the  two 
wires.  Suppose,  for  instance,  qpn  is  an  iron  wire  5  metres  in  length  and 
3  mm.  square  in  section,  and  qxn  a  copper  wire. 

The  first  might  be  replaced  by  a  copper  wire  a  metre  in  length,  whose 
section  would  be  |  x  j  (taking  the  conductivity  of  copper  at  7  times  that  of 
iron)  or  -—  square  mm.  The  second  wire  might  be  replaced  by  a  copper 
wire  a  metre  in  length  with  a  section  of  f  square  mm.  These  two  wires 
would  present  the  same  resistance  as  a  copper  wire  a  metre  in  length,  and 
with  a  section  of  ^  +  f  -  —5  square  millimetres. 

The  principal  current  would  divide  along  the  wires  in  two  portions,  which 
would  be  as  —  :  |. 

The  most  important  laws  of  divided  circuits  are  as  follows  : — 

i.  The  sum  of  the  strengths  in  the  divided  parts  of  a  circuit  is  equal  to 
the  strength  of  the  principal  current. 

ii.  The  strengths  of  the  currents  in  the  divided  parts  of  a  circuit  are 
inversely  as  their  resistances  ;  or,  what  is  the  same,  the  division  of  a  current 
into  partial  currents  which  lie  between  two  points  is  directly  as  the  respective 
conductivities  of  these  branches. 

And  as  problems  on  divided  circuits  frequently  occur  in  telegraphy,  the 
following  formulae,  which  include  these  laws,  are  given  for  a  simple  case  : — 

If  C  be  the  strength  of  the  current  in  the  undivided  part  of  the  circuit 
rqpnm,  and  if  c  is  the  strength  in  one  branch  (say)  in  the  above  figure  qpn 
and  c'  in  qxn  ;  if  R,  r,  and  r,  are  the  corresponding  resistances,  the  electro- 
motive force  being  E,  then 

c  =    E  (r_+_rj  c=       _Ef^  _E r^_ 

Rr  +  r^  rrl  Rr  +  Rrx  +  rrl  Rr  -±  Rrx  +  rr^ 

The  resistance  R:  of  the  whole  circuit  is 

R^R+^i, 

r  +  r 

and  therefore  the  total  resistance  of  the  branch  currents  qpn  and  qxn  is 


-956]  Currents  of  Muscle  at  Rest.  883 


CHAPTER  X. 

ANIMAL   ELECTRICITY. 

955.  Muscular  currents. — The  existence  of  electrical  currents  in  living 
muscle  was  first  indicated  by  Galvani,  but  his  researches  fell  into  oblivion 
after  the  discovery  of  the  Voltaic  pile,  which  was  supposed  to  explain  all  the 
phenomena.     Since  then,  Xobili,  Matteucci,  and  others,  especially,  in  late 
years,  Du  Bois  Reymond,  have  shown  that  electric  currents  do  exist  in  living 
muscles  and  nerves,  and  have  investigated  their  laws. 

For  investigating  these  currents  it  is  necessary  to  have  a  delicate  gal- 
vanometer, and  also  electrodes  which  will  not  become  polarised  or  give  a 
current  of  their  own,  and  which  will  not  in  any  way  alter  the  muscle  when 
placed  in  contact  with  it ;  the  electrodes  which  satisfy  these  conditions  best 
are  those  of  Du  Bois  Reymond,  as  modified  by  Bonders.  Each  consists  of 
a  glass  tube,  one  end  of  which  is  narrowed  and  stopped  by  a  plug  of  paste 
made  by  moistening  china-clay  with  a  half  per  cent,  solution  of  common  salt ; 
the  tube  is  then  partially  filled  with  a  saturated  solution  of  sulphate  of  zinc, 
and  into  this  dips  the  end  of  a  piece  of  thoroughly  amalgamated  zinc  wire, 
the  other  end  of  which  is  connected  by  a  copper  wire  with  the  galvanometer; 
the  moistened  china-clay  is  a  conducting  medium  which  is  perfectly  neutral 
to  the  muscle,  and  amalgamated  zinc  in  solution  of  sulphate  of  zinc  does  not 
become  polarised. 

956.  Currents  of  muscle  at  rest. — In  describing  these  experiments  the 
surface  of  the  muscle  is  called  the  natural  longitudinal  section  ;  the  tendon, 
the  natural  transverse  section  ;  and  the  surfaces  obtained  by  cutting  the 
muscle  longitudinally  or  transversely  are  respectively  the  artificial  longitu- 
dinal and  artificial  transverse  sections. 

If  a  living  irritable  muscle  be  removed  from  a  recently  killed  frog,  and 
the  clay  of  one  electrode,  be  placed  in  contact  with  its  surface,  and  of  the 
other  with  its  tendon,  the  galvanometer  will  indicate  a  current  from  the 
former  to  the  latter  ;  showing,  therefore,  that  the  surface  of  the  muscle  is 
positive  with  respect  to  the  tendon.  By  varying  the  position  of  the  elec- 
trodes, and  making  various  artificial  sections,  it  is  found — 

1.  That  any  longitudinal  section  is  positive  to  any  transverse. 

2.  That  any  point  of  a  longitudinal  section  nearer  the  middle  of  the 
muscle  is  positive  to  any  other  point  of  the  same  section  farther  from  the 
centre. 

3.  In  any  artificial  transverse  section  any  point  nearer  the  periphery'  is 
positive  to  one  nearer  the  centre. 

4.  The  current  obtained  between  two  points  in  a  longitudinal  or  in  a 


884 


Dynamical  Electricity. 


[956- 


Fig. 


transverse  section  is  always  much  more  feeble  than  that  obtained  between 
two  different  sections. 

5.  No  current  is  obtained  if  two  points  of  the  same  section  equidistant 
from  its  centre  be  taken. 

6.  To  obtain  these  currents  it  is  not  necessary  to  employ  a  whole  muscle, 
or  a  considerable  part  of  one,  but  the  smallest  fragment  that  can  be  experi- 
mented with  is  sufficient. 

7.  If  a  muscle  be  cut  straight  across,  the  most  powerful  current  is  that 
from  the  centre  of  the  natural  longitudinal  section  to  the  centre  of  the  arti- 
ficial transverse  ;  but  if  the  muscle  be 
cut  across  obliquely,  as  in  fig.  846,  the 
most   positive    point   is   moved   from    c 
towards  b,  and  the  most  negative  from 

/a  d  towards  a  ('  Currents  of  inclination  '). ' 
To  explain  the  existence  and  rela- 
tions of  these  muscular  currents,  it  may  be  supposed  that  each  muscle  is 
made  up  of  regularly  disposed  electromotor  elements,  which  may  be  re- 
garded as  cylinders  whose  axes  are  parallel  to  that  of  the  muscle,  and 
whose  sides  are  charged  with  positive  and  their  ends  with  negative  electri- 
city ;  and,  further,  that  all  are  suspended  and  enveloped  in  a  conducting 
medium.  In  such  a  case  (fig.  847),  it  is  clear  that  throughout  most  of  the 
muscle  the  positive  electricities  of  the  opposed  surfaces  would  neutralise  one 
another,  as  would  also  the  negative  charges  of  the  ends  of  the  cylinders  ;  so 
that,  so  long  as  the  muscle  was  intact,  only  the  charges  at  its  sides  and  ends 
would  be  left  to  manifest  themselves  by  the  production  of  electromotive 
phenomena ;  the  whole  muscle  being  enveloped  in  a  conducting  stratum,  a 
current  would  constantly  be  passing  from  the  longitudinal  to  the  transverse 
section,  and,  a  part  of  this  being  led  off  by  the  wire  circuit,  would  manifest 
itself  in  the  galvanometer. 

This  theory  also  explains  the  currents  between  two  different  points  on 
the  same  section  ;  the  positive  charge  at  b,  for  instance  (fig.  846),  would  have 

more  resistance  to  overcome  in 
getting  to  the  transverse  section 
than  that  at  d,  therefore  it  has 
a  higher  tension  ;  and  if  b  and 
d  are  connected  by  the  elec- 
trodes, b  will  be  found  positive 
to  d,  and  a  current  will  pass 
from  the  former  to  the  latter. 

What  are  called  currents  of 
inclination  are  also  explicable 

Fi°  8  on    the   above   hypothesis,    for 

the  oblique  section  can  be  re- 
presented as  a  number  of  elements  arranged  as  in  fig.  845,  so  that  both  the 
longitudinal  surfaces  and  the  ends  of  the  cylinders  are  laid  bare,  and  it  can 
thus  be  regarded  as  a  sort  of  oblique  pile  whose  positive  pole  is  towards  b 
and  its  negative  at  «,  and  whose  current  adds  itself  algebraically  to  the 
ordinary  current  and  displaces  its  poles  as  above  mentioned. 

A  perfectly  fresh  muscle,  very  carefully  removed,  with  the  least  possible 


-960] 


Electrical  Fish.  885 


contact  with  foreign  matters,  sometimes  gives  almost  no  current  between  its 
different  natural  sections,  and  the  current  always  becomes  more  marked 
after  the  muscle  has  been  exposed  a  short  time  ;  nevertheless,  the  pheno- 
mena are  vital,  for  the  currents  disappear  completely  with  the  life  of  the 
muscle,  sometimes  becoming  first  irregular  or  even  reversed  in  direction. 

957.  Rheoscopic  frog.     Contraction  without  metals. — The  existence 
of  the  muscular  currents  can  be  manifested  without  a  galvanometer,  by  using 
another  muscle  as  a  galvanoscope. 

Thus,  if  the  nerve  of  one   living 
muscle  of  a  frog  be  dropped  sud- 
denly on  another  living  muscle,  so 
as   to  come    in   contact   with    its 
longitudinal   and    transverse    sec- 
tions,  a  contraction   of   the    first  .  a 
muscle  will  occur,  due  to  the  stimu- 
lation of  its  nerve  by  the  passage  through  it  of  the  electric  current  derived 
from  the  surface  of  the  second. 

958.  Currents  in  active  muscle. — When  a  muscle  is  made  to  contract 
there  occurs  a  sudden  diminution  of  its  natural  electric  current,  as  indicated 
by  the  galvanometer.     This  is  so  instantaneous  that,  in  the  case  of  a  single 
muscular  contraction,  it  does  not  overcome  the  inertia  of  the  needle  of  the 
galvanometer ;  but  if  the  contractions  be  made  to  succeed  one  another  very 
rapidly — that  is,  if  the  muscle  be  tetanised  (827) — then  the  needle  swings 
steadily  back  towards  zero  from  the  position  in  which  the  current  of  the 
resting  muscle  had  kept  it,  often  gaining  such  momentum  in  the  swing  as  to 
pass  beyond  the  zero  point,  but  soon  reverting  to  some  point  between  zero 
and  its  original  position. 

The  negative  variation  in  the  case  of  a  simple  muscular  contraction  can, 
however,  be  made  manifest  by  using  another  muscle  as  a  rheoscope  ;  if  the 
nerve  of  this  second  muscle  be  laid  over  the  first  muscle  in  such  a  position 
that  the  muscular  current  passes  through  it,  and  the  first  muscle  be  then  made 
to  contract,  the  sudden  alteration  in  the  strength  of  its  current  stimulates 
the  nerve  laid  on  it  (827),  and  so  causes  a  contraction  of  the  muscle  to  which 
the  latter  belongs. 

The  same  phenomenon  can  be  demonstrated  in  the  muscles  of  warm- 
blooded animals  ;  but  with  less  ease,  on  account  of  the  difficulty  of  keeping 
them  alive  after  they  are  laid  bare  or  removed  from  the  body.  Experiments 
made  by  placing  electrodes  outside  the  skin,  or  passing  them  through  it,  are 
inexact  and  unsatisfactory. 

959.  Electric  currents  in  nerve. — From  nerves  the  same  electromotor 
indications  can  be  obtained  as  from  muscles  ;  at  least,  as  far  as  their  smaller 
size  will  permit ;  the  currents  are  more  feeble  than  the  muscular  ones,  but 
can  be  demonstrated  by  the  galvanometer  in  a  similar  way.     Negative  vari- 
ation has  been  proved  to  occur  in  active  nerve  as  in  active  muscle.     The 
effect  of  a  constant  current  passed  through  one  part  of  a  nerve  on  the  amount 
of  the  normal  nerve-current,  measured  at  another  part,  has  already  been 
described  (Chap.  III.  Electrotonus). 

960.  Electrical  fish. — Electrical  fish  are  those  fish  which  have  the  re- 
markable property  of  giving,  when  touched,  shocks  like  those  of  the  Leyden 


886  Dynamical  Electricity.  [960- 

jar.  Of  these  fish  there  are  several  species,  the  best  known  of  which  are  the 
torpedo,  the  gymnotus,  and  the  silurus.  The  torpedo,  which  is  very  common 
in  the  Mediterranean,  has  been  carefully  studied  by  Becquerel  and  Breschet 
in  France,  and  by  Matteucci  in  Italy.  The  gymnotus  was  investigated  by 
Humboldt  and  Bonpland  in  South  America,  and  in  England  by  Faraday, 
who  had  the  opportunity  of  examining  live  specimens. 

The  shock  which  they  give  serves  both  as  a  means  of  offence  and  of 
defence.  It  is  purely  voluntary,  and  becomes  gradually  weaker  as  it  is 
repeated  and  as  these  animals  lose  their  vitality,  for  the  electrical  action 
soon  exhausts  them  materially.  According  to  Faraday,  the  shock  which  the 
gymnotus  gives  is  equal  to  that  of  a  battery  of  15  jars  exposing  a  coating 
of  25  square  feet,  which  explains  how  it  is  that  horses  frequently  give  way 
under  the  repeated  attacks  of  the  gymnotus. 

Numerous  experiments  show  that  these  shocks  are  due  to  ordinary 
electricity.  For  if,  touching  with  one  hand  the  back  of  the  animal,  the 
belly  is  touched  with  the  other,  or  with  a  metal  rod,  a  violent  shock  is  felt 
in  the  wrists  and  arms  ;  while  no  shock  is  felt  if  the  animal  is  touched  with 
an  insulating  body.  Further,  when  the  back  is  connected  with  one  end  of  a 
galvanometer  wire  and  the  belly  with  the  other,  at  each  discharge  the  needle 
is  reflected  but  immediately  turns  to  zero,  which  shows  that  there  is  an 
instantaneous  current ;  and,  moreover,  the  direction  of  the  needle  shows  that 
the  current  goes  from  the  back  to  the  belly  of  the  fish.  Lastly,  if  the  current 
of  a  torpedo  be  passed  through  a  helix  in  the  centre  of  which  is  a  small  steel 
bar,  the  latter  is  magnetised  by  the  passage  of  a  discharge. 

By  means  of  the  galvanometer,  Matteucci  established  the  following 
facts  :— 

i.  When  a  torpedo  is  lively,  it  can  give  a  shock  in  any  part  of  its  body  ; 
but  as  its  vitality  diminishes,  the  parts  at  which  it  can  give  a  shock  are  nearer 
the  organ  which  is  the  seat  of  the  development  of  electricity.  2.  Any  point 
of  the  back  is  always  positive  as  compared  with  the  corresponding  point  of 
the  belly.  3.  Of  any  two  points  at  different  distances  from  the  electrical 
organ,  the  nearest  always  plays  the  part  of  a  positive  pole,  and  the  farthest 
that  of  negative  pole.  With  the  belly  the  reverse  in  the  case. 

The  organ  where  the  electricity  is  produced  in  the  torpedo  is  double,  and 
formed  of  two  parts  symmetrically  situated  on  two  sides  of  the  head,  and 
attached  to  the  skull  bone  by  the  internal  face.  Each  part  consists  of  nearly 
parallel  lamellae  of  connective  tissue  enclosing  small  chambers,  in  which  lie 
the  so-called  electrical  plates,  each  of  which  has  a  final  nerve-ramification 
distributed  on  one  of  its  faces.  This  face,  on  which  the  nerve  ends,  is  turned 
the  same  way  in  all  the  plates,  and  when  the  discharge  takes  place  is  always 
negative  to  the  other. 

Matteucci  investigated  the  influence  of  the  brain  on  the  discharge.  For 
this  purpose  he  laid  bare  the  brain  of  a  living  torpedo,  and  found  that  the  first 
three  lobes  could  be  irritated  without  the  discharge  being  produced,  and  that 
when  they  were  removed  the  animal  still  possessed  the  faculty  of  giving  a 
shock.  The  fourth  lobe,  on  the  contrary,  could  not  be  irritated  without  an 
immediate  production  of  the  discharge  ;  but  if  it  was  removed,  all  disengage- 
ment of  electricity  disappeared,  even  if  the  other  lobes  remained  untouched. 
Hence  it  would  appear  that  the  primary  source  of  the  electricity  elaborated 


-961]  Application  of  Electricity  to  Medicine.  887 

is  the  fourth  lobe,  whence  it  is  transmitted  by  means  of  the  nerves  to  the 
two  organs  described  above,  which  act  as  multipliers.  In  the  silurus  the 
head  appears  also  to  be  the  seat  of  the  electricity  ;  but  in  the  gymnotus  it  is 
found  in  the  tail. 

961.  Application  of  electricity  to  medicine. — The  first  applications  of 
electricity  to  medicine  date  from  the  discovery  of  the  Leyden  jar.  Nollet 
and  Boze  appear  to  have  been  the  first  who  thought  of  the  application,  and 
soon  the  spark  and  the  electrical  frictions  became  a  universal  panacea,  but  it 
must  be  admitted  that  subsequent  trials  did  not  come  up  to  the  hopes  of  the 
early  experimentalists. 

After  the  discovery  of  dynamic  electricity  Galvani  proposed  its  applica- 
tion to  medicine  ;  since  which  time  many  physicists  and  physiologists  have 
been  engaged  upon  this  subject,  and  yet  there  is  still  much  uncertainty  as  to 
the  real  effects  of  electricity,  the  cases  in  which  it  is  to  be  applied,  and  the 
best  mode  of  applying  it.  Practical  men  prefer  the  use  of  currents  to  that 
of  statical  electricity,  and,  except  in  a  few  cases,  discontinuous  to  con- 
tinuous currents.  There  is,  finally,  a  choice  between  the  currents  of  the 
battery  and  induction  currents  ;  further,  the  effects  of  the  latter  differ, 
according  as  induction  currents  of  the  first  or  second  order  are  used.  In 
fact,  since  induction  currents,  although  very  intense,  have  a  very  feeble 
chemical  action,  it  follows  that,  when  they  traverse  the  organs,  they  do  not 
produce  the  chemical  effects  of  the  current  of  the  battery,  and  hence  do  not 
tend  to  produce  the  same  disorganisation.  Further  in  electrifying  the 
muscles  of  the  face,  induction  currents  are  to  be  preferred,  for  these  currents 
only  act  feebly  on  the  retina,  while  the  currents  of  the  battery  act  energetically 
on  this  organ,  and  may  affect  it  dangerously.  There  is  a  difference  in  the 
action  of  induced  currents  of  different  orders  ;  for  while  the  primary  induced 
current  causes  lively  muscular  actions,  but  has  little  action  on  the  cutaneous 
sensibility,  the  secondary  induced  current,  on  the  contrary,  increases  the 
cutaneous  sensibility  to  such  a  point  that  its  use  ought  to  be  proscribed  to 
persons  whose  skin  is  very  irritable. 

Hence  electrical  currents  should  not  be  applied  in  therapeutics  without  a 
thorough  knowledge  of  their  various  properties.  They  ought  to  be  used 
with  great  prudence,  for  their  continued  action  may  produce  serious  accidents. 
Matteucci  says  :  '  In  commencing,  a  feeble  current  must  always  be  used. 
This  precaution  now  seems  to  me  the  more  important,  as  I  did  not  think  it 
so  before  seeing  a  paralytic  person  seized  with  almost  tetanic  convulsions 
under  the  acti6n  of  a  current  formed  of  a  single  element.  Take  care  not  to 
continue  the  application  too  long,  especially  if  the  current  is  energetic. 
Rather  apply  a  frequently-interrupted  current  than  a  continuous  one,  espe- 
cially if  it  be  strong ;  but  after  twenty  or  thirty  shocks,  at  most,  let  the 
patient  take  a  few  moments'  rest.' 

Of  late  years,  however,  feeble  continuous  currents  have  come  more  into 
use.  They  are  frequently  of  great  service  when  applied  skilfully,  so  as  to 
throw  the  nerves  of  the  diseased  part  into  a  state  of  cathelectrotonus  or 
anelectrotonus  (828),  according  to  the  object  which  is  wished  for  in  any 
given  case. 


888  Meteorology.  [962- 


ELEMENTARY   OUTLINES 

OF 

METEOROLOGY  AND  CLIMATOLOGY. 


METEOROLOGY. 

962.  Meteorology. — The  phenomena  which  are  produced  in  the  atmo- 
sphere are  called  meteors  ;  and  meteorology  is  that  part  of  physics  which  is 
concerned  with  the  study  of  these  phenomena. 

A  distinction  is  made  between  aerial  meteors,  such  as  winds,  and  hurri- 
canes, and  whirlwinds  ;  aqueous  meteors,  comprising  fogs,  clouds,  rain,  dew, 
snow,  and  hail ;  and  luminous  meteors,  as  lightning,  the  rainbow,  the  aurora 
borealis. 

963.  Meteorograph. — The  importance  of  being  able  to  make  continuous 
observations  of  various  meteorological  phenomena  has  led  to  the  construc- 
tion of  various  forms  of  automatic  arrangements  for  this  purpose,  of  which 
that  of  Osier  in  England  may  be  specially  mentioned.    One  of  the  most  com- 
prehensive and  complete  is  Secchi's  meteorograph^  of  which  we  will  give  here 
a  description. 

It  consists  of  a  base  of  masonry  about  2  feet  high  (fig.  849) ;  on  this  are 
fixed  four  columns,  about  2^  yards  high,  which  support  a  table  on  which  is 
a  clockwork  regulating  the  whole  of  the  movements  of  the  machine.  The 
phenomena  are  registered  on  two  sheets  which  move  downwards  on  two 
opposite  sides,  their  motion  being  regulated  by  clockwork.  One  of  them 
occupies  10  days  in  so  doing,  and  on  it  are  registered  the  direction  and 
velocity  of  the  wind,  the  temperature  of  the  air,  the  height  of  the  barometer, 
and  the  occurrence  of  rain  ;  on  the  second,  which  only  takes  two  days,  the 
barometric  height  and  the  occurrence  of  rain  are  repeated,  but  on  a  much 
larger  scale  ;  this  gives,  moreover,  the  moisture  of  the  air. 

Direction  of  the  wind.  The  four  principal  directions  of  the  wind  are 
registered  by  means  of  four  pencils  fixed  at  the  top  of  thin  brass  rods,  a,  b,  c, 
d  (fig.  849),  which  are  provided  at  the  bottom  ends  with  soft  iron  keepers 
attracted  by  two  electro-magnets,  E,  E',  for  west  and  north,  and  by  two  other 
electro-magnets  lower  down  for  south  and  east.  These  four  electro-magnets, 
as  well  as  all  the  others  on  the  apparatus,  are  worked  by  a  single  sand 
battery  (894)  of  twenty-four  elements.  The  passage  of  the  current  in  one  or 
the  other  of  these  electro-magnets  is  regulated  by  means  of  a  vane  (fig.  850 


-963]  Meteorograph. 

consisting  of  two  plates  at  an  angle  of  thirty  degrees  with  each  other,  by 
which  greater  steadiness  is  obtained  than  with  a  single  plate.     In  the  rod  of 


Fig.  849. 

the  vane  is  a  small  brass  plate  o  ;  this  part  is  in  the  centre  of  four  metal 
sectors  insulated  from  each  other,  and  each  provided  with  a  binding  screw, 

QQ 


890 


Meteorology. 


[963- 


\ 


Fig.  850. 


by  which  connection  is  established  with  the  binding  screw  K,  and  the  electro- 
magnets E  E'.     The  battery  current  reaches  the  rod  of  the  vane  by  the  wire 

rt,  and  thence  the  sliding  contact  0,  which 
leads  it  to  the  electro-magnet,  for  the  north, 
for  instance. 

If  the  current  passed  constantly  in  this 
electro-magnet,  the  pencil  on  the  rod  d  would 
be  stationary ;  but  from  the  electro-magnet 
E'  the  current  passes  into  a  second  electro- 
magnet n,  over  the  clockwork,  and  is  thereby 
alternately  opened  and  closed,  as  will  be 
seen  in  speaking  of  the  velocity  of  the  wind. 
Hence  the  armature  of  the  rod  d,  alternately 
free  and  attracted,  oscillates  ;  and  its  pencil, 
which  is  always  pressed  against  the  paper 
AD  by  the  elasticity  of  the  rod,  traces  on  it 
a  series  of  parallel  dashes,  as  the  paper 
descends,  and  so  long  as  the  wind  is  in  the 
north.  If  the  wind  changes  then  to  west,  for 
instance,  the  rod  a  oscillates,  and  its  pencil 
traces  a  different  series  of  marks.  The  rate 
of  displacement  of  the  paper  being  known, 
we  get  the  direction  of  the  prevalent  wind  at 
a  given  moment. 

Velocity  of  the  wind. — This  is  indicated  by  a  Robinson's  anemometer, 
and  is  registered  in  two  ways  :  by  two  counters  which  mark  in  decametres 

and  kilometres  the  distance  travelled  by  the 
wind  ;  and  by  a  pencil  which  traces  on  a 
table  a  curve,  the  ordinates  of  which  are 
proportional  to  the  velocity  of  the  wind. 

Robinson,  who  originally  devised  this 
form  of  anemometer  (fig.  851),  proved  that 
its  velocity  is  proportional  to  that  of  the 
wind  ;  in  the  present  apparatus  the  length 
of  the  arms  is  so  calculated  that  each  revo- 
lution corresponds  to  a  velocity  often  metres 
(963).  The  anemometer  is  placed  at  a  con- 
siderable distance  from  the  meteorograph, 
and  is  connected  with  it  by  a  copper  wire  d, 
which  passes  to  the  electro-magnet  n  of  the 
counter.  On  its  rod  there  is,  moreover,  an 
excentric,  which  at  each  turn  touches  a  me- 
tallic contact  in  connection  with  the  wire  d. 
The  battery  current  reaches  the  anemome- 
ter by  a  wire  a,  the  current  is  closed  once 
at  each  rotation,  and  passes  to  the  electro- 
magnet «,  which  moves  the  needle  of  the 
dial  through  one  division.  There  are  fifty  such  divisions  which  represent 


Fig.  85r. 


-963]  Meteorograph.  891 

as  many  turns  of  the  vane,  and  therefore  so  many  multiples  of  ten  metres. 
The  lower  dial  marks  the  kilometres. 

The  curve  of  velocities  is  traced  on  the  sheet  by  a  pencil  /,  fixed  to  a 
horizontal  rod.  This  is  joined  at  its  two  ends  to  two  guide  rods,  o  and  y, 
which  keep  it  parallel.  The  pencil  and  the  rod  are  moved  laterally  by  a 
chain  which  passes  over  two  pulleys  r'  and  r,  and  is  then  coiled  over  a  pulley 
placed  on  the  shaft  of  the  counter,  but  connected  with  it  merely  by  a  ratchet 
wheel ;  and,  moved  thus  by  the  counter  and  the  chain,  the  pencil  traces 
ever}-  hour  on  the  sheet  a  line  the  length  of  which  is  proportional  to  the 
velocity  of  the  wind.  From  hour  to  hour  an  excentric  moved  by  clockwork 
detaches,  from  the  shaft  of  the  counter,  the  pulley  on  which  is  coiled  the 
chain,  and  this  pulley  becoming  out  of  gear  a  weight  p,  connected  with  the 
pencil  /,  restores  this  to  its  starting-point.  All  the  lines  V,  traced  succes- 
sively by  the  pencil,  start  from  the  same  straight  line  as  ordinates,  and  their 
ends  give  the  curve  of  velocities. 

The  counters  on  the  right  and  left  are  worked  by  electro -magnets  ;//  m\ 
and  are  intended  to  denote  the  velocity  of  special  winds  :  for  instance,  those 
of  the  north  and  south,  by  connecting  their  electro-magnets  with  the  north 
and  south  sectors  of  the  vane  (fig.  850). 

Temperature  of  the  air. — This  is  indicated  by  the  expansion  and  con- 
traction of  a  copper  wire  16  metres  in  length  stretched  backwards  and  for- 
wards on  a  fir  plank  8  metres  in  length.  The  whole  being  placed  on  the 
outside — on  the  roof,  for  instance — the  expansion  and  contraction  are  trans- 
mitted by  a  system  of  levers  to  a  wire  o,  which  passes  to  the  meteorograph, 
where  it  is  joined  to  a  bent  lever  /.  This  is  jointed  to  a  horizontal  rod  j, 
which  supports  a  pencil,  and  at  the  other  end  is  jointed  to  a  guide  rod  x. 
Thus  the  pencil,  sharing  the  oscillations  of  the  whole  system,  traces  the  curve 
of  the  temperatures. 

Pressure  of  the  atmosphere. — This  is  registered  by  the  oscillations  of  a 
barometer  B,  suspended  at  one  end  of  a  bent  scale  beam  I  F,  playing  on  a 
knife  edge  (fig.  849).  The  arm  F  supports  a  counterpoise  ;  to  the  arm  I  is 
suspended  the  barometer  B,  which  is  wider  at  the  top  than  at  the  bottom. 
A  wooden  flange,  or  floater  Q,  fixed  to  the  lower  part  of  the  tube,  plunges  in 
a  bath  of  mercury,  so  that  the  buoyancy  of  the  liquid  counterbalances  part  of 
the  weight  of  the  barometer.  Owing  to  the  large  diameter  of  the  barometric 
chamber,  a  very  slight  variation  of  level  in  this  chamber  makes  the  tube 
oscillate,  and  with  it  the  scale  beam  I  F.  To  the  axis  of  this  is  fixed  a  triangle 
ghk,  jointed  to  a  horizontal  rod,  which  in  turn  is  connected  with  a  guide  rod 
s.  In  the  middle  of  this  rod  is  a  pencil  which,  sharing  in  the  oscillations  of 
the  triangle  ghk,  traces  the  curve  H  of  pressure.  A  bent  lever  at  the  bottom 
of  the  barometer  tube  keeps  this  in  a  vertical  position. 

Rainfall. — This  is  registered  between  the  direction  of  the  winds  and  the 
curve  H,  by  a  pencil  at  the  end  of  a  rod  u,  which  is  worked  by  an  electro- 
magnet e.  On  the  roof  is  a  funnel  which  collects  the  rain,  and  a  long  tube 
leads  the  water  to  a  small  water  balance,  with  the  cups  placed  near  the 
meteorograph  (fig.  852).  To  the  axis  of  the  scale  beam  one  pole  of  the  battery 
is  connected  ;  the  left  cup  being  full,  tips  up,  and  a  contact  a  closes  the 
current,  which  passes  then  to  one  of  the  binding  screws  C  and  hence  to  the 

Q  Q2 


892  Meteorology.  [963- 

electro-magnet  e.  Then  the  right  cup,  being  in  turn  full,  tips  in  the  opposite 
direction,  and  the  contact  b  now  transmits  the  current  to  the  electro-magnet. 
Thus,  at  each  oscillation  this  latter  attracts  its  arma- 
ture, and  with  it  the  rod  <z,  which  makes  a  mark  by 
means  of  a  pencil  at  the  end.  If  the  rain  is  abundant 
the  oscillations  of  the  beam  are  rapid,  and  the  marks 
being  very  close  together  give  a  deep  shade  ;  if  on  the 
contrary  the  oscillations  are  slow,  the  marks  are  at  a 
greater  distance  and  give  a  light  shade.  When  the 
rain  ceases,  the  oscillations  cease  also,  and  the  pencil 
makes  no  mark. 

To  complete  this  description  of  the  first  face  of 
the  meteorograph  :  S  is  the  alarum  bell  of  the  clock- 
work, O  O  a  cord  supporting  a  weight  which  moves 
the  works  of  the  hour  hand.  L  Z  is  a  second  cord  that 
supports  the  weight  which  works  the  alarum ;  the 
wheel  U,  placed  below  the  clockwork,  winds  up  the 
Fig.  852.  sheet  AD,  when  it  is  at  the  bottom  of  its  course. 

The  second  sheet,  fig.  853,  gives  the  barometric  height  and  the  rainfall 
like  the  first,  but  on  a  larger  scale,  since  the  motion  of  the  sheet  is  five 
times  as  rapid.  Its  principal  function  is  that  of  registering  the  moisture  of 
the  air.  This  is  effected  by  means  of  the  psychrometer  (fig.  854).  T  and  T' 
are  two  thermometers  fixed  on  two  plates.  The  muslin  which  covers  the 
second  is  kept  continually  moist  by  water  dropping  on  it.  In  each  of  the 
bulbs  are  fused  two  platinum  wires  ;  the  stems  of  the  thermometers  are 
open  at  the  top,  and  in  them  are  immersed  two  platinum  wires  m  and  ;z, 
suspended  to  a  metal  frame  movable  on  four  pulleys  supported  by  a  fixed 
piece  B.  The  frame  A  in  contact  with  the  current  of  the  battery  is  sus- 
pended to  a  steel  wire  L,  which  passes  over  a  pulley  to  the  meteorograph 
(fig.  853).  Here  is  a  long  triangular  lever  W,  which  supports  a  small  wheel 
to  which  is  fixed  the  wire  L.  The  lever  W,  which  turns  about  an  axisy^  is 
moved  by  a  rod  a,  by  means  of  an  excentric  which  the  clock  works  every 
quarter  of  an  hour.  At  each  oscillation  the  lever  W  transmits  its  movement 
to  a  small  chariot,  on  which  is  an  electro-magnet  x,  and  at  the  same  time  to 
the  steel  wire  L,  which  supports  the  frame  A  (fig.  852).  The  chariot  moved 
towards  the  left  by  the  rotation  of  the  excentric,  lets  the  frame  sink.  The 
moment  the  first  platinum  wire  reaches  the  mercurial  column  of  the  dry 
bulb  thermometer  which  is  the  highest,  the  current  is  closed,  and  passes  into 
the  electro-magnet  of  the  chariot.  An  armature  at  once  causes  a  pencil  to 
mark  a  point  on  the  sheet  which  is  the  beginning  of  a  line  representing  the 
path  of  the  dry  bulb  thermometer.  As  the  frame  continues  to  descend,  the 
second  platinum  wire  touches  the  mercury  of  the  wet  bulb,  and  closes  a 
current  in  a  relay  M,  which  opens  the  circuit  of  the  electro-magnet  x.  The 
pencil  is  then  detached ;  then  returning  upon  itself  the  chariot  reproduces 
the  closing  and  opening  of  the  circuit  in  the  opposite  direction,  the  pencil 
makes  another  mark,  which  is  the  end  of  the  line.  There  are  thus  formed 
two  series  of  dots  arranged  in  two  curves,  one  of  which  represents  the  path 
of  the  dry,  and  the  other  the  path  of  the  wet  bulb.  The  horizontal  distance 
of  the  two  points  of  these  curves  is  proportional  to  the  difference  / — /15  of 


-963] 


Meteorograph. 


893 


the  temperatures    indicated   at   the  same  moment   by  the  thermometers 
(fig.  854). 


Fig.  853. 


Quantity  of  rain. — The   quantity  of  rain  which  falls  in  a  given  time 
is  registered  on  a  disc  of  paper  on  a  pulley  R.     On  the  groove  of  this  is 


894 


Meteorology. 


[963- 


coiled  a  chain  to  which  is  suspended  a  brass  tube  P.  This  is  fixed  at  the 
bottom  to  a  float  which  plunges  in  a  reservoir  placed  in  the  base  of  the 
meteorograph.  On  passing  out  of  the  water  balance  (fig.  852)  the  water 
passes  into  this  reservoir,  and  as  its  section  is  one 
fourth  that  of  the  funnel,  the  height  of  water  which 
falls  is  quadrupled  ;  it  is  measured  on  a  scale  G, 
divided  into  millimetres. 

As  the  float  rises,  a  weight  Z  moves  the  pulley 
in  the  contrary  direction,  and  its  rotation  is  propor- 
tional to  the  height  of  water  which  has  fallen.  A 
pencil  moves  at  the  same  time  from  the  centre  to 
one  circumference  of  the  paper  disc  with  a  velocity 
of  5  mm.  in  24  hours  :  hence  the  quantity  of  rain 
which  falls  every  day  is  noted  on  a  different  place 
on  the  paper  disc. 

964.  Direction  and  velocity  of  winds. — 
Winds  are  currents  moving  in  the  atmosphere  with 
variable  directions  and  velocities.  There  are  eight 
principal  directions  in  which  they  blow — north, 
north-east,  east,  south-east,  south,  south-west,  west 
and  north-west.  Mariners  further  divide  each  of 
the  distances  between  these  eight  directions  into 
four  others,  making  in  all  32  directions  which  are 
called  points  or  rhumbs.  A  figure  of  32  rhumbs 
on  a  circle,  in  the  form  of  a  star,  is  known  as  the 
mariner's  card. 

Velocity  is  determined  by  means  of  the 
anemometer  (fig.  850),  a  small  vane  with  fans, 
which  the  wind  turns  ;  the  velocity  is  deduced  from 
the  number  of  turns  made  in  a  given  time.  In  our  climate  the  mean  velocity 
is  from  1 8  to  20  feet  in  a  second.  With  a  velocity  of  less  than  18  inches  in 
a  second  no  movement  is  perceptible  and  smoke  ascends  straight ;  with  a 
velocity  between  \\  and  2  feet  per  second  the  wind  is  perceptible  and  moves 
a  pennant  ;  from  13  to  22  feet  it  is  moderate,  it  stretches  a  flag  and  moves 
the  leaves  of  trees  ;  with  from  23  to  36  feet  velocity  it  is  fresh  and  moves 
the  branches  of  trees  ;  with  36  to  56  feet  it  is  strong  and  moves  the  larger 
branches  and  the  smaller  stems  ;  with  a  velocity  of  56  to  90  feet  it  is  a 
storm,  and  entire  trees  are  moved,  and  from  90  to  120  it  is  a  hurricane. 

To  measure  the  pressure  of  the  wind  a  plate  is  used  which  by  means  of  a 
vane  is  always  kept  in  a  direction  opposite  that  of  the  wind.  Behind  the 
plate  are  one  or  more  springs  which  are  the  more  pressed  the  greater  is  the 
pressure  of  the  wind  against  the  plate.  Knowing  the  distance  through  which 
the  plate  is  pressed,  we  can  calculate  the  pressure  which  the  wind  exerts  on 
the  plate  in  question. 

With  some  degree  of  approximation  and  for  low  velocities  the  pressure 
may  be  taken  as  proportional  to  the  square  of  the  velocity.  Thus,  if  the 
pressure  on  the  square  foot  is  0*005  pound  with  a  velocity  of  1-5  foot  in 
a  second,  it  is  0*02  pound  with  a  velocity  of  3'ofeet,  and  0*123  with  a  velocity 
of  7-33  feet. 


Fig.  854. 


-966]  Regular,  Periodical,  and  Variable  Winds.  895 

965.  Causes  of  winds. — Winds  are  produced  by  a  disturbance  of  the 
equilibrium  in  some  part  of  the  atmosphere  ;  a  disturbance  always  resulting 
from  a  difference  in  temperature  between  adjacent  countries.     Thus,  if  the 
temperature  of  a  certain  extent  of  ground  becomes  higher,  the  air  in  contact 
with  it  becomes  heated,  it  expands  and  rises  towards  the  higher  regions  of 
the  atmosphere  ;  whence  it  flows,  producing  winds  which  blow  from  hot  to 
cold  countries.     But  at  the  same  time  the  equilibrium  is  destroyed  at  the 
surface  of  the  earth,  for  the  barometric  pressure  on  the  colder  adjacent  parts 
is  greater  than  on  that  which  has  been  heated,  and  hence  a  current  will  be 
produced  with  a  velocity  dependent  on  the  difference  between  these  pres- 
sures ;  thus  two  distinct  winds  will  be  produced — an  upper  one  setting  out- 
wards from  the  heated  region,  and  a  lower  one  setting  inwards  towards  it. 

966.  Regular,  periodical,  and  variable  winds. — According  to  the  more 
or  less  constant  directions  in  which  winds  blow,  they  may  be  classed  as 
regular,  periodical,  and  variable  winds. 

i.  Regular  winds  are  those  which  blow  all  the  year  through  in  a  virtually 
constant  direction.  These  winds,  which  are  also  known  as  the  trade  winds, 
are  uninterruptedly  observed  far  from  the  land  in  equatorial  regions,  blowing 
from  the  north-east  to  the  south-west  in  the  northern  hemisphere,  and  from 
the  south-east  to  the  north-west  in  the  southern  hemisphere.  They  prevail 
on  the  two  sides  of  the  equator  as  far  as  30°  of  latitude,  and  they  blow  in 
the  same  direction  as  the  apparent  motion  of  the  sun  ;  that  is,  from  east  to 
west. 

The  air  above  the  equator  being  gradually  heated,  rises  as  the  sun  passes 
round  from  east  to  west,  and  its  place  is  supplied  by  the  colder  air  from  the 
north  or  south.  The  direction  of  the  wind,  however,  is  modified  by  this  fact, 
that  the  velocity  which  this  colder  air  has  derived  from  the  rotation  of  the 
earth — namely,  the  velocity  of  the  surface  of  the  earth  at  the  point  from 
which  it  started — is  less  than  the  velocity  of  the  surface  of  the  earth  at  the 
point  at  which  it  has  now  arrived  :  hence  the  currents  acquire,  in  reference 
to  the  equator,  the  constant  direction  which  constitutes  the  trade  winds. 

ii.  Periodical  winds  are  those  which  blow  regularly  in  the  same  direction 
at  the  same  seasons  and  at  the  same  hours  of  the  day  :  the  monsoon, 
simoom,  and  the  land  and  sea  breeze  are  examples  of  this  class.  The  name 
monsoon  is  given  to  winds  which  blow  for  six  months  in  one  direction  and 
for  six  months  in  another.  They  are  principally  observed  in  the  Red  Sea 
and  in  the  Arabian  Gulf,  in  the  Bay  of  Bengal  and  in  the  Chinese  Sea. 
These  winds  blow  towards  the  continents  in  summer,  and  in  a  contrary 
direction  in  winter.  The  simoom  is  a  hot  wind  that  blows  over  the  deserts 
of  Asia  and  Africa,  and  which  is  characterised  by  its  high  temperature  and 
by  the  sands  which  it  raises  in  the  atmosphere  and  carries  with  it.  During 
the  prevalence  of  this  wind  the  air  is  darkened,  -the  skin  feels  dry,  the 
respiration  is  accelerated,  and  a  burning  thirst  is  experienced. 

This  wind  is  known  under  the  name  of  sirocco  in  Italy  and  Algiers,  where 
it  blows  from  the  great  Desert  of  Sahara.  In  Egypt,  where  it  prevails  from 
the  end  of  April  to  June,  it  is  called  kamsin.  The  natives  of  Africa,  in  order 
to  protect  themselves  from  the  effects  of  the  too  rapid  perspiration  occasioned 
by  this  wind,  cover  themselves  with  fatty  substances. 

The  land  and  sea  breeze  is  a  wind  which  blows  on  the  sea-coast,  during 


896  Meteorology. 

the  day  from  the  sea  towards  the  land,  and  during  the  night  from  the  land  to 
the  sea.  For  during  the  day  the  land  becomes  more  heated  than  the  sea,  in 
consequence  of  its  lower  specific  heat  and  greater  conductivity,  and  hence  as 
the  superincumbent  air  becomes  more  heated  than  that  upon  the  sea,  it  as- 
cends and  is  replaced  by  a  current  of  colder  and  denser  air  flowing  from  the 
sea  towards  the  land.  During  the  night  the  land  cools  more  rapidly  than  the 
sea,  and  hence  the  same  phenomenon  is  produced,  but  in  a  contrary  direction. 
The  sea  breeze  commences  after  sunrise,  increases  to  three  o'clock  in  the 
afternoon,  decreases  towards  evening,  and  is  changed  into  a  land  breeze 
after  sunset.  These  winds  are  only  perceived  at  a  slight  distance  from  the 
shores.  They  are  regular  in  the  tropics,  but  less  so  in  our  climates  ;  and 
traces  of  them  are  seen  as  far  as  the  coasts  of  Greenland.  The  proximity  of 
mountains  also  gives  rise  to  periodical  daily  breezes. 

iii.  Variable  winds  are  those  which  blow  sometimes  in  one  direction  and 
sometimes  in  another,  alternately,  without  being  subject  to  any  law.  In  mean 
latitudes  the  direction  of  the  winds  is  very  variable  ;  towards  the  poles  this 
irregularity  increases,  and  under  the  arctic  zone  the  winds  frequently  blow 
from  several  points  of  the  horizon  at  once.  On  the  other  hand,  in  approach- 
ing the  torrid  zone,  they  become  more  regular.  The  south-west  wind  prevails 
in  the  north  of  France,  in  England,  and  in  Germany  ;  in  the  south  of  France 
the  direction  inclines  towards  the  north,  and  in  Spain  and  Italy  the  north 
wind  predominates. 

967.  Xiaw  of  the  rotation  of  winds. — Spite  of  the  great  irregularity 
which  characterises  the  direction  of  the  winds  in  our  latitude,  it  has  been  as- 
certained that  the  wind  has  a  preponderating  tendency  to  veer  round  accord- 
ing to  the  sun's  motion — that  is  to  pass  from  north,  through  north-east,  east, 
south-east  to  south,  and  so  on  round  in  the  same  direction  from  west  to 
north  ;  that  it  often  makes  a  complete  circuit  in  that  direction,  or  more 
than  one  in  succession,  occupying  many  days  in  doing  so,  but  that  it  rarely 
veers,  and  very  rarely  or  never  makes  a  complete  circuit  in  the  opposite 
direction.  This  course  of  the  winds  is  most  regularly  observed  in  winter. 
According  to  Leverrier,  the  displacement  of  the  north-east  by  the  south- 
west wind  arises  from  the  occurrence  of  a  whirlwind  formed  upon  the  Gulf- 
stream.  For  a  station  in  south  latitude  a  contrary  law  of  rotation  prevails. 

This  law,  though  more  or  less  suspected  for  a  long  time,  was  first  formally 
enunciated  and  explained  by  Dove,  and  is  known  as  Dove's  law  of  rotation 
of  winds. 

967^.  Weather  charts. — A  considerable  advance  has  been  made  in 
weather  forecasts  by  the  frequent  and  systematic  publication  of  weather 
charts ;  that  is  to  say,  maps  in  which  the  barometric  pressure,  the  tempe- 
rature, the  force  of  the  wind,  &c.,  are  expressed  for  considerable  areas,  in  an 
exact  and  comprehensive  manner.  A  careful  study  of  such  maps  renders 
possible  a  forecast  of  the  weather  for  a  day  or  more  in  advance.  We  can 
here  do  little  more  than  explain  the  meaning  of  the  principal  terms  in  use. 

If  lines  are  drawn  through  those  places  on  the  earth's  surface  where  the 
corrected  barometric  height  at  a  given  time  is  the  same,  such  lines  are 
called  isobarometric  lines,  or  more  briefly,  isobaric  lines,  or  isobars.  Between 
any  two  points  on  the  same  isobar  there  is  no  difference  of  pressure, 
isobars  are  usually  drawn  for  a  difference  of  5  mm.,  or  of  —  of  an  inch. 


-968]  Fogs  and  Mists.  897 

If  we  take  a  horizontal  line  between  two  isobars,  and  at  that  point  at 
which  the  pressure  is  greatest  draw  a  perpendicular  line  on  any  suitable 
scale,  which  shall  represent  the  difference  in  pressure  between  the  two  places, 
the  line  drawn  from  the  top  of  this  perpendicular  to  the  lower  isobar  will 
form  an  angle  with  the  horizontal,  and  the  steepness  of  this  angle  is  a 
measure  of  the  fall  in  pressure  between  the  two  stations,  and  is  called  the 
baromettic  gradient.  Gradients  are  usually  expressed  in  England  and 
America  in  hundredths  of  an  inch  of  mercury  for  one  degree  of  60  nautical 
miles,  and  on  the  Continent  in  millimetres  for  the  same  distance.  The 
closer  are  the  isobars,  the  steeper  is  the  gradient,  and  the  more  powerful 
the  wind ;  and  though  no  exact  relationship  can  be  proved  between  the 
steepness  of  the  gradient  and  the  force  of  the  wind,  it  may  be  mentioned 
that  a  gradient  of  about  6  represents  a  strong  breeze ;  and  a  gradient 
of  10,  or  a  difference  in  pressure  of  j1^  of  an  inch  for  60  miles,  is  a  stiff 
gale. 

The  direction  of  the  wind  is  from  the  place  of  higher  pressure  to  that  of 
lower  ;  and  in  this  respect  the  law  of  Buys  Ballot  may  be  mentioned,  which 
has  been  found  to  hold  in  all  cases  in  the  northern  hemisphere  where  local 
configuration  does  not  come  into  play.  If  we  stand  with  our  back  to  the 
wind,  the  line  of  lower  pressure  is  on  the  left  hand.  For  places  in  the 
southern  hemisphere  exactly  the  opposite  law  holds. 

If  in  any  area  the  pressure  is  lower,  the  wind  blows  round  that  area,  the 
place  of  lowest  pressure  being  on  the  left.  The  direction  of  the  wind  is, 
in  short,  opposite  that  of  the  hands  of  a  watch.  Such  circulation  is  called 
cyclonic;  it  is  that  which  is  characteristic  of  the  West  Indian  hurricanes,  which 
are  known  as  cyclones.  Conversely  the  wind  blows  round  an  area  of  higher 
pressure  in  the  same  direction  as  the  hands  of  a  watch  ;  and  this  circulation 
is  called  anti-cyclonic. 

Cyclonic  systems  are  by  far  the  most  frequent,  and  are  characterised  by 
steep  gradients ;  the  air  in  them  tends  to  move  in  towards  the  centre,  and 
thence  to  the  upper  regions  of  the  atmosphere.  They  bring  with  them,  over 
the  greater  part  of  the  region  which  they  cover,  much  moisture,  an  abundance 
of  cloud,  and  heavy  rain.  Anti-cyclonic  systems  have  the  opposite  charac- 
teristics ;  the  gradients  are  slight,  the  wind  light,  and  moving  with  the  hands 
of  a  watch.  The  air  is  dry,  so  that  there  is  but  little  cloud,  and  no  rain. 
Cyclonic  systems,  from  the  dampness  of  the  air,  produce  warm  weather  in 
winter,  and  cold,  wet  weather  in  summer.  Anti-cyclonic  systems  bring 
our  hardest  frosts  in  winter,  and  greatest  heat  in  summer,  as  there  is  but 
little  moisture  in  the  air  to  temper  the  extremes  of  climate.  Both  systems 
travel  over  the  earth's  surface,  the  cyclones  rapidly,  but  the  anti-cyclones 
more  slowly. 

968.  Togs  and  mists. — When  aqueous  vapours  rising  from  a  vessel  of 
boiling  water  diffuse  in  the  colder  air,  they  are  condensed  ;  a  sort  of  cloud 
is  formed  which  consists  of  a  number  of  small  hollow  vesicles  of  water, 
which  remain  suspended  in  the  air.  These  are  usually  spoken  of  as  vapours, 
yet  they  are  not  so,  at  any  rate  not  in  the  physical  sense  of  the  word  ;  for  in 
reality  they  are  partially  condensed  vapours. 

When  this  condensation  of  aqueous  vapour  is  not  occasioned  by  contact 
with  cold  solid  bodies,  but  takes  place  throughout  large  spaces  of  the  atmo- 

QQ3 


898 


Meteorology. 


sphere,  they  constitute  'fogs  or  mists,  which,  in  fact,  are  nothing  more  than 
the  appearance  seen  over  a  vessel  of  hot  water. 

A  chief  cause  of  fogs  consists  in  the  moist  soil  being  at  a  higher  tem- 
perature than  the  air.  The  vapours  which  then  ascend  condense  and  become 
visible.  In  all  cases,  however,  the  air  must  have  reached  its  point  of  satura- 
tion before  condensation  takes  place.  Fogs  may  also  be  produced  when  a 
current  of  hot  and  moist  air  passes  over  a  river  .at  a  lower  temperature  than 
its  own,  for  then  the  air  being  cooled,  as  soon  as  it  is  saturated,  the  excess  of 
vapour  present  is  condensed.  The  distinction  between  mists  and  fogs  is 
one  of  degree  rather  than  of  kind.  A  fog  is  a  very  thick  mist. 

When  water  is  coated  with  a  layer  of  coal  tar,  it  is  prevented  from  eva- 
porating. Frankland  ascribes  the  dry  fog  met  with  in  London  to  the  large 
quantities  of  coal  tar  and  paraffine  vapour  which  are  sent  into  the  atmosphere, 
and  which,  condensing  on  the  vesicles  of  fog,  prevent  their  evaporation. 

969.  Clouds. — Clouds  are  masses  of  vapour,  condensed  into  little  drops 
of  vesicles  of  extreme  minuteness,  like  fogs.  There  is  no  difference  of  kind 


Fig.  855- 

between  fogs  and  clouds.  Fogs  are  clouds  resting  on  the  ground.  To  a 
person  enveloped  in  it,  a  cloud  on  a  mountain  appears  like  a  fog.  They 
always  result  from  the  condensation  of  vapours  which  rise  from  the  earth. 
According  to  their  appearance,  they  have  been  divided  by  Howard  into  four 
principal  kinds  :  the  nimbus,  the  strattis,  the  cumulus,  and  the  cirrus.  These 
four  kinds  are  represented  in  fig.  855.  and  are  designated  respectively  by  one, 
two,  three,  and  four  birds  on  the  wing. 

The  cirrus  consists  of  small  whitish  clouds,  which  have  a  fibrous  or  wispy 
appearance,  and  occupy  the  highest  regions  of  the  atmosphere.  The  name 
of  mares'  tails,  by  which  they  are  generally  known,  well  describes  their 


-969]  Clouds.  899 

appearance.  From  the  low  temperature  of  the  spaces  which  they  occupy, 
it  is  more  than  probable  that  cirrus  clouds  consist  of  frozen  particles  ;  and 
hence  it  is  that  haloes,  corona?,  and  other  optical  appearances,  produced  by 
refraction  and  reflection  from  ice  crystals,  appear  almost  always  in  these 
clouds  and  their  derivatives.  Their  appearance  often  precedes  a  change  of 
weather. 

The  cumulus  are  rounded  spherical  forms  which  look  like  mountains 
piled  one  on  the  other.  They  are  more  frequent  in  summer  than  in  winter, 
and  after  being  formed  in  the  morning  they  generally  disappear  towards 
evening.  If,  on  the  contrary,  they  become  more  numerous,  and  especially 
if  surmounted  by  cirrus  clouds,  rain  or  storms  may  be  expected. 

Stratus  clouds  consist  of  very  large  and  continuous  horizontal  sheets, 
which  chiefly  form  at  sunset,  and  disappear  at  sunrise.  They  are  frequent 
in  autumn  and  unusual  in  spring  time,  and  are  lower  than  the  preceding. 

The  nimbus,  or  rain  clouds,  which  are  sometimes  classed  as  one  of  the 
fundamental  varieties,  are  properly  a  combination  of  the  three  preceding 
kinds.  They  aftect  no  particular  form,  and  are  solely  distinguished  by  a 
uniform  grey  tint,  and  by  fringed  edges.  They  are  indicated  on  the  right  of 
the  figure  by  the  presence  of  one  bird. 

The  fundamental  forms  pass  into  one  another  in  the  most  varied  manner  ; 
Howard  has  classed  these  traditional  forms  as  cirro-cumulus,  cirro-stratus, 
and  cumulo-stratus,  and  it  is  often  very  difficult  to  tell,  from  the  appearance 
of  a  cloud,  which  type  it  most  resembles.  The  cirro-cumulus  is  most 
characteristically  known  as  a  'mackerel-sky  ; '  it  consists  of  small  roundish 
masses,  disposed  with  more  or  less  irregularity  and  connection.  It  is  fre- 
quent in  summer,  and  attendant  on  warm  and  dry  weather.  Cirro-stratus 
appears  to  result  from  the  subsidence  of  the  fibres  of  cirrus  to  a  horizontal 
position,  at  the  same  time  approaching  laterally.  The  form  and  relative 
position  when  seen  in  the  distance  frequently  give  the  idea  of  shoals  of  fish  ; 
the  tendency  of  cumulo-stratus  is  to  spread,  settle  down  into  the  nimbus,  and 
finally  fall  as  rain. 

The  height  of  clouds  varies  greatly  ;  in  the  mean  it  is  from  1,300  to  1,500 
yards  in  winter,  and  from  3,300  to  4,400  yards  in  summer.  But  they  often 
exist  at  greater  heights  ;  Gay-Lussac,  in  his  balloon  ascent,  at  a  height  of 
7,630  yards,  observed  cirrus-clouds  above  him,  which  appeared  to  be  at  a 
considerable  height.  In  Ethiopia,  M.  d'Abbadie  observed  storm  clouds 
whose  height  was  only  230  yards  above  the  ground. 

In  order  to  explain  the  suspension  of  clouds  in  the  atmosphere,  Halley 
first  proposed  the  hypothesis  of  vesicular  vapours.  He  supposed  that  clouds 
are  formed  of  an  infinity  of  extremely  minute  vesicles,  hollow,  like  soap  bubbles 
filled  with  air,  which  are  hotter  than  the  surrounding  air  :  so  that  these 
vesicles  float  in  the  air  like  so  many  small  balloons.  Others  assume  that 
clouds  and  fogs  consist  of  extremely  minute  droplets  of  water  which  are 
retained  in  the  atmosphere  by  the  ascensional  force  of  currents  of  hot  air, 
just  as  light  powders  are  raised  by  the  wind.  Ordinarily,  clouds  do  not 
appear  to  descend,  but  this  absence  of  downward  motion  is  only  apparent. 
In  fact,  clouds  do  usually  fall  slowly,  but  then  the  lower  part  is  continually 
dissipated  on  coming  in  contact  with  the  lower  and  more  heated  layers  ;  at 
the  same  time  the  upper  part  is  always  increasing  from  the  condensation  of 


900  Meteorology.  [969- 

new  vapours ;  so  that  from  these  two  actions  clouds  appear  to  retain  the 
same  height. 

970.  Formation  of  clouds. — Many  causes  may  concur  in  the  formation 
of  clouds.  The  usual  cause  of  the  formation  of  a  cloud  is  the  ascent,  into 
higher  regions  of  the  atmosphere,  of  air  laden  with  aqueous  vapour  ;  it 
thereby  expands,  being  under  diminished  pressure,  and  in  consequence  of 
this  expansion  it  is  cooled,  and  this  cooling  produces  a  condensation  of 
vapour.  Hence  it  is  that  high  mountains,  stopping  the  currents  of  air  and 
forcing  them  to  rise,  are  an  abundant  source  of  rain.  If  the  air  is  quite  dry 
its  temperature  would  be  one  degree  lower  for  every  301  metres.  The  case 
is  different  with  moist  air ;  for  when  the  air  has  ascended  so  high  that  its 
temperature  has  fallen  to  the  dew-point,  aqueous  vapour  is  condensed,  and 
in  consequence  of  this  heat  is  liberated  ;  when  the  dew-point  is  thus  attained, 
and  the  air  is  saturated,  the  cooling  due  to  the  ascent  and  expansion  of  air 
is  counteracted  by  this  liberation  of  latent  heat,  so  that  the  diminution  of 
temperature  with  the  height  is  considerably  slower  in  the  case  of  moist  than 
of  dry  air. 

The  following  calculation  will  give  us  the  quantity  of  water  separated  in 
a  given  case  : — Suppose  air  at  a  temperature  of  20°  to  be  saturated  with 
aqueous  vapour  at  that  temperature  ;  the  pressure  of  the  vapour  will  be  17-4 
mm.,  and  the  weight  contained  in  one  cubic  metre  of  air  17*1  grammes. 

If  the  air  has  risen  to  a  height  of  3,500  metres,  it  has  come  under  a 
pressure  which  is  only  f  of  what  it  was  ;  its  temperature  is  4°  and  its  vo- 
lume about  i^  times  what  it  originally  was.  As  it  remains  saturated  the 
pressure  will  be  6'i  mm.,  and  the  quantity  of  vapour  will  be  6 '4  grammes 
in  a  cubic  metre  ;  that  is  to  say,  6*4  x  i£  =  9-6  grammes  in  the  whole  mass  of 
what  was  originally  a  cubic  metre.  The  pressure  of  aqueous  vapour  has 
sunk  during  the  ascent  from  17*4  mm.  to  6'i  mm  and  its  weight  17*1 
grammes  to  9-6  grammes ;  that  is,  a  weight  of  7-5  grammes  has  been  deposited, 
for  that  mass  of  air  which  at  the  sea  level  occupied  a  space  of  one  cubic 
metre.  These  7-5  grammes  are  in  the  form  of  the  small  droplets  which 
constitute  fogs  or  clouds. 

If  the  mass  of  air  had  risen  to  a  height  of  8,500  metres,  where  the  pres- 
sure is  only  one-third  that  on  the  sea-level,  the  temperature  is  —28°,  and 
the  space  it  occupies  three  times  as  great  as  at  first.  The  pressure  of 
aqueous  vapour  is  0*5  mm.,  and  its  weight  0*6  gramme  in  a  cubic  metre. 
Hence  of  the  entire  quantity  of  aqueous  vapour  originally  present  there  are 
now  only  i-8  gramme  left,  and  the  remaining  15*3  grammes  would  be 
separated  as  water  or  ice.  A  similar  calculation  will  show  that  at  a  height 
of  4,200  metres,  where  the  temperature  is  zero  and  the  pressure  f,  the  quan- 
tity of  water  present  in  the  original  cubic  metre  is  only  8-2  grammes,  the 
rest  being  deposited. 

Thus,  a  mass  of  air  which,  at  the  sea-level,  occupies  a  space  of  a  cubic 
metre,- and  is  saturated  with  aqueous  vapour  at  20°,  and  then  contains  17-1 
grammes,  will  only  contain  9'6  grammes  at  a  height  of  3,500  metres,  8'2 
grammes  at  4,200  metres,  and  r8  gramme  at  8,500  metres.  Hence,  while 
a  mass  of  air  rises  from  the  sea- level  to  a  height  of  4,200  ft.,  8*9  grammes  of 
aqueous  vapour  are  separated  as  cloud  vesicles  ;  at  8,500  metres  or  about 
double  the  height,  6-4  grammes  are  separated  in  the  form  of  ice. 


-971]  Rain.  901 

A  hot,  moist  current  of  air,  mixing  with  a  colder  current,  undergoes  a 
cooling,  which  brings  about  a  condensation  of  the  vapour.  Thus  the  hot 
and  moist  winds  of  the  south  and  south-west,  mixing  with  the  colder  air  of 
our  latitude.';,  give  rain.  The  winds  of  the  north  and  north-east  tend  also, 
in  mixing  with  our  atmosphere,  to  condense  the  vapours  ;  but  as  these  winds, 
owing  to  their  low  temperature,  are  very  dry,  the  mixture  rarely  attains  satu- 
ration, and  generally  gives  no  rain. 

The  formation  of  clouds  in  this  way  is  thus  explained  by  Hutton : — The 
tension  of  aqueous  vapour,  and  therewith  the  quantity  present  in  a  given 
space  when  saturated,  diminishes  according  to  a  geometric  progression, 
while  the  temperature  falls  in  arithmetrical  progression,  and  therefore  the 
elasticity  of  the  vapour  present  at  any  time  is  reduced  by  a  fall  of  temperature 
more  rapidly  than  in  direct  proportion  to  the  fall.  Hence,  if  a  current  of 
warm  air,  saturated  with  aqueous  vapour,  meet  a  current  of  cold  air  also 
saturated,  the  air  acquires  the  mean  temperature  of  the  two,  but  can  only 
retain  a  portion  of  the  vapour  in  the  invisible  condition,  and  a  cloud  or  mist 
is  formed.  Thus,  suppose  a  cubic  metre  of  air  at  10°  C.  mixes  with  a  cubic 
metre  of  air  at  20°  C.,  and  that  they  are  respectively  saturated  with  aqueous 
vapour.  By  formula  (401)  it  is  easily  calculated  that  the  weight  of  water 
contained  in  the  cubic  metre  of  air  at  10°  C.  is  9*397  grammes,  and  in  that 
at  20°  C.  is  17-632  grammes,  or  27-029  grammes  in  all.  When  mixed  they 
produce  two  cubic  metres  of  air  at  1 5°  C. ;  but  as  the  weight  of  water  re- 
quired to  saturate  this  is  only  2x12-8^25-6  grammes,  the  excess,  1-429 
gramme,  will  be  deposited  in  the  form  of  mist  or  clouds. 

971.  Sain. — When  by  the  constant  condensation  of  aqueous  vapour  the 
individual  vapour  vesicles  become  larger  and  heavier,  and  when  finally  indi- 
vidual vesicles  unite,  they  form  regular  drops  which  fall  as  rain. 

The  quantity  of  rain  which  falls  annually  in  any  given  place,  or  the  annual 
rainfall,  is  measured  by  means  of  a  rain  gauge  ox  pluviometer.  Ordinarily  it 
consists  of  a  cylindrical  vessel 
M  (figs.  856  and  857),  closed  at 
the  top  by  a  funnel-shaped  lid, 
in  which  there  is  a  very  small 
hole,  through  which  the  rain 
falls.  At  the  bottom  of  the 
vessel  is  a  glass  tube,  A,  in 
which  the  water  rises  to  the 
same  height  as  inside  the  rain 
gauge,  and  is  measured  by  a 
scale  on  the  side,  as  shown  in 
the  figures. 

The  apparatus  being  placed  Fig-  856.  Fig.  857. 

in  an   exposed   situation,   if  at 

the  end  of  a  month  the  height  of  water  in  the  tube  is  two  inches,  for  example, 
it  shows  that  the  water  has  attained  this  height  in  the  vessel,  and,  conse- 
quently, that  a  layer  of  two  inches  in  depth  expresses  the  quantity  of  rain 
which  this  extent  of  surface  has  received. 

It  has  been  noticed  that  the  quantity  of  rain  indicated  by  the  rain  gauge 
is  greater  as  this  instrument  is  nearer  the  ground.  This  has  been  ascribed 


9O2  Meteorology.  [971- 

to  the  fact  that  the  rain-drops,  which  are  generally  colder  than  the  layers  of 
air  which  they  traverse,  condense  the  vapour  in  these  layers,  and  therefore 
constantly  increase  in  volume.  Hence  more  rain  falls  on  the  surface  of  the 
ground  than  at  a  certain  height.  But  it  has  been  objected  that  the  excess  of 
the  quantity  of  rain  which  falls,  over  that  at  a  certain  height,  is  six  or  seven 
times  that  which  could  arise  from  condensation,  even  during  the  whole  course 
of  the  rain-drops  from  the  clouds  to  the  earth.  The  difference  must  there- 
fore be  ascribed  to  purely  local  causes,  and  it  is  now  assumed  that  the 
difference  arises  from  eddies  produced  in  the  air  about  the  rain  gauge,  which 
are  more  perceptible  as  it  is  higher  above  the  ground  ;  as  these  eddies  dis- 
perse the  drops  which  would  otherwise  fall  into  the  instrument,  they  diminish 
the  quantity  of  water  which  it  receives. 

In  any  case  it  is  clear  that  if  rain-drops  traverse  moist  air,  they  will,  from 
their  temperature,  condense  aqueous  vapour  and  increase  in  volume.  If,  on 
the  contrary,  they  traverse  dry  air,  the  drops  tend  to  vaporise,  and  less  rain 
falls  than  at  a  certain  height ;  it  might  even  happen  that  the  rain  did  not 
reach  the  earth. 

Many  local  circumstances  may  affect  the  quantity  of  rain  which  falls  in' 
different  countries  ;  but,  other  things  being  equal,  most  rain  falls  in  hot  cli- 
mates, for  there  the  vaporisation  is  most  abundant.  The  rainfall  decreases, 
in  fact,  from  the  equator  to  the  poles.  At  London  it  is  23-5  inches  ;  at 
Bordeaux  it  is  25-8  ;  at  Madeira  it  is  277  ;  at  Havannah  it  is  91-2,  and  at 
St.  Domingo  it  is  107-6.  The  quantity  varies  with  the  season  ;  in  Paris,  in 
winter,  it  is  4-2  inches  ;  in  spring  6-9  ;  in  summer  6*3,  and  in  autumn  4-8 
inches.  The  heaviest  annual  rainfall-  at  any  place  on  the  globe  is  on  the 
Khasi  Hills  in  Bengal,  where  it  is  600  inches  ;  of  which  500  inches  fall  in 
seven  months. 

The  driest  recorded  place  in  England  is  Lincoln,  where  the  mean  rainfall 
is  20  inches ;  and  the  wettest  is  Stye,  at  the  head  of  Borrowdale  in  Cumber- 
land, where  it  amounts  to  165  inches. 

An  inch  of  rain  on  a  square  yard  of  surface  expresses  a  fall  of  4674 
pounds,  or  4-67  gallons.  On  an  acre  it  corresponds  to  22,622  gallons, 
or  ioo'9935  tons.  100  tons  per  inch  per  acre  is  a  ready  way  of  remembering 
this. 

972.  Waterspouts. — These  are  masses  of  vapour  suspended  in  the  lower 
layers  of  the  atmosphere  which  they  traverse,  and  endowed  with  a  gyratory 
motion  rapid  enough  to  uproot  trees,  upset  houses,  and  break  and  destroy 
everything  with  which  they  come  in  contact. 

These  meteors,  which  are  generally  accompanied  by  hail  and  rain,  often 
emit  lightning  and  thunder,  producing  the  sound  of  carriages  rolling  over  a 
stony  road.  Many  of  them  have  no  gyratory  motion,  and  about  a  quarter 
of  those  observed  are  produced  in  a  calm  atmosphere. 

When  they  take  place  on  the  sea  they  present  a  curious  phenomenon. 
The  water  is  disturbed,  and  rises  in  the  form  of  a  cone,  while  the  clouds  are 
depressed  in  the  form  of  an  inverted  cone ;  the  two  cones  then  unite  and 
form  a  continuous  column  from  the  sea  to  the  clouds  (fig.  858),  which  are 
called  waterspouts.  Even,  however,  on  the  high  seas  the  water  of  these 
waterspouts  is  never  salt,  proving  that  they  are  formed  of  condensed  vapours, 
and  not  of  sea  water  raised  by  aspiration. 


-973]  Influence  of  Aqueous  Vapour  on  Climate.  903 

The  origin  of  these  is  not  known.  Kasmtz  assumes  that  they  are  due 
principally  to  two  opposite  winds  which  pass  by  the  side  of  each  other,  or  to 
a  very  high  wind  which  prevails  in  the  higher  regions  of  the  atmosphere. 
Peltier  and  many  others  ascribe  to  them  an  electric  origin. 


Fig.  858. 

973.  Influence  of  aqueous  vapour  on  climate. — Tyndall  has  applied 
the  property  possessed  by  aqueous  vapour  of  powerfully  absorbing  and 
radiating  heat,  to  the  explanation  of  some  obscure  points  in  meteorological 
science.  He  has  established  the  fact,  that  in  a  tube  4  feet  long,  the  atmospheric 
vapour  on  a  day  of  average  dryness  absorbs  10  per  cent,  of  obscure  heat. 
With  the  earth  warmed  by  the  sun,  as  a  source,  at  the  very  least  10  per 
cent,  of  its  heat  is  intercepted  within  10  feet  of  the  surface.  The  absorption 
and  radiation  of  aqueous  vapour  is  more  than  16,000  times  that  possessed 
by  air. 

The  radiative  power  of  aqueous  vapour  may  be  the  main  cause  of  the 
torrential  rains  that  occur  in  the  tropics,  and  also  of  the  formation  of  cumuli 
clouds  in  our  own  latitudes.  The  same  property  probably  causes  the 
descent  of  very  fine  rain,  called  serein,  which  has  more  the  characteristics 
of  falling  dew,  as  it  appears  a  short  time  after  sunset,  when  the  sky  is  clear  ; 
its  production  has  therefore  been  attributed  to  the  cold,  resulting  from  the 
radiation  of  the  air.  It  is  not  the  air,  however,  but  the  aqueous  vapour 
in  the  air,  which  by  its  own  radiation  chills  itself,  so  that  it  condenses  into 
strein. 

The  absorbent  power  of  aqueous  vapour  is  of  even  greater  importance. 
Whenever  the  air  is  dry,  terrestrial  radiation  at  night  is  so  rapid  as  to  cause 
intense  cold.  Thus,  in  the  central  parts  of  Asia,  Africa,  and  Australia,  th« 
daily  range  of  the  thermometer  is  enormous  ;  in  the  interior  of  the  last-named 


904  Meteorology.  [973- 

continent  a  difference  in  temperature  of  jio  less  than  40°  C.  has  been  recorded 
within  24  hours.  In  India,  and  even  in  the  Sahara,  owing  to  the  copious 
radiation,  ice  has  been  formed  at  night.  But  the  heat  which  aqueous  vapour 
absorbs  most  largely  is  of  the  kind  emitted  from  sources  of  low  temperature  ; 
it  is  to  a  large  extent  transparent  to  the  heat  emitted  from  the  sun,  whilst  it 
is  almost  opaque  to  the  heat  radiated  from  the  earth.  Consequently,  the 
solar  rays  penetrate  our  atmosphere  with  a  loss,  as  estimated  by  Pouillet,  of 
only  25  per  cent,  when  directed  vertically  downwards,  but  after  warming 
the  earth  they  cannot  retraverse  the  atmosphere.  Through  thus  preventing 
the  escape  of  terrestrial  heat,  the  aqueous  vapour  in  the  air  moderates  the 
extreme  chilling  which  is  due  to  the  unchecked  radiation  from  the  earth, 
and  raises  the  temperature  of  that  region  over  which  it  is  spread.  In 
TyndalFs  words  : — '  Aqueous  vapour  is  a  blanket  more  necessary  to  the 
vegetable  life  of  England  than  clothing  is  to  man.  Remove  for  a  single 
summer  night  the  aqueous  vapour  from  the  air  which  overspreads  this 
country,  and  every  plant  capable  of  being  destroyed  by  a  freezing  tempera- 
ture would  perish.  The  warmth  of  our  fields  and  gardens  would  pour  itself 
unrequited  into  space,  and  the  sun  would  rise  upon  an  island  held  fast  in  the 
iron  grip  of  frost.' 

974.  Tyndall's  researches. — Tyndall  found  that  by  the  action  of  solar 
and  of  the  electric  light  on  vapours  under  a  great  degree  of  attenuation,  they 
are  decomposed.  This  new  reaction  not  only  puts  a  powerful  agent  of 
chemical  decomposition  into  the  hands  of  chemists,  but  it  has  led  Tyndall 
to  important  conclusions  regarding  the  origin  of  the  blue  colour  of  the  sky, 
and  the  polarisation  of  daylight. 

He  used  a  glass  tube  with  glass  ends,  which  could  be  exhausted  and  then 
filled  with  air  charged  with  the  vapours  of  volatile  liquids,  by  allowing  the 
air  to  pass  through  small  Wolff  bottles  containing  them.  By  mixing  the  air 
charged  with  vapour,  with  different  proportions  of  pure  air  and  by  varying 
the  degree  of  exhaustion,  it  was  possible  to  have  a  vapour  under  any  degree 
of  attenuation.  The  tube  could  also  be  filled  with  the  vapour  of  a  liquid 
alone.  The  tube  having  been  filled  with  air  charged  with  vapour  of  nitrite  01 
amyle,  a  somewhat  convergent  beam  from  the  electric  lamp  was  passed  into 
the  tube.  For  a  moment  the  tube  appeared  optically  empty,  but  suddenly  a 
shower  of  liquid  spherules  was  precipitated  on  the  path  of  the  beam  forming 
a  luminous  white  cloud.  The  nature  of  the  substance  thus  precipitated  was 
not  specially  investigated. 

This  effect  was  not  due  to  any  chemical  action  between  the  vapour  and 
the  air,  for  when  either  dry  oxygen  or  dry  hydrogen  was  used  instead  of  air, 
or  when  the  vapour  was  admitted  alone,  the  effect  was  substantially  the  same. 
Nor  was  it  due  to  any  heating  effect,  for  the  beam  had  been  previously  sifted 
by  passing  through  a  solution  of  alum,  and  through  the  thick  glass  of  the 
lens.  The  unsifted  beam  produced  the  same  effect ;  the  obscure  calorific 
rays  did  not  seem  to  interfere  with  the  result. 

The  sun's  light  also  effects  the  decomposition  of  the  nitrite  of  amyle 
vapour  ;  and  this  decomposition  was  found  to  be  mainly  due  to  the  more 
refrangible  rays. 

When  the  electric  light,  before  entering  the  experimental  tube,  was  made 
to  pass  through  a  layer  of  the  liquid  nitrite  of  amyle  an  eighth  of  an  inch  in 


-974]  Tyndairs  Researches.  905 

thickness,  the  luminous  effect  was  not  appreciably  diminished,  but  the 
chemical  action  was  almost  entirely  stopped.  Thus  that  special  constituent 
of  the  luminous  radiation  which  effects  the  decomposition  of  the  vapour  is 
absorbed  by  the  liquid.  The  decomposition  of  liquid  nitrite  of  amyle  by  light, 
if  it  take  place  at  all,  is  far  less  rapid  and  distinct  than  that  of  the  vapour. 
The  circumstance  that  the  absorption  is  the  same  whether  the  nitrite  is  in 
the  liquid  or  in  the  vaporous  state,  is  considered  by  Tyndall  as  a  proof  that 
the  absorption  is  not  the  act  of  the  molecule  as  a  whole,  but  that  it  is  atomic ; 
that  is,  that  it  is  to  the  atoms  that  the  peculiar  rate  of  vibration  is  trans- 
ferred, which  brings  about  the  decomposition  of  the  body. 

By  varying  the  nature  of  the  vapour,  the  shape  of  a  cloud  could  be 
greatly  varied,  and  in  many  cases  presented  the  most  fantastic  arid  beautiful 
forms. 

It  was  also  found  that  a  vapour  which  when  alone  resists  the  action  of 
light  may,  by  being  associated  with  another  gas  or  vapour,  exhibit  a  vigor- 
ous or  even  violent  action.  Thus,  when  the  tube  was  filled  with  atmospheric 
air,  mixed  with  nitrite  of  butyle  vapour,  the  electric  light  produced  very  little 
effect.  But  with  half  an  atmosphere  of  this  mixture,  and  half  an  atmosphere 
of  air  which  had  passed  through  hydrochloric  acid,  the  action  of  the  light 
was  almost  instantaneous.  In  another  case  mixed  air  and  nitrite  of  butyle 
vapour  were  passed  into  the  tube  so  as  to  depress  the  barometer  the  ^  of 
an  inch  ;  that  is,  the  mixed  air  and  vapour  were  under  a  pressure  of  ~ 
of  an  atmosphere.  Air  passed  through  aqueous  hydrochloric  acid  was 
introduced  until  the  pressure  was  3  inches.  The  condensed  beam  passed 
through  at  first  without  change,  but  afterwards  a  superb  blue  cloud  was 
formed. 

In  cases  where  the  vapours  are  under  a  sufficient  degree  of  attenuation, 
whatever  otherwise  be  their  nature,  the  visible  action  commences  with  the 
formation  of  a  blue  cloud.  The  term  '  cloud,'  however,  must  not  be  understood 
in  its  ordinary  sense  ;  the  blue  cloud  is  invisible  in  ordinary  daylight,  and 
to  be  seen  must  be  surrounded  by  darkness,  //  alone  being  illuminated  by  a 
powerful  beam  of  light.  The  blue  cloud  differs  in  many  important  particu- 
lars from  the  finest  ordinary  clouds,  and  may  be  considered  to  occupy  an 
intermediate  position  between  these  clouds  and  true  cloudless  vapour. 

By  graduating  the  quantity  of  vapour,  the  precipitation  may  be  obtained 
of  any  required  degree  of  fineness  :  forming  either  particles  distinguishable 
by  the  naked  eye,  or  particles  beyond  the  reach  of  the  highest  microscopic 
power.  The  case  is  similar  to  that  of  carbonic  acid  gas,  which,  diffused  in 
the  atmosphere,  resists  the  decomposing  action  of  solar  light,  but  when  in 
contiguity  with  the  chlorophyle  in  the  leaves  of  plants,  is  decomposed. 

When  the  blue  cloud  produced  in  these  experiments  was  examined  by 
any  polarising  arrangement,  the  light  emitted  laterally  from  the  beam — that 
is,  in  a  direction  at  right  angles  to  its  axis — was  found  to  be  perfectly  polar- 
ised. This  phenomenon  was  observed  in  its  greatest  perfection  the  more 
perfect  the  blue  of  the  sky.  It  is  produced  by  any  particles,  provided  they 
are  sufficiently  fine.  This  is  quite  analogous  to  the  light  of  the  blue  sky 
When  this  is  examined  by  a  NicoFs  prism,  or  any  other  analyser,  it  is  found 
that  the  light  emitted  at  right  angles  to  the  path  of  the  sun's  rays  is 
polarised. 


906  Meteorology.  [974- 

The  phenomena  of  the  firmamental  blue,  and  the  polarisation  of  the 
sky  light,  thus  find  definite  solutions  in  these  experiments.  We  need  only 
assume  the  existence  of  excessively  fine  particles  of  water  in  the  higher 
regions  of  the  atmosphere  ;  for  particles  of  any  kind  produce  this  effect.  It 
is  easy  to  conceive  the  existence  of  such  particles  in  the  higher  regions, 
even  on  a  hot  summer's  day.  For  the  vapour  must  there  be  in  a  state 
of  extreme  attenuation  ;  and,  inasmuch  as  the  oxygen  and  nitrogen  of  the 
atmosphere  behave  like  a  vacuum  to  radiant  heat,  the  extremely  attenuated 
particles  of  aqueous  vapour  are  practically  in  contact  with  the  absolute  cold 
of  space. 

'  Suppose  the  atmosphere  surrounded  by  an  envelope  impervious  to  light, 
but  with  an  aperture  on  the  sunward  side,  through  which  a  parallel  beam  of 
solar  light  could  enter  and  traverse  the  atmosphere.  Surrounded  on  all 
sides  by  air  not  directly  illuminated,  the  track  of  such  a  beam  would  re- 
semble that  of  the  parallel  beam  of  the  electric  light  through  an  incipient 
cloud.  The  sunbeam  would  be  blue,  and  it  would  discharge  light  laterally 
in  the  same  condition  as  that  discharged  by  the  incipient  cloud.  The  azure 
revealed  by  such  a  beam  would  be  to  all  intents  and  purposes  a  blue  cloud.' 

975.  Dew.  Hoar  frost.— Dew  is  merely  aqueous  vapour  which  has 
condensed  on  bodies  during  the  night  in  the  form  of  minute  globules.  It  is 
occasioned  by  the  chilling  which  bodies  near  the  surface  of  the  earth  expe- 
rience in  consequence  of  nocturnal  radiation.  Their  temperature  having  then 
sunk  several  degrees  below  that  of  the  air,  it  frequently  happens,  especially 
in  hot  seasons,  that  this  temperature  is  below  that  at  which  the  atmo- 
sphere is  saturated.  The  layer  of  air  which  is  immediately  in  contact  with 
the  chilled  bodies,  and  which  has  virtually  the  same  temperature,  then  de- 
posits a  portion  of  the  vapour  which  it  contains  ;  just  as  when  a  bottle  of 
cold  water  is  brought  into  a  warm  room,  it  becomes  covered  with  moisture, 
owing  to  the  condensation  of  aqueous  vapour  upon  it. 

According  to  this  theory,  which  was  first  propounded  by  Dr.  Wells,  all 
causes  which  promote  the  cooling  of  bodies  increase  the  quantity  of  dew. 
These  causes  are  the  emissive  power  of  bodies,  the  state  of  the  sky,  and 
the  agitation  of  the  air.  Bodies  which  have  a  great  radiating  power  more 
readily  become  cool,  and  therefore  ought  to  condense  more  vapour.  In  fact, 
there  is  generally  no  deposit  of  dew  on  metals,  whose  radiating  power  is 
very  small,  especially  when  they  are  polished  ;  while  the  ground,  sand,  glass, 
and  plants,  which  have  a  great  radiating  power,  become  abundantly  covered 
with  dew. 

The  state  of  the  sky  also  exercises  a  great  influence  on  the  formation  of 
dew.  If  the  sky  is  cloudless,  the  planetary  spaces  send  to  the  earth  an  in- 
appreciable quantity  of  heat,  while  the  earth  radiates  very  considerably,  and 
therefore  becoming  very  much  chilled,  there  is  an  abundant  deposit  of  dew. 
But  if  there  are  .clouds,  as  their  temperature  is  far  higher  than  that  of  the 
planetary  spaces,  they  radiate  in  turn  towards  the  earth,  and  as  bodies  on 
the  surface  of  the  earth  only  experience  a  feeble  chilling,  no  deposit  of  dew 
takes  place. 

Wind  also  influences  the  quantity  of  vapour  deposited.  If  it  is  feeble,  it 
increases  it,  inasmuch  as  it  renews  the  air  ;  if  it  is  strong,  it  diminishes  it, 
as  it  heats  the  bodies  by  contact,  and  thus  does  not  allow  the  air  time  to 


-977]  Hail.  907 

become  cooled.  Finally,  the  deposit  of  dew  is  more  abundant  according  as 
the  air  is  moister,  for  then  it  is  nearer  its  point  of  saturation. 

Hoar  frost  and  rime  are  nothing  more  than  dew  which  has  been  de- 
posited on  bodies  cooled  below  zero,  and  has  therefore  become  frozen.  The 
flocculent  form  which  the  small  crystals  present,  of  which  rime  is  formed, 
shows  that  the  vapours  solidify  directly  without  passing  through  the  liquid 
state.  Hoar  frost,  like  dew,  is  formed  on  bodies  which  radiate  most,  such 
as  the  stalks  and  leaves  of  vegetables,  and  is  chiefly  deposited  on  the  parts 
turned  towards  the  sky. 

976.  Snow.  Sleet.— Snow  is  water  solidified  in  stellate  crystals,  vari- 
ously modified,  and  floating  in  the  atmosphere.  These  crystals  arise  from 
the  congelation  of  the  minute  vesicles  which  constitute  the  clouds,  when  the 
temperature  of  the  latter  is  below  zero.  They  are  more  regular  when  formed 
in  a  calm  atmosphere.  Their  form  may  be  investigated  by  collecting  them 
on  a  black  surface,  and  viewing  them  through  a  strong  lens.  The  regularity 
and  at  the  same  time  variety  of  their  forms  are  truly  beautiful.  Fig.  859 
shows  some  of  the  forms  as  seen  through  a  microscope. 


Fig.  859. 

It  snows  most  in  countries  near  the  poles,  or  which  are  high  above  the 
sea  level.  Towards  the  poles  the  earth  is  constantly  covered  with  snow  ;  the 
same  is  the  case  on  high  mountains,  where  there  are  perpetual  snows,  even 
in  equatorial  countries. 

Sleet  is  also  solidified  water,  and  consists  of  small  icy  needles  pressed 
together  in  a  confused  manner.  Its  formation  is  ascribed  to  the  sudden 
congelation  of  the  minute  globules  of  the  clouds  in  an  agitated  atmo- 
sphere. 

977.  Bail. — Hail  is  a  mass  of  compact  globules  of  ice  of  different  sizes, 
which  fall  in  the  atmosphere.  In  our  climate  hail  falls  principally  during 
spring  and  summer,  and  at  the  hottest  times  of  the  day  ;  it  rarely  falls  at 
night.  The  fall  of  hail  is  always  preceded  by  a  peculiar  noise. 

Hail  is  generally  the  precursor  of  storms,  it  rarely  accompanies  them, 
and  follows  them  more  rarely  still.  Hail  falls  from  the  size  of  small  peas 
to  that  of  an  egg  or  an  orange.  The  formation  of  hailstones  has  never  been 


908  Meteorology.  [977- 

altogether  satisfactorily  accounted  for ;  nor  more  especially  their  great 
size. 

978.  Ice.  Revelation. — Ice  is  an  aggregate  of  snow  crystals,  such  as 
are  shown  in  fig.  859.  The  transparency  of  ice  is  due  to  the  close  contact 
of  these  crystals,  which  causes  the  individual  particles  to  blend  into  an  un- 
broken mass,  and  renders  the  substance  optically,  as  well  as  mechanically, 
continuous.  When  large  masses  of  ice  slowly  melt  away,  a  crystalline  form 
is  sometimes  seen  by  the  gradual  disintegration  into  rude  hexagonal  prisms  : 
a  similar  structure  is  frequently  met  with,  but  in  greater  perfection,  in  the  ice 
caves  or  glaciers  of  cold  regions. 

An  experiment  of  Tyndall  has  more  clearly  revealed  the  beautiful  struc- 
ture of  ice.  When  a  piece  of  ice  is  cut  parallel  to  its  planes  of  freezing,  and 
the  radiation  from  any  source  of  light,  as  the  sun,  a  gas  or  oil  flame,  is  per- 
mitted to  pass  through  it,  the  disintegration  of  the  substance  proceeds  in  a 
remarkable  way.  By  observing  the  plate  of  ice  through  a  lens,  numerous 
small  crystals  will  be  seen  studding  the  interior  of  the  block  ;  as  the  heat 
continues  these  crystals  expand,  and  finally  assume  the  shape  of  six-rayed 
stars  of  exquisite  beauty. 

This  is  a  kind  of  negative  crystallisation,  the  crystals  produced  being 
composed  of  water  ;  they  owe  their  formation  to  the  molecular  disturbance 
caused  by  the  absorption  of  heat  from  the  source.  Nothing  is  easier  than  to 
reproduce  this  phenomenon,  if  care  be  taken  in  cutting  the  ice.  The  planes 
of  freezing  can  be  found  by  noting  the  direction  of  the  bubbles  in  ice,  which 
are  either  sparsely  arranged  in  striae  at  right  angles  to  the  surface,  or  thickly 
collected  in  beds  parallel  to  the  surface  of  the  water.  A  warm  and  smooth 
metal  plate  should  be  used  to  level  and  reduce  the  ice  to  a  slab  not  exceeding 
half  an  inch  in  thickness. 

A  still  more  important  property  of  ice  remains  to  be  noticed.  Faraday 
discovered  that  when  two  pieces  of  melting  ice  are  pressed  together  they 
freeze  into  one  at  their  points  of  contact.  This  curious  phenomenon  is  now 
known  under  the  name  of  regelation.  The  cause  of  it  has  been  the  subject 
of  much  controversy,  but  the  simplest  explanation  seems  to  be  that  given 
by  its  discoverer.  The  particles  on  the  exterior  of  a  block  of  ice  are  held  by 
cohesion  on  one  side  only  :  when  the  temperature  is  at  o°  C,  these  exterior 
particles,  being  partly  free,  are  the  first  to  pass  into  the  liquid  state,  and  a  film 
of  water  covers  the  solid.  But  the  particles  in  the  interior  of  the  block  are 
bounded  on  all  sides  by  the  solid  ice,  the  force  of  cohesion  is  here  a  maximum, 
and  hence  the  interior  ice  has  no  tendency  to  pass  into  a  liquid,  even  when 
the  whole  mass  is  at  o°.  If  the  block  be  now  split  in  halves,  a  liquid  film 
instantly  covers  the  fractured  surfaces,  for  the  force  of  cohesion  on  the 
fractured  surfaces  has  been  lessened  by  the  act.  By  placing  the  halves 
together,  so  that  their  original  position  shall  be  regained,  the  liquid  films 
on  the  two  fractured  surfaces  again  become  bounded  by  ice  on  both  sides. 
The  film  being  excessively  thin,  the  force  of  cohesion  is  able  to  act  across 
it ;  the  consequence  of  this  is,  the  liquid  particles  pass  back  into  the  solid 
state,  and  the  block  is  reunited  by  regelation.  Not  only  do  ice  and  ice  thus 
freeze  together,  but  regelation  also  takes  place  between  moist  ice  and  any 
non-conducting  solid  body,  as  flannel  or  sawdust :  a  similar  explanation  to 
that  just  given  has  been  applied  here,  substituting  another  solid  for  the  ice 


-979]  Glaciers.  909 

on  one  side.  It  must  be  remarked,  however,  that  many  eminent  philosophers 
dissent  from  the  explanation  here  given. 

Whatever  may  be  the  true  cause  of  regelation,  there  can  be  no  doubt 
that  this  interesting  observation  of  Faraday's  explains  many  natural  phe- 
nomena. For  example,  the  formation  of  a  snowball  depends  on  the 
regelation  of  the  snow  granules  composing  it ;  and  as  regelation  cannot 
take  place  at  temperatures  below  o°  C,  for  then  both  snow  and  ice 
are  dry,  it  is  only  possible  to  make  a  coherent  snowball  when  the  snow  is 
melting. 

The  snow  bridges,  also,  which  span  wide  chasms  in  the  Alps  and  else- 
where, and  over  which  men  can  walk  in  safety,  owe  their  existence  to  the 
regelation  of  gradually  accumulating  particles  of  snow. 

Bottomley  has  made  a  very  instructive  experiment  which  illustrates 
regelation.  A  block  of  ice  is  suspended  on  two  supports,  and  a  fine  piano 
wire  with  heavy  weights  at  each  end  is  laid  across  it.  After  some  time  the 
wire  has  slowly  cut  its  way  through,  but  the  cut  surfaces  have  reunited,  and, 
excepting  a  few  bubbles,  show  no  trace  of  the  operation  ;  the  wire  is  below 
zero,  as  is  proved  by  placing  it  in  cold  water,  upon  which  some  ice  forms 
about  it. 

979.  Glaciers. — Tyndall  has  applied  this  regelating  property  of  ice  to 
the  explanation  of  the  formation  and  motion  of  glaciers,  of  which  the  follow- 
ing is  a  brief  description  : — In  elevated  regions,  what  is  termed  the  snow 
line  marks  the  boundary  of  eternal  snow,  for  above  this  the  heat  of  summer 
is  unable  to  melt  the  winter's  snow.  By  the  heat  of  the  sun  and  the  con- 
sequent percolation  of  water  melted  from  the  surface,  the  lower  portions  of 
the  snow  field  are  raised  to  o°  C.  ;  at  the  same  time  this  part  is  closely 
pressed  together  by  the  weight  of  the  snow  above,  regelation  therefore  sets 
in,  converting  the  loose  snow  into  a  coherent  mass. 

By  increasing  pressure  the  intermingled  air  which  renders  snow  opaque 
becomes  ejected  and  transparent ;  ice  then  results.  Its  own  gravity,  and 
the  pressure  from  behind,  urge  downwards  the  glacier  which  has  thus  been 
formed.  In  its  descent  from  the  mountain  the  glacier  behaves  in  all 
respects  like  a  river,  passing  through  narrow  gorges  with  comparative 
velocity,  and  then  spreading  out  and  moving  slowly  as  its  bed  widens. 
Further,  just  as  the  central  portions  of  a  river  move  faster  than  the  sides, 
so  Forbes  ascertained  that  the  centre  of  a  glacier  moves  quicker  than  its 
margin,  and  from  the  same  reason  (the  difference  in  the  friction  encoun- 
tered) the  surface  moves  more  rapidly  than  the  bottom.  To  explain  these 
facts  Forbes  assumed  ice  to  be  a  viscous  body  capable  of  flexure,  and 
flowing  like  lava  ;  but  as  ice  has  not  the  properties  of  a  viscous  sub- 
stance, the  now  generally  accepted  explanation  of  glacier  motion  is  that 
supplied  by  the  theory  of  regelation.  According  to  this  theory,  the  brittle 
ice  of  the  glacier  is  crushed  and  broken  in  its  passage  through  narrow 
channels,  such  as  that  of  Trelaporte  on  Mont  Blanc;  and  then,  as  it 
emerges  from  the  gorge  which  confined  it,  becomes  reunited  by  virtue  of 
regelation  ;  in  this  instance  forming  the  well-known  Mer  de  Glace.  By 
numerous  experiments  Tyndall  has  established  that  regelation  is  adequate 
to  furnish  this  explanation,  and  he  has  artificially  imitated,  on  a  small  scale, 
the  moulding  of  glaciers  by  the  crushing  and  subsequent  regelation  of  ice.^ 


9io 


Meteorology. 


980- 


980.  Atmospheric    electricity.     Franklin's  experiment. — The  most 
frequent  luminous  phenomena,  and  the  most  remarkable  for  their  effects, 
are  those  produced  by  the  free  electricity  in  the  atmosphere.     The  first 
physicists  who  observed  the  electric  spark  compared  it  to  the  gleam  of 
lightning,  and  its  crackling  to  the  sound  of  thunder.     But  Franklin,  by  the 
aid  of  powerful  electrical  batteries,  first  established  a  complete   parallel 
between  lightning  and  electricity  ;  and  he  indicated,  in  a  memoir  published 
in  1749,  the  experiments  necessary  to  attract  electricity  from  the  clouds  by 
means  of  pointed  rods.     The  experiment  was  tried  by 
Dalibard  in  France  ;  and  Franklin,  pending  the  erec- 
tion of  a  pointed  rod  on  a  spire  in  Philadelphia,  had  the 
happy  idea  of  flying  a  kite,  provided  with  a  metallic 
point,  which  could  reach  the  higher  regions  of  the 
atmosphere.     In  June  1752,  during   stormy  weather, 
he  flew  the  kite  in  a  field  near   Philadelphia.     The 
kite  was  flown  with  ordinary  pack-thread,  at  the  end 
of  which  Franklin  attached  a  key,  and  to  the  key  a 
silk  cord,  in  order  to  insulate  the  apparatus  ;  he  then 
fixed  the  silk  cord  to  a  tree,  and  having  presented 
his  hand  to  the  key,  at  first  he  obtained  no  spark. 
He  was  beginning  to  despair  of  success,  when,  ram 
having  fallen,  the  cord  became  a  good  conductor,  and 
a  spark  passed.     Franklin,  in  his  letters,  describes  his 
emotion  on  witnessing  the  success  of  the  experiment 
as  being  so  great  that  he  could  not  refrain  from  tears. 
Franklin  imagined  that  the  kite  withdrew  from  the 
cloud  its  electricity  ;    it  is,  in  fact,  a  simple  case  of 
induction,  and  depends  on  the  inductive  action  which 
the  thunder  cloud  exerts  upon  the  kite  and  the  cord. 

981.  Apparatus  to  investigate  the  electricity  of 
the  atmosphere. —  The  apparatus  used  to  ascertain 
the  presence  of  electricity  in  the  atmosphere  are  :  the 
electroscope,  either  with  pith  balls,  straw,  or  gold 
leaf;  the  apparatus  first  used  by  Dalibard,  and  which 
consisted  of  an  insulated  iron  rod,  36  yards  in  height ; 
arrows  discharged  into  the  atmosphere,  and  even  kites 
and  captive  balloons. 

To  observe  the  electricity  in  fine  weather,  when 
the  quantity  is  generally  small,  an  electrometer  is  used, 
as  devised  by  Saussure  for  this  kind  of  investigation. 
It  is  an  electroscope  similar  to  that  already  described,  but  the  rod  to  which 
the  gold  leaves  are  fixed  is  surmounted  by  a  conductor  2  feet  in  length, 
and  terminate  either  in  a  knob  or  a  point  (fig.  860)  To  protect  the  appa- 
ratus against  rain,  it  is  covered  with  a  metallic  shield  4  inches  in  diameter. 
The  glass  case  is  square,  instead  of  being  round,  and  a  divided  scale  on  its 
inside  face  indicates  the  divergence  of  the  gold  leaves  or  of  the  straws. 
This  electrometer  only  gives  signs  of  atmospheric  electricity  as  long  as  it  is 
raised  in  the  atmosphere,  so  that  it  is  in  layers  of  air  of  higher  electrical 
potential  than  its  own. 


Fig.  860. 


-981]   Apparatus  to  investigate  Electricity  of  the  Atmosphere.  91  I 

To  investigate  the  electricity  of  the  atmosphere,  Saussure  also  used  a 
copper  ball,  which  he  projected  vertically  with  his  hand.  This  ball  was 
fixed  to  one  end  of  a  metallic  wire,  the  other  end  of  which  was  attached  to  a 
ring,  which  could  glide  along  the  conductor  of  the  electrometer.  From  the 
divergence  of  the  straws,  or  of  the  gold  leaves,  the  electrical  condition  of 
the  air  at  the  height  which  the  ball  attained  could  be  determined.  Becquerel, 
in  experiments  made  on  the  St.  Bernard,  improved  Saussure's  apparatus  by 
substituting  for  the  knob  an  arrow,  which  was  projected  into  the  atmosphere 
by  means  of  a  bow.  A  gilt  silk  thread,  88  yards  long,  was  fixed  with  one 
end  to  the  arrow,  while  the  other  end  was  attached  to  the  stem  of  an  elec- 
troscope. Peltier  used  a  gold-leaf  electroscope,  at  the  top  of  which  was  a 
somewhat  large  copper  globe.  Provided  with  this  instrument,  the  observer 
places  himself  in  a  prominent  position — it  is  then  quite  sufficient  to  raise 
the  electroscope  even  a  foot  or  so  to  obtain  signs  of  electricity. 


Fig.  861. 

To  observe  the  electricity  of  clouds,  where  the  potential  is  very  con- 
siderable, use  is  made  of  a  long  bar  terminating  in  a  point.  This  bar, 
which  is  insulated  with  care,  is  fixed  to  the  summit  of  a  building,  and  its 
lower  end  is  connected  with  an  electrometer,  or  even  with  electric  chimes 
(fig.  630),  which  announce  the  presence  of  thunder  clouds.  As,  however,  the 
bar  can  then  give  dangerous  shocks,  a  metal  ball  must  be  placed  near  it, 
which  is  well  connected  with  the  ground,  and  which  is  nearer  the  bar  than 
the  observer  himself ;  so  that  if  a  discharge  should  ensue,  it  will  strike  the 
ball  and  not  the  observer.  Richmann,  of  St.  Petersburg,  was  killed  in  an 
experiment  of  this  kind,  by  a  discharge  which  struck  him  on  the  forehead. 

Sometimes  also  captive  balloons  or  kites  have  been  used,  provided  with 
a  point,  and  connected  by  means  of  a  gilt  cord  with  an  electrometer. 

A  good  collector  of  atmospheric  electricity  consists  of  a  fishing-rod  with 


912  Meteorology.  [981- 

an  insulated  handle  which  projects  from  an  upper  window.  At  the  top  is 
a  bit  of  lighted  tinder  held  in  a  metal  forceps,  the  smoke  of  which,  being 
an  excellent  conductor,  conveys  the  electricity  of  the  air  down  a  wire  attached 
to  the  rod.  A  sponge  moistened  with  alcohol,  and  set  on  fire,  is  also  an 
excellent  conductor. 

A  very  convenient  instrument  for  investigating  atmospheric  electricity 
has  been  introduced  by  Sir  W.  Thomson  ;  one  form  of  which,  used  in  the 
meteorological  observatory  of  Montsouris,  is  represented  in  fig.  86 1.  It  con- 
sists of  a  large  metal  vessel  A  resting  on  three  insulating  glass  legs  fixed  to 
the  top  of  a  tall  column  of  cast  iron.  A  sheet  metal  mantle  B  protects  the 
supports  from  the  rain.  The  apparatus  is  arranged  in  the  open,  and  can  be 
filled  with  water  from  a  pipe  C.  The  water  issues  through  a  long  lateral 
jet  in  A,  in  a  stream  so  fine  that  the  volume  of  the  water  is  not  appreciably 
altered.  An  insulated  wire  z  passing  through  the  column,  connects  the  vessel 
A  with  an  electrometer  placed  indoors. 

The  manner  in  which  electricity  of  the  atmosphere  is  registered  is  seen 
from  fig.  862,  which  represents  the  form  in  use  at  the  above  observatory.  In 
a  light  tight  box  is  a  band  of  sensitised  photographic  paper  stretched  on 
the  surface  of  a  cylinder  and  moved  by  clockwork. 

In  one  side  of  the  box  is  a  long  cylindrical  glass  lens  L  ;  in  front  of  which  at 
E  are  two  quadrant  electrometers.  Both  of  these  are  connected  with  the 
same  collector  of  electricity,  placed  outside,  and  their  sectors  are  charged 
by  the  same  source  of  electricity,  but  one  of  them  is  ten  times  as  sensitive 
as  the  other.  Near  one  side  of  the  box  is  a  gas  burner  with  an  opaque 
chimney  A,  in  two  opposite  sides  of  which  are  longitudinal  slits,  through 
which  the  light  passes  to  two  total-reflection  prisms  (545)  p p\  which  are 
arranged  so  as  to  send  two  pencils  of  light  on  the  mirrors  m  mf  of  the 
electrometer.  This  is  shown  on  a  larger  scale  on  the  left  of  the  figure  :  the 
two  pencils  fall  upon  the  lens  L,  which  concentrates  in  a  point  the  slices  of 
light  issuing  from  the  chimney  and  reflected  from  the  mirror.  These  follow 
the  motion  of  the  mirror,  and  thus  impress  on  the  sensitive  paper  the  curves 
which  measure, the  electrical  potential  of  the  air. 

There  is  also  an  arrangement  by  which  an  electro-magnet  puts  the 
electrometers  to  earth  for  a  few  minutes  at  every  hour,  and  thus  discharges 
them.  The  mirrors  revert  then  to  their  original  position  and  recommence  a 
new  trace. 

If  we  replace  the  electrometer  with  its  mirror  attached  by  a  magneto- 
meter, we  can  easily  see  how  the  variations  in  the  magnetic  declination  may 
be  recorded  (702). 

982.  Ordinary  electricity  of  the  atmosphere. — By  means  of  the  dif- 
ferent apparatus  which  have  been  described,  it  has  been  found  that  the 
presence  of  electricity  in  the  atmosphere  is  not  confined  to  stormy  weather, 
out  that  the  atmosphere  always  contains  free  electricity,  usually  positive,  but 
sometimes  negative.  When  the  sky  is  cloudless,  the  electricity  is  always 
positive,  but  it  varies  in  amount  with  the  height  of  the  locality,  and  with  the 
time  of  day.  The  amount  is  greatest  in  the  highest  and  most  isolated 
places.  No  trace  of  positive  electricity  is  found  in  houses,  streets,  and 
under  trees  ;  in  towns  positive  electricity  is  most  perceptible  in  large  open 
spaces,  on  quays,  or  on  bridges.  In  all  cases,  positive  electricity  is  only 


-963] 


Ordinary  Electricity  of  the  Atmosphere. 


913 


found  at  a  certain  height  above  the  ground.     On  flat  land,  it  only  becomes 
perceptible  at  a  height  of  five  feet  ;  above  that  point  it  increases  according 


Fig.  862. 

to  a  law  which  is  not  fully  made  out,  but  which  seems  to  depend  on  the 
hygrometric  state  of  the  air. 

At  sunrise  the  free  positive  electricity  is  feeble  ;  it  increases  up  to  i  r 
o'clock,  according  to  the  season,  and  then  attains  its  first  maximum.  It 
then  decreases  rapidly  until  a  little  before  sunset,  and  then  increases  till  it 
reaches  its  second  maximum,  a  few  hours  after  sunset  ;  the  remainder  of 
the  night  the  electricity  decreases  until  sunrise.  Thus  the  greatest  amount 
of  electricity  i«  observed  when  the  barometric  pressure  is  greatest.  These 
increasing  and  decreasing  periods,  which  are  observed  all  the  year,  are 
more  perceptible  when  the  sky  is  clearer,  and  the  weather  more  settled. 
The  positive  electricity  of  fine  weather  is  much  stronger  in  winter  than  in 
summer. 

When  the  sky  is  clouded,  the  electricity  is  sometimes  positive  and  some- 
times negative.  It  often  happens  that  the  electricity  changes  its  sign 
several  times  in  the  course  of  the  day,  owing  to  the  passage  of  an  electrified 
cloud.  During  storms,  and  when  it  rains  or  snows,  the  atmosphere  may  be 
positively  electrified  one  day,  and  negatively  the  next,  and  the  number  of 
the  two  sets  of  days  are  virtually  equal. 

From  a  long  series  of  observations  on  the  electricity  of  the  atmosphere 

R  R 


Meteorology.  [982- 

made  in  the  early  morning,  Dellman  found  that  the  electricity  increased 
with  the  density  of  the  fog,  but  in  a  far  more  rapid  ratio. 

The  electricity  of  the  ground  has  been  found  by  Peltier  to  be  always 
negative,  but  to  different  extents,  according  to  the  hygrometric  state  and 
temperature  of  the  air. 

983.  Causes  of  tbe   atmospheric  electricity. — Many  hypotheses  have 
been  propounded  to  explain  the  origin  of  the  atmospheric  electricity.     It 
must  be  confessed,  however,  that  our  knowledge  of  the  origin  of  atmospheric 
electricity  is  in  a  very  unsatisfactory  state. 

Volta  first  showed  that  the  evaporation  of  water  produced  electricity. 
Pouillet  subsequently  showed  that  no  electricity  is  produced  by  the  evapora- 
tion of  distilled  water ;  but  that  if  an  alkali  or  a  salt  is  dissolved,  even  in 
small  quantity,  the  vapour  is  positively  and  the  solution  is  negatively 
electrified.  The  reverse  is  the  case  if  the  water  contains  acid.  Hence  it 
has  been  assumed  that,  as  the  waters  which  exist  on  the  surface  of  the  earth 
and  on  the  sea  always  contain  salt  dissolved,  the  vapours  disengaged  ought 
to  be  positively  and  the  earth  negatively  electrified.  The  development  of 
electricity  by  evaporation  may  be  observed  by  heating  strongly  a  platinum 
dish,  adding  to  it  a  small  quantity  of  liquid,  and  placing  it  on  the  upper 
plate  of  the  condensing  electroscope  (fig.  641),  taking  care  to  connect  the 
lower  plate  with  the  ground.  When  the  water  of  the  capsule  is  evaporated, 
the  connection  with  the  ground  is  broken,  and  the  upper  plate  raised.  The 
gold  leaves  then  diverge  if  the  water  contained  salts,  but  remain  quiescent 
if  the  water  was  pure. 

Reasoning  from  such  experiments,  Pouillet  ascribed  the  development  of 
electricity  by  evaporation  to  the  separation  of  particles  of  water  from  the 
substances  dissolved  ;  but  Reich  and  Riess  showed  that  the  electricity  dis- 
engaged during  evaporation  could  be  attributed  to  the  friction  which  the 
particles  of  water  carried  away  in  the  current  of  vapour  exercise  against  the 
sides  of  the  vessel,  just  as  in  Armstrong's  electrical  machine  (758).  By  a 
recent  series  of  experiments,  Gaugain  has  arrived  at  the  same  result  ;  and 
thinks  it  no  longer  allowable  to  ascribe  the  atmospheric  electricity  to  any 
changes  that  take  place  during  the  tranquil  evaporation  of  sea  water. 

984.  Electricity   of  clouds. — In   general    the    clouds   are    electrified, 
sometimes  positively  and  sometimes  negatively,  and  only  differ  in  their  higher 
or  lower  potential.     The  formation  of  positive  clouds  is  usually  ascribed 
to  the  vapours  which  are  disengaged  from  the  ground,  and  condense  in  the 
higher  regions.     Negative  clouds  are  supposed  to  result  from  fogs,  which,  by 
their  contact  with  the  ground,  become  charged  with  negative  electricity, 
which  they  retain  on  rising  into  the  atmosphere  ;  or  that,  separated  from  the 
ground  by  layers  of  moist  air,  they  have  been  negatively  electrified  by  induc- 
tion from  the  positive  clouds,  which  have  repelled  into  the  ground  positive 
electricity. 

985.  Xiigbtningr — This,  as  is  well  known,  is  the  dazzling  light  emitted  by 
the  electric  spark  when  it  shoots  from  clouds  charged  with  electricity.     In 
the  lower  regions  of  the  atmosphere  the  light  is  white,  but  in  the  higher 
regions,  where  the  air  is  more  rarefied,  it  takes  a  violet  tint ;  as  does  the 
spark  of  the  electrical  machine  in  a  rarefied  medium  (787). 

The  flashes  of  lightning  are  often  more  than  a  mile,   and  sometimes 


-986]  Thunder.  915 

extend  to  four  or  five  miles,  in  length  ;  they  generally  pass  through  the 
atmosphere  in  a  zigzag  direction  :  a  phenomenon  ascribed  to  the  resistance 
offered  by  the  air  condensed  by  the  passage  of  a  strong  discharge.  The 
spark  then  diverges  from  a  right  line,  and  takes  the  direction  of  least  resis- 
tance. In  vacuo,  electricity  passes  in  a  straight  line. 

Several  kinds  of  lightning  flashes  may  be  distinguished — i.  the  zigzag 
flashes,  which  move  with  extreme  velocity  in  the  form  of  a  line  of  fire  with 
sharp  outlines,  and  which  entirely  resemble  the  spark  of  an  electrical 
machine  ;  2.  the  sheet  flashes  which,  instead  of  being  linear,  like  the  pre- 
ceding, fill  the  entire  horizon  without  having  any  distinct  shape.  This  kind, 
which  is  most  frequent,  appears  to  be  produced  in  the  cloud  itself,  and  to 
illuminate  the  mass.  According  to  Kundt,  the  number  of  sheet  discharges 
are  to  the  zigzag  discharges  as  1 1  :  6  ;  and  from  spectrum  observations  it 
would  appear  that  the  former  are  brush  discharges  between  clouds,  while 
the  latter  are  true  electrical  discharges  between  the  clouds  and  the  earth. 
Another  kind,  called  heat  lightning,  is  ascribed  to  distant  lightning  flashes 
w  hich  are  below  the  horizon,  but  illuminate  the  higher  strata  of  clouds  so 
that  their  brightness  is  visible  at  great  distances  ;  they  produce  no  sound, 
probably  in  consequence  of  the  fact  of  their  being  so  far  off  that  the  rolling 
of  thunder  cannot  reach  the  ear  of  the  observer.  There  is  further  the  very 
unusual  phenomenon  of  globe  lightning,  or  the  flashes  which  appear  in  the 
form  of  globes  of  fire.  These,  which  are  sometimes  visible  for  as  much  as 
ten  seconds,  descend  from  the  clouds  to  the  earth  with  such  slowness,  that 
the  eye  can  follow  them.  They  often  rebound  on  reaching  the  ground  ;  at 
other  times  they  burst  and  explode  with  a  noise  like  that  of  the  report  of 
many  cannon. 

The  duration  of  the  light  of  the  first  three  kinds  does  not  amount  to  the 
millionth  of  a  second,  as  was  determined  by  Wheatstone  by  means  of  his 
rotating  wheel,  which  was  turned  so  rapidly  that  the  spokes  were  invisible  : 
on  illuminating  it  by  the  lightning  flash,  its  duration  was  so  short  that 
whatever  the  velocity  of  rotation  of  the  wheel,  it  appeared  quite  stationary  ; 
that  is,  its  displacement  is  not  perceptible  during  the  time  the  lightning 
exists. 

The  light  produced  by  a  lightning  flash  must  be  comparable  to  the  sun 
in  brightness,  though  it  does  not  appear  to  us  brighter  than  ordinary  moon- 
light. But  considering  its  excessively  brief  duration,  and  that  the  full 
effect  of  any  light  on  the  eye  is  only  produced  when  its  duration  is  at 
least  the  tenth  of  a  second,  it  follows  that  a  landscape  continuously  illu- 
minated by  the  lightning  flash  would  appear  100,000  times  as  bright  as  it 
actually  appears  to  us. 

986.  Thunder. —  Thunder  is  the  violent  report  which  succeeds  lightning 
in  stormy  weather.  The  lightning  and  the  thunder  are  always  simultaneous ; 
but  an  interval  of  several  seconds  is  always  observed  between  these  two 
phenomena,  which  arises  from  the  fact  that  sound  only  travels  at  the  rate  of 
about  1,100  feet  in  a  second  (232),  while  the  passage  of  light  is  almost  instan- 
taneous. Hence  an  observer  will  only  hear  the  noise  of  thunder  five  or  six 
seconds,  for  instance,  after  the  lightning,  according  as  the  distance  of  the 
thunder-cloud  is  five  or  six  times  1,100  feet.  The  noise  of  thunder  arises 
from  the  disturbance  which  the  electric  discharge  produces  in  the  air,  and 

R  R  2 


gi6  Meteorology.  [986- 

which  may  be  witnessed  in  Kinnersley's  thermometer  (fig.  652).  Near  the 
place  where  the  lightning  strikes,  the  sound  is  dry  and  of  short  duration. 
At  a  greater  distance  a  series  of  reports  are  heard  in  rapid  succession.  At  a 
still  greater  distance  the  noise,  feeble  at  the  commencement,  changes  into  a 
prolonged  rolling  sound  of  varying  intensity.  If  the  lightning  is  at  a  greater 
distance  than  14  or  15  miles,  it  is  no  longer  heard,  for  sound  is  more  imper- 
fectly propagated  through  air  than  through  solid  bodies  ;  hence,  there  are 
lightning  discharges  without  thunder  ;  these  occur  at  times  when  the  sky  is 
cloudless. 

Some  attribute  the  noise  of  the  rolling  of  thunder  to  the  reflection  of 
sound  from  the  ground  and  from  the  clouds.  Others  have  considered  the 
lightning  not  as  a  single  discharge,  but  as  a  series  of  discharges,  each  of 
which  gives  rise  to  a  particular  sound.  But  as  these  partial  discharges 
proceed  from  points  at  different  distances,  and  from  zones  of  unequal  density, 
it  follows  not  only  that  they  reach  the  ear  of  the  observer  successively,  but 
that  they  bring  sounds  of  unequal  density,  which  occasion  the  duration  and 
inequality  of  the  rolling.  The  phenomenon  has  finally  been  ascribed  to 
the  zigzags  of  lightning  themselves,  assuming  that  the  air  at  each  salient 
angle  is  at  its  greatest  compression,  which  would  produce  the  unequal  inten- 
sity of  the  sound. 

987.  Effects  of  lightning. — The  lightning  discharge  is  the  electric  dis- 
charge which  strikes  between  a  thunder-cloud  and  the  ground.  The  latter, 
by  the  induction  from  the  electricity  of  the  cloud,  becomes  charged  with 
contrary  electricity  ;  and  when  the  tendency  of  the  two  electricities  to  com- 
bine exceeds  the  resistance  of  the  air,  the  spark  passes,  which  is  often  ex- 
pressed by  saying  that  a  thunderbolt  has  fallen.  Lightning  in  general 
strikes  from  above,  but  ascending  lightning  is  also  sometimes  observed  ; 
probably  this  is  the  case  when  the  clouds  being  negatively  the  earth  is 
positively  electrified,  for  experiments  show  that  at  the  ordinary  pressure 
the  positive  fluid  passes  through  the  atmosphere  more  easily  than  negative 
electricity. 

From  the  first  law  of  electrical  attraction,  the  discharge  ought  to  fall  first 
on  the  nearest  and  best-conducting  objects,  and,  in  fact,  trees,  elevated 
buildings,  metals,  are  particularly  struck  by  the  discharge.  Hence  it  is  im- 
prudent to  stand  under  trees  during  a  thunder-storm. 

The  effects  of  lightning  are  very  varied,  and  of  the  same  kind  as  those  of 
batteries  (783),  but  of  far  greater  intensity.  The  lightning  discharge  kills 
men  and  animals,  sets  fire  to  combustibles,  melts  metals,  breaks  bad 
conductors  in  pieces.  When  it  penetrates  the  ground  it  melts  the  siliceous 
substances  on  its  path,  and  thus  produces  in  the  direction  of  the  discharge 
those  remarkable  vitrified  tubes  called  fulgurites,  some  of  which  are  as  much 
as  12  yards  in  length  ;  in  most  cases  there  are  found  to  be  accumulations  of 
.water  below  such  fulgurites.  When  it  strikes  bars  of  iron,  it  magnetises 
them,  and  often  inverts  the  poles  of  compass  needles. 

After  the  passage  of  lightning,  a  highly  peculiar  odour  is  frequently 
produced,  like  that  perceived  in  a  room  in  which  an  electrical  machine 
is  being  worked.  This  is  due  to  the  formation  of  ozone,  a  peculiar  allotropic 
modification  of  oxygen  (793). 

Heated  air  conducts  better  than  cold  air,  probably  only  owing  to  its 


-989]  Lightning  Conductor.  917 

lesser  density.  Hence  it  is  that  large  numbers  of  animals  are  often  killed 
by  a  single  discharge,  as  they  crowd  together  in  a  storm,  and  a  column  of 
warm  air  rises  from  the  group. 

988.  Return  snook. — This  is  a  violent  and  sometimes  fatal  shock  which 
men  and  animals  experience,  even  when  at  a  great  distance  from  the  place 
where  the  lightning  discharge  passes.     It  is  caused  by  the  inductive  action 
which  the  thunder-cloud  exerts  on  bodies  placed  within  the  sphere  of  its 
activity.     These  bodies  are  then,  like  the  ground,  charged  with  the  opposite 
electricity  to  that  of  the  cloud  ;  but  when  the  latter  is  discharged  by  the 
recombination  of  its  electricity  with  that  of  the  ground,  the  induction  ceases, 
and  the  bodies  reverting  rapidly  from  the  electrical  state  to  the  neutral  state, 
the  concussion  in  question  is  reproduced — the  return  shock.     A  gradual  de- 
composition and  reunion  of  the  electricity  produces  no  visible  effects  ;  yet  it 
is  alleged  that  such  disturbances  of  the  electrical  equilibrium  are  perceived 
by  nervous  persons. 

The  return  shock  is  always  less  violent  than  the  direct  one  ;  there  is  no 
instance  of  its  having  produced  any  inflammation,  yet  plenty  of  cases  in 
which  it  has  killed  both  men  and  animals  ;  in  such  cases  no  broken  limbs, 
wounds,  or  burns  are  observed. 

The  return  shock  may  be  imitated  by  placing  a  gold-leaf  electroscope 
connected  by  a  wire  with  the  ground  near  an  electrical  machine  ;  when  the 
machine  is  worked,  at  each  spark  taken  from  the  prime  conductor  the  gold 
leaves  of  the  electroscope  diverge. 

989.  Xiightnlng-  conductor. — The  ordinary7  form  of  this  instrument  is  an 
iron  rod,  through  which  passes  the  electricity  of  the  ground  attracted  by  the 
opposite  electricity  of  the  thunder-clouds.     It  was  invented  by  Franklin, 
in  1755. 

There  are  two  principal  parts  in  a  lightning  conductor  ;  the  rod  and  the 
'conductor.  The  rod  is  a  pointed  bar  of  iron,  fixed  vertically  to  the  roof  of 
the  edifice  to  be  protected  ;  it  is  from  6  to  10  feet  in  height,  and  its  basal 
section  is  about  2  or  3  inches  in  diameter.  The  conductor  is  a  bar  of  iron, 
which  descends  from  the  bottom  of  the  rod  to  the  ground,  which  it  penetrates 
to  some  distance.  As,  in  consequence  of  their  rigidity,  iron  bars  cannot 
always  be  well  adapted  to  the  exterior  of  buildings,  they  are  best  formed  of 
wire  cords,  such  as  are  used  for  rigging  and  for  suspension  bridges.  In  a 
report  made  by  the  Academy  of  Science  on  the  construction  of  lightning 
conductors,  the  use  of  copper  instead  of  iron  wire  in  these  conductors  is 
recommended,  inasmuch  as  copper  is  a  better  conductor  than  iron.  The 
metallic  section  of  the  cords  ought  to  be  about  £  a  square  inch,  and  the  indi- 
vidual wires  0*04  to  O'o6  inch  in  diameter;  they  ought  to  be  twisted  in 
three  strands,  like  an  ordinary  cord  The  conductor  is  usually  led  into  a 
well,  and  to  connect  it  better  with  the  soil  it  ends  in  two  or  three  branches. 
If  there  is  no  well  near,  a  hole  is  dug  in  the  soil  to  the  depth  of  6  or  7  yards, 
and  the  foot  of  the  conductor  having  been  introduced,  the  hole  is  filled 
with  powdered  coke,  which  conducts  very  well  and  preserves  the  metal  from 
oxidation. 

The  action  of  a  lightning  conductor  depends  on  induction  and  the  power 
of  points  (731)  ;  when  a  storm-cloud  positively  electified,  for  instance,  rises 
in  the  atmosphere,  it  acts  inductively  on  the  earth  repels  the  positive  and 


9 i 8  Meteorology. 

attracts  the  negative  fluid,  which  accumulates  on  bodies  placed  on  the  surface 
of  the  soil,  the  more  abundantly  as  these  bodies  are  at  a  greater  height. 
The  density  is  then  greatest  on  the  highest  bodies,  which  are  therefore  most 
exposed  to  the  electric  discharge  ;  but  if  these  bodies  are  provided  with 
metal  points,  like  the  rods  of  conductors,  the  negative  electricity,  withdrawn 
from  the  soil  by  the  influence  of  the  cloud,  flows  into  the  atmosphere,  and 
neutralises  the  positive  electricity  of  the  cloud.  Hence,  not  only  does  a 
lightning  conductor  tend  to  prevent  the  accumulation  of  electricity  on  the 
surface  of  the  earth,  but  it  also  tends  to  restore  the  clouds  to  their  natural 
state,  both  which  concur  in  preventing  lightning  discharges.  This  mode  of 
action  of  lightning  conductors  is  often  overlooked  ;  it  is  stated  in  reference 
to  Pietermaritzberg,  that  until  lightning  rods  became  common  in  that  town, 
it  was  constantly  visited  by  thunder-storms  at  certain  seasons.  They  come 
as  frequently  as  ever,  but  cease  to  give  flashes  on  reaching  the  town  ; 
they  do  so,  however,  when  they  have  passed  over  it.  The  disengagement  of 
electricity  is,  nevertheless,  so  abundant  at  times,  that  the  conductor  is  in- 
adequate to  discharge  the  electricity  of  the  ground,  and  the  lightning  strikes  ; 
but  the  conductor  receives  the  discharge,  in  consequence  of  its  greater 
conductivity,  and  the  edifice  is  preserved. 

A  conductor,  to  be  efficient,  ought  to  satisfy  the  following  conditions :  i. 
the  rod  ought  to  be  so  large  as  not  to  be  melted  if  the  discharge  passes  ;  ii. 
it  ought  to  terminate  in  a  point  to  give  readier  issue  to  the  electricity  disen- 
gaged by  induction  from  the  ground  ;  iii.  ,the  conductor  must  be  continuous 
from  the  point  to  the  ground,  and  the  connection  between  the  rod  and 
the  ground  must  be  as  intimate  as  possible  ;  iv.  if  the  building  which  is 
provided  with  a  lightning  conductor  contains  metallic  surfaces  of  any  ex- 
tent, such  as  zinc  roofs,  metal  gutters,  or  ironwork,  these  ought  to  be  con- 
nected with  the  conductor.  If  the  last  two  conditions  are  not  fulfilled,  there 
is  a  great  danger  of  lateral  discharges  ;  that  is  to  say,  that  the  discharge 
takes  place  between  the  conductor  and  the  edifice,  and  then  it  increases  the 
danger. 

Colladon  concludes  from  the  observation  of  a  series  of  lightning  dis- 
charges, that  a  tall  tree  such  as  a  poplar,  whose  roots  are  in  dry  ground, 
may  act  as  a  good  lightning  conductor,  if  on  the  other  side  of  the  house 
there  does  not  happen  to  be  a  well  or  pool,  towards  which  the  electricity  can 
spring  through  the  house. 

990.  Rainbow. — The  rainbow  is  a  luminous  meteor  which  appears  in 
the  clouds  opposite  the  sun  when  they  are  resolved  into  rain.  It  consists  of 
seven  concentric  arcs,  presenting  successively  the  colours  of  the  solar  spec- 
trum. Sometimes  only  a  single  bow  is  perceived,  but  there  are  usually 
two  ;  a  lower  one,  the  colours  of  which  are  very  bright,  and  an  external  or 
secondary  one,  which  is  paler,  and  in  which  the  order  of  the  colours  is  re- 
versed. In  the  interior  rainbow  the  red  is  the  highest  colour  ;  in  the  other 
rainbow  the  violet  is.  It  is  seldom  that  three  bows  are  seen  ;  theoretically 
a  greater  number  may  exist,  but  their  colours  are  so  feeble  that  they  are  not 
perceptible. 

The  phenomenon  of  the  rainbow  is  produced  by  the  decomposition  of  the 
white  light  of  the  sun  when  it  passes  into  the  drops,  and  by  its  reflection 
from  their  inside  face.  In  fact,  the  same  phenomenon  is  witnessed  in  dew- 


-  99  0]  Rainbow.  g  i  g 

drops  and  in  jets  of  water ;  in  short,  wherever  solar  light  passes  into  drops 
of  water  under  a  certain  angle. 

The  appearance  and  the  extent  of  the  rainbow  depend  on  the  position  of 
the  observer,  and  on  the  height  of  the  sun  above  the  horizon  ;  hence  only 
some  of  the  rays  refracted  by  the  rain-drops,  and  reflected  in  their  concavity 
to  the  eye  of  the  spectator,  are  adapted  to  produce  the  phenomenon.  Those 
which  do  so  are  called  effective  rays. 

To  explain  this  let  n  (fig.  863)  be  a  drop  of  water,  into  which  a  solar  ray 
Srf  penetrates.  At  a  point  of  incidence,  #,  part  of  the  light  is  reflected  from 
the  surface  of  the  liquid  ;  another,  entering  it,  is  decomposed  and  traverses 
the  drop  in  the  direction  ab.  Arrived  at  £,  part  of  the  light  emerges  from  the 
rain-drop ;  the  other  part  is  reflected  from  the  concave  surface,  and  tends  to 


Fig.  863. 

emerge  at  g.  At  this  point  the  light  is  again  partially  reflected  ;  the  re- 
mainder emerges  in  a  direction  ^O,  which  forms  with  the  incident  ray,  S#, 
an  angle  called  the  angle  of  deviation.  It  is  such  rays  as  ^O,  proceeding 
from  the  side  next  the  observer,  which  produce  on  the  retina  the  sensation  of 
colours,  provided  the  light  is  sufficiently  intense. 

It  can  be  shown  mathematically  that  in  the  case  of  a  series  of  rays  which 
impinge  on  the  same  drop,  and  only  undergo  a  reflection  in  the  interior,  the 
angle  of  deviation  increases  from  the  ray  S"#,  for  which  it  is  zero*  up  to  a 
certain  limit,  beyond  which  it  decreases,  and  that  near  this  limit  rays  passing 
parallel  into  a  drop  of  rain  also  emerge  parallel.  From  this  parallelism  a 
beam  of  light  is  produced  sufficiently  intense  to  impress  the  retina  ;  these 
are  the  rays  which  emerge  parallel  and  are  efficient. 

As  the  different  colours  which  compose  white  light  are  unequally  refran- 
gible, the  maximum  angle  of  deviation  is  not  the  same  for  all.  For  red  rays 
the  angle  of  deviation  corresponding  to  the  active  rays  is  42°  2',  and  for  violet 
rays  it  is  40°  17'.  Hence,  for  all  drops  placed  so  that  rays  proceeding  from 
the  sun  to  the  drop  make,  with  those  proceeding  from  the  drop  to  the  eye,  an 
angle  of  42°  2',  this  organ  will  receive  the  sensation  of  red  light ;  this  will  be 
the  case  with  all  drops  situated  on  the  circumference  of  the  base  of  a  cone, 
the  summit  of  which  is  the  spectator's  eye  ;  the  axis  of  this  cone  is  parallel 
to  the  sun's  rays,  and  the  angle  formed  by  the  two  opposed  generating  lines 


920  Meteorology.  [990- 

is  84° 4'.     This  explains  the  formation  of  the  red  band  in  the  rainbow;  the 
angle  of  the  cone  in  the  case  of  the  violet  band  is  80°  34'. 

The  cones  corresponding  to  each  band  have  a  common  axis  called  the 
visual  axis.  As  this  right  line  is  parallel  to  the  rays  of  the  sun,  it  follows 
that  when  this  axis  is  on  the  horizon,  the  visual  axis  is  itself  horizontal,  and 
the  rainbow  appears  as  a  semicircle.  If  the  sun  rises,  the  visual  axis  sinks, 
and  with  it  the  rainbow.  Lastly,  when  the  sun  is  at  a  height  of  42°  2',  the 
arc  disappears  entirely  below  the  horizon.  Hence  the  phenomenon  of  the 
rainbow  never  takes  place  except  in  the  morning  and  evening. 

What  has  been  said  refers  to  the  interior  arc.  The  secondary  bow  is 
formed  by  rays  which  have  undergone  two  reflections,  as  shown  by  the  ray 
S'/V#feO,  in  the  drop  p.  The  angle  S'lO  formed  by  the  emergent  and 
incident  ray  is  called  the  angle  of  deviation.  The  angle  is  no  longer  suscep- 
tible of  a  maximum,  but  of  a  minimum,  which  varies  for  each  kind  of  rays, 
and  to  which  also  efficient  rays  correspond.  It  is  calculated  that  the  mini- 
mum angle  from  violet  rays  is  54°  7'.  and  for  red  rays  only  50°  $7' ;  hence  it 
is  that  the  red  bow  is  here  on  the  inside,  and  the  violet  arc  on  the  outside. 
There  is  a  loss  of  light  for  every  internal  reflection  in  the  drop  of  rain,  and 
therefore  the  colours  of  the  secondary  bow  are  always  feebler  than  those  of 
the  internal  one.  The  secondary  bow  ceases  to  be  visible  when  the  sun  is 
54°  above  the  horizon. 

The  moon  sometimes  produces  rainbows  like  the  sun,  but  they  are  very 
pale. 

991.  Aurora  borealis. — The  aurora  borealis,  or  northern  light,  or  more 
properly,  polar  aurora,  is  a  remarkable  luminous  phenomenon  which  is  fre- 
quently seen  in  the  atmosphere  at  the  two  terrestrial  poles.  The  following 
is  a  description  of  an  aurora  borealis  observed  at  Bossekop,  in  Lapland,  lat. 
70°,  in  the  winter  of  1838-1839  : — 

*  In  the  evening,  between  4  and  8  o'clock,  the  upper  part  of  the  fog  which 
usually  prevails  to  the  north  of  Bossekop  became  coloured.  This  light 
became  more  regular,  and  formed  an  indistinct  arc  of  a  pale  yellow,  with  its 
concave  side  turned  towards  the  earth,  while  its  summit  was  in  the  magnetic 
meridian. 

'  Blackish  rays  soon  separated  the  luminous  parts  of  the  arc.  Luminous 
rays  formed,  becoming  alterately  rapidly  and  slowly  longer  and  shorter, 
their  lustre  suddenly  increasing  and  diminishing.  The  bottom  of  these  rays 
always  showed  the  brightest  light,  and  formed  a  more  or  less  regular  arc. 
The  length  of  the  rays  was  very  variable,  but  they  always  converged  towards 
the  same  point  of  the  horizon,  which  was  in  the  prolongation  of  the  north 
end  of  the  dipping  needle  ;  sometimes  the  rays  were  prolonged  as  far  as 
their  point  of  meeting,  and  thus  appeared  like  a  fragment  of  an  immense 
cupola. 

'  The  arc  continued  to  rise  in  an  undulatory  motion  towards  the  zenith. 
Sometimes  one  of  its  feet  or  even  both  left  the  horizon  ;  the  folds  became 
more  distinct  and  more  numerous  ;  the  arc  was  now  nothing  more  than  a 
long  band  of  rays  convoluted  in  very  graceful  shapes,  forming  what  is  called 
the  boreal  crown.  The  lustre  of  the  rays  varied  suddenly  in  intensity,  and 
attained  that  of  stars  of  the  first  magnitude  ;  the  rays  darted  with  rapidity, 
the  curves  formed  and  re-formed  like  the  folds  of  a  serpent  (fig.  864),  the  base 


-991]  Aurora  Borealis.  921 

was  red,  the  middle  green,  while  the  remainder  retained  its  bright  yellow 
colour.  Lastly,  the  lustre  diminished,  the  colours  disappeared  ;  everything 
became  feebler  or  suddenly  went  out.' 

A  French  scientific  commission  to  the  North  observed  150  aurora.1 
boreales  in  200  days  ;  it  appears  that  at  the  poles,  nights  without  an  aurora 
borealis  are  quite  exceptional,  so  that  it  may  be  assumed  that  they  take  place 
every  night,  though  with  varying  intensity.  They  are  visible  at  a  consider- 
able distance  from  the  poles,  and  over  an  immense  area.  Sometimes  the  same 
aurora  borealis  has  been  seen  at  the  same  time  at  Moscow,  Warsaw,  Rome, 
and  Cadiz.  Their  height  is  variously  estimated  at  from  90  to  460  miles. 
Mr.  Newton  found  the  mean  height  of  30  aurorae  to  be  133  miles;  they 
are  most  frequent  at  the  equinoxes,  and  least  so  at  the  solstices.  The 
number  differs  in  different  years  ;  attaining  a  maximum  every  11  years  at 


Fig.  864. 

the  same  time  as  the  sun-spots,  and  like  these  a  minimum  which  is  about  5 
or  6  years  from  the  maximum.  The  years  1844,  1855,  1860,  and  1877  are 
poor  in  the  appearance  of  the  aurora. 

There  is,  moreover,  a  period  of  about  60  years  ;  for  the  years  1728,  1780, 
and  1842  have  been  remarkable  for  the  prevalence  of  the  aurora.  The  last 
two  periods  are  also  remarkable  for  the  occurrence  of  disturbances  in  the 
earth's  magnetism. 

Numerous  hypotheses  have  been  devised  to  account  for  the  aurora? 
boreales.  The  constant  direction  of  their  arc  as  regards  the  magnetic  me- 
ridian, and  their  action  on  the  magnetic  needle  (702),  seem  to  show  that  they 
ought  to  be  attributed  to  electric  currents  in  the  higher  regions  of  the  atmo- 
sphere. In  high  latitudes  the  aurora  borealis  acts  powerfully  on  the  wires  of 
the  electric  telegraph  ;  the  alarums  are  for  a  long  time  violently  rung,  and 
despatches  frequently  interrupted  by  the  spontaneous  abnormal  working  of 
the  apparatus. 

RR3 


922  Meteorology.  [991- 

The  spectrum  of  the  aurora  borealis  has  been  found  by  Vogel  to  consist 
of  five  lines  in  the  green,  and  of  an  indistinct  line  in  the  blue  :  to  which  must 
be  added  a  red  line  due  to  the  red  protuberances  ;  these  lines  are  the  same 
as  those  of  nitrogen  greatly  rarefied  and  at  a  low  temperature. 

According  to  De  la  Rive  aurorae  boreales  are  due  to  electric  discharges 
which  take  place  in  polar  regions  between  the  positive  electricity  of  the 
atmosphere  and  the  negative  electricity  of  the  earth  ;  electricities  which 
themselves  are  separated  by  the  action  of  the  sun,  principally  in  the  equa- 
torial regions. 

The  occurrence  of  irregular  currents  of  electricity  which  manifest  them- 
selves by  abnormal  disturbances  of  telegraphic  communications  is  not  in- 
frequent ;  such  currents  have  received  the  name- of  earth  currents.  Sabine 
has  found  that  these  magnetic  disturbances  are  .due  to  a  peculiar  action  of 
the  sun,  and  probably  independently  of  its  radiant  heat  and  light.  It  has 
also  been  ascertained  that  the  aurora  borealis  as  well  as  earth  currents  in- 
variably accompany  these  magnetic  disturbances.  According  to  Balfour 
Stewart,  aurorae  and  earth  currents  are  to  be  regarded  as  secondary  currents 
due  to  small  but  rapid  changes  in  the  earth's  magnetism  ;  he  likens  the 
body  of  the  earth  to  the  magnetic  core  of  a  RuhmkorfFs  machine  (905)  ;  the 
lower  strata  of  the  atmosphere  forming  the  insulator,  while  the  upper  and 
rarer,  and  therefore  electrically  conducting  strata,  may  be  considered  as  the 
secondary  coil. 

On  this  analogy  the  sun  may  perhaps  be  likened  to  the  primary  current 
which  performs  the  part  of  producing  changes  in  the  magnetic  state  of  the 
core.  Now  in  RuhmkorfPs  machine  the  energy  of  the  secondary  current  is 
derived  from  that  of  the  primary  current.  Thus,  if  the  analogy  be  correct, 
the  energy  of  the  aurora  borealis  may  in  like  manner  come  from  the  sun  ; 
but  until  we  know  more  of  the  connection  between  the  sun  and  terrestrial 
magnetism,  these  ideas  are  to  be  accepted  with  some  reserve. 


-993]     Causes  which  modify  the  Temperature  of  the  Air.         923 


CLIMATOLOGY. 

992.  Mean  temperature. — The  mean  daily  temperature,  or  simply  tem- 
perature, is  that  obtained  by  adding  together  24  hourly  observations,  and 
diving  by  24.     A  very  close  approximation  to  the  mean  temperature  is  ob- 
tained by  taking  the  mean  of  the  highest  and  lowest  temperatures  of  the 
day  and  of  the  night,  which  are  determined  by  means  of  the  maximum  and 
minimum  thermometers.     These  ought  to  be  protected  from  the  solar  rays, 
to  be  raised  above  the  ground,  and  far  from  all  objects  which  might  influence 
them  by  their  radiation. 

The  temperature  of  a  month  is  the  mean  of  those  of  30  days,  and  the 
temperature  of  the  year  is  the  mean  of  those  12  months.  Finally,  the 
temperature  of  a  place  is  the  mean  of  its  annual  temperature,  for  a  great 
series  of  years.  The  mean  temperature  of  London  is  8'28°  C.,  or  46-9°  F. 
The  temperatures  in  all  cases  are  those  of  the  air  and  not  those  of  the 
ground. 

993.  Causes  which  modify  the  temperature  of  the  air. — The  principal 
causes  which  modify  the  temperature  of  the  air  are  the  latitude  of  a  place 
its  height,  the  direction  of  the  winds,  and  proximity  of  seas. 

Influence  of  the  latitude. — The  influence  of  the  latitude  arises  from  the 
greater  or  less  obliquity  of  the  solar  rays ;  for  as  the  quantity  of  heat  absorbed 
is  greater  the  nearer  the  rays  are  to  the  normal  incidence  (414),  the  heat  ab- 
sorbed decreases  from  the  equator  to  the  poles,  for  the  rays  are  then  more 
oblique.  This  loss  is  however,  in  summer,  in  the  temperate  and  arctic 
zones,  partially  compensated  by  the  length  of  the  days.  Under  the  equator, 
where  the  length  of  the  days  is  constant,  the  temperature  is  almost  invari- 
able ;  in  the  latitude  of  London,  and  in  more  northerly  countries,  where  the 
days  are  very  unequal,  the  temperature  varies  greatly  ;  but  in  summer  it 
sometimes  rises  almost  as  high  as  under  the  equator.  The  lowering  of  the 
temperature  produced  by  the  latitude  is  small  :  thus,  in  a  latitude  1 1 5  miles 
north  of  France,  the  temperature  is  only  i°  C.  lower. 

Influence  of  height.  The  height  of  a  place  has  a  much  more  consider- 
able influence  on  the  temperature  than  its  latitude.  In  the  temperate  zone 
a  diminution  of  i°  C  corresponds  in  the  mean  to  an  ascent  of  1 80 yards. 

The  cooling  on  ascending  in  the  atmosphere  has  been  observed  in 
balloon  ascents,  and  a  proof  of  it  has  been  seen  in  the  perpetual  snows 
which  cover  the  highest  mountains.  It  is  caused  by  the  greater  rarefaction 
of  the  air,  which  necessarily  diminishes  its  absorbing  power;  besides  which 
the  air  is  at  a  greater  distance  from  the  ground,  which  heats  it  by  contact ; 
and  finally  dry  air  is  very  diathermanous. 

The  law  of  the  diminution  of  temperature  ccrresponding  to  a  greater 


924  Meteorology.  [993- 

height  in  the  atmosphere  has  not  been  made  out,  in  consequence  of  the 
numerous  disturbing  causes  •  which  modify  it,  such  as  the  prevalent  winds, 
the  hygrometric  state,  the  time  of  day,  &c.  The  difference  between  the 
temperature  of  two  places  at  unequal  heights  is  not  proportional  to  the 
difference  of  level,  but  for  moderate  heights  an  approximation  to  the  law 
may  be  made.  As  the  mean  of  a  series  of  very  careful  observations  made 
during  balloon  ascents,  a  diminution  of  i°  C.  corresponded  to  an  increase  in 
height  of  232  yards. 

Direction  of  winds.  As  winds  share  the  temperature  of  the  countries 
which  they  have  traversed,  their  direction  exercises  great  influence  on  the 
air  in  any  place.  In  Paris,  the  hottest  winds  are  the  south  ;  then  come  the 
south-east,  the  south-west,  the  west,  the  east,  the  north-west,  north  ;  and 
lastly,  the  north-east,  which  is  the  coldest.  The  character  of  the  wind 
changes  with  the  seasons  :  the  east  wind,  which  is  cold  in  winter,  is  warm  in 
summer. 

Proximity  of  the  sea.  The  neighbourhood  of  the  sea  tends  to  raise  the 
temperature  of  the  air,  and  to  render  it  uniform.  The  average  temperature 
of  the  sea  in  equatorial  and  polar  countries  is  always  higher  than  that  of  the 
atmosphere.  With  reference  to  the  uniformity  of  the  temperature,  it  has 
been  found  that  in  temperate  regions — that  is,  from  25°  to  50°  of  latitude — the 
difference  between  the  highest  and  lowest  temperature  of  a  day  does  not 
exceed,  on  the  sea,  2°  to  3° ;  while  upon  the  continent  this  amounts  to  from 
1 2°  to  1 5°.  In  islands  the  uniformity  of  temperature  is  very  perceptible,  even 
during  the  greatest  heats.  In  continents,  on  the  contrary,  the  winters  for 
the  same  latitudes  become  colder,  and  the  difference  between  the  tempera- 
ture of  summer  and  winter  becomes  greater. 

994.  Gulf  Stream. — A  similar  influence  to  that  of  the  winds  is  exerted 
by  currents  of  warm  water.     To  one  of  these,  the  Gulf  Stream,  the  mildness 
of  he  climate  in  the  north-west  of  Europe  is  mainly  due.     This  great  body  of 
water,  taking  its  origin  in  equatorial  regions,  flows  through  the  Gulf  of  Mexico, 
from  whence  it  derives  its  name  ;  passing  by  the  southern  shores  of  North 
America,  it  makes  its  way  in  a  north-westerly  direction  across  the  Atlantic 
and  finally  washes  the  coast  of  Ireland  and  the  north-west  of  Europe  gene- 
rally.    Its  temperature  in  the  Gulf  is  about  28°  C.  ;  and  it  is  usually  a  little 
more  than  5°  C.  higher  than  the  rest  of  the  ocean  on  which  it  floats,  owing 
to  its  lower  specific  gravity.     To  its  influence  is  due  the  milder  climate  of 
west  Europe  as  compared  with  that  of  the  opposite  coast  of  America  ;  thus 
the  river  Hudson,  in  the  latitude  of  Rome,  is  frozen  over  three  months  in  the 
year.     It  also  causes  the  polar  regions  to  be  separated  from  the  coasts  of 
Europe  by  a  girdle  of  open  sea ;  and  thus  the  harbour  of  Hammerfest  is 
open  the  year  round.     Besides  its  influence  in  thus  moderating  climate,  the 
Gulf  Stream  is  an  important  help  to  navigators. 

995.  Xsottoermal  lines. — When  on  a  map  all  the  points  whose  tempera- 
ture is  known  to  be  the  same  are  joined,  curves  are  obtained  which  Hum- 
boldt  first  noticed,  and  which  he  called  isothermal  lines.     If  the  temperature 
of  a  place  only  varied  with  the  obliquity  of  the  sun's  rays — that  is,  with  the 
latitude — isothermal  lines  would  all  be  parallel  to  the  equator  ;  but  as  the 
temperature  is  influenced  by  many  local  causes,  especially  by  the  height,  the 
isothermal  lines  are  always  more  or  less  curved.     On  the  sea,  however,  they 


-997]  Distribution  of  Temperature  on  the  Surf  ace  of  the  Globe.  925 

are  almost  parallel.  A  distinction  is  made  between  isothermal  lines,  isothcral 
////«\v,and  isochimcnal  lines,  where  the  mean  general,\hz  mean  summer,  and  the 
mean  winter  temperatures  are  respectively  constant.  An  isothermal  zone  is 
the  space  comprised  between  two  isothermal  lines.  Kupffer  also  distinguishes 
isogeothermic  lines  where  the  mean  temperature  of  the  soil  is  constant. 

996.  Climate. — By  the  climate  of  a  place  is  understood  the  whole  of  the 
meteorological  conditions  to  which  a  place  is  subjected  ;  its  mean  annual 
temperature,  summer  and  winter  temperatures,  and  by  the  extremes  within 
which  these  are  comprised.      Some  writers   distinguish   seven   classes   of 
climates,  according  to  their  mean  annual  temperature  :  a  hot  climate  from 
30°  to  25°  C.  ;  a  warm  climate  from  25°  to  20°  C.  ;  a  mild  climate  from  20°  to 
1 5°  C.  ;  a  temperate  climate  from  1 5°  to  10°  C.  ;  a  cold  climate  from  1 1°  to  5° 
C.  ;  a  very  cold  climate  from  5°  to  zero  C.  ;  and  an  arctic  climate  where  the 
temperature  is  below  zero. 

Those  climates,  again,  are  classed  as  constant  climates,  where  the  dif- 
ference between  the  mean  and  summer  and  winter  temperature  does  not 
exceed  6°  to  8° ;  variable  climates,  where  the  difference  amounts  to  from 
1 6°  to  20° ;  and  extreme  climates,  where  the  difference  is  greater  than  30°. 
The  climates  of  Paris  and  London  are  variable  ;  those  of  Pekin  and  New 
York  are  extreme.  Island  climates  are  generally  little  variable,  as  the 
temperature  of  the  sea  is  constant ;  and  hence  the  distinction  between  land 
and  sea  climates.  Marine  climates  are  characterised  by  the  fact  that  the 
difference  between  the  temperature  of  summer  and  winter  is  always  less 
than  in  the  case  of  continental  climates.  But  the  temperature  is  by  no 
means  the  only  character  which  influences  climates  ;  there  are,  in  addition, 
the  moisture  of  the  air,  the  quantity  and  frequency  of  the  rains,  the  number 
of  storms,  the  direction  and  intensity  of  the  winds,  and  the  nature  of  the  soil. 

997.  Distribution  of  temperature  on  tbe  surface  of  the  globe. — The 
temperature  of  the  air  on  the  surface  of  the  globe  decreases  from  the  equator 
to  the  poles  ;  but  it  is  subject  to  perturbing  causes  so  numerous  and  so 
purely  local,  that  its  decrease  cannot  be  expressed  by  any  law.     It  has 
hitherto  not  been  possible  to  do  more  than  obtain  by  numerous  observations 
the  mean  temperature  of  each  place,  or  the  maximum  and  minimum  tempe- 
ratures.    The  following  table  gives  a  general  idea  of  the  distribution  of  heat 
in  the  northern  hemisphere  : — 

Mean  temperature  at  different  latitudes. 

Abyssinia        .         .         .  31-0°  C.  Paris        .         .         .  10-8°  C. 

Calcutta  ....  28-5  Brussels  .         .         .  10-2 

Jamaica  ....  26*1  Strasburg         .  9-8 

Senegal  ....  24-6  Geneva    ...  97 

Rio  de  Janeiro         .         .  23-1  Boston     ...  9-3 

Cairo       .        .         .         .  22-4  London    ...  8-3 

Constantine     .         .  17 '2  Stockholm        .         .  5-5 

Naples    ....  167  Moscow    .         .         .  3-5 

Mexico   ....  16-6  St.  Petersburg .         .  3-5 

Marseilles       .         .         .  14*1  St.  Gothard      .         .  _ro 

Constantinople       .         .  137  Greenland        .         .  -77 

Pekin     ....  127  Melville  Island         .  -187 


926  Meteorology.  [997- 

These  are  mean  temperatures.  The  highest  temperature  which  has  been 
observed  on  the  surface  of  the  globe  is  47*4°  at  Esne,  in  Egypt,  and  the 
lowest  is  -  75°  in  the  Arctic  Expedition  of  1876  ;  which  gives  a  difference 
of  122°  between  the  extreme  temperatures  observed  on  the  surface  of  the 
globe. 

The  highest  temperature  observed  at  Paris  was  38-4°  on  July  8,  1793, 
and  the  lowest  —23-5  on  December  26,  1798.  The  highest  observed  at 
Greenwich  was  35°  C.  in  1808,  and  the  lowest  —20°  C.  in  1838. 

No  arctic  voyagers  have  succeeded  in  reaching  the  poles,  in  consequence 
of  these  seas  being  completely  frozen,  and  hence  the  temperature  is  not 
known.  In  our  hemisphere  the  existence  of  a  single  glacial  pole — that  is,  a 
place  where  there  was  the  maximum  cold — has  been  long  assumed.  But  the 
bendings  which  the  isothermal  lines  present  in  the  northern  hemisphere  have 
shown  that  in  this  hemisphere  there  are  two  cold  poles — one  in  Asia,  to  the 
north  of  Gulf  Taymour  ;  and  the  other  in  America,  north  of  Barrow's  Straits, 
about  1 5°  from  the  earth's  north  pole.  The  mean  temperature  of  the  first  of 
these  poles  has  been  estimated  at  —17°,  and  that  of  the  second  at  —19°. 
With  respect  to  the  austral  hemispheres,  the  observations  are  not  sufficiently 
numerous  to  tell  whether  there  are  one  or  two  poles  of  greatest  cold,  or  to 
determine  their  position. 

998.  Temperature  of  lakes,  seas,  and  spring-s. — In  the  tropics  the 
temperature  of  the  sea  is  generally  the  same  as  that  of  the  air  ;  in  polar 
regions  the  sea  is  always  warmer  than  the  atmosphere. 

The  temperature  of  the  sea  under  the  torrid  zone  is  always  about  26°  to 
27°  at  the  surface  :  it  diminishes  as  the  depth  increases,  and  in  temperate 
as  well  as  in  tropical  regions  the  temperature  of  the  sea  at  great  depths  is 
between  2-5°  and  3-5°.  The  temperature  of  the  lower  layers  is  caused  by 
submarine  currents  which  carry  the  cold  water  of  the  polar  seas  towards  the 
equator. 

The  variations  in  the  temperature  of  lakes  are  more  considerable  ;  their 
surface,  which  becomes  frozen  in  winter,  may  become  heated  to  20°  or  25°  in 
summer.  The  temperature  of  the  bottom,  on  the  contrary,  is  virtually  4°, 
which  is  that  of  the  maximum  density  of  water. 

Springs  which  arise  from  rain  water  which  has  penetrated  into  the  crust 
of  the  globe  to  a  greater  or  less  depth  necessarily  tend  to  assume  the  tempe- 
rature of  the  terrestrial  layers  which  they  traverse.  Hence,  when  they  reach 
the  surface  their  temperature  depends  on  the  depth  which  they  have  attained. 
If  this  depth  is  that  of  the  layer  of  invariable  temperature,  the  springs  have  a 
temperature  of  10°  or  n°  in  this  country,  for  this  is  the  temperature  of  this 
layer,  or  about  the  mean  annual  temperature.  If  the  springs  are  not  very 
copious,  their  temperature  is  raised  in  summer  and  cooled  in  winter,  by  that 
of  the  layers  which  they  traverse  in  passing  from  the  invariable  layer  to  the 
surface.  But  if  they  come  from  below  the  layer  of  invariable  temperature, 
their  temperature  may  considerably  exceed  the  mean  temperature  of  the 
place,  and  they  are  then  called  thermal  springs.  The  following  list  gives 
the  temperature  of  some  of  them  : — 

Wildbad 37'5°C. 

Vichy  ......  40 


-999]  Distribution  of  Land  and  Water.  927 

Bath  ...  46 

Ems  .....  46 

Baden-Baden          ...  67-5 

Chaudes-Aigues     .....  88 

Trincheras ......  67 

Great  Geyser,  in  Iceland,  at  a  depth  of  66  ft.      .  124 

From  their  high  temperature  they  have  the  property  of  dissolving  many 
mineral  substances  which  they  traverse  in  their  passage,  and  hence  form 
mineral  waters.  The  temperature  of  mineral  waters  is  not  modified  in 
general  by  the  abundance  of  rain  or  of  dryness  ;  but  it  is  by  earthquakes, 
after  which  they  have  sometimes  been  found  to  rise  and  at  others  to  sink. 

999.  Distribution  of  land  and  water. — The  distribution  of  water  on  the 
surface  of  the  earth  exercises  great  influence  on  climate.  The  area  covered 
by  \\  ;iter  is  considerably  greater  than  that  of  the  dry  land  ;  and  the  distribu- 
tion is  unequal  in  the  two  hemispheres.  The  entire  surface  of  the  globe 
occupies  about  200  millions  of  square  miles,  nearly  f  of  which  is  covered  by 
water  ;  that  is,  the  extent  of  the  water  is  nearly  three  times  as  great  as  that 
of  the  land.  The  surface  of  the  sea  in  the  southern  hemisphere  is  to  that  in 
the  northern  in  about  the  ratio  of  13  to  9. 

The  depth  of  the  open  sea  is  very  variable  ;  the  lead  generally  reaches 
the  bottom  at  about  300  to  450  yards  ;  in  the  ocean  it  is  often  1,300  yards, 
and  instances  are  known  in  which  a  bottom  has  not  been  reached  at  a  depth 
of  4,500.  It  has  been  computed  that  the  total  mass  of  the  water  does  not 
exceed  that  of  a  liquid  layer  surrounding  the  earth  with  a  depth  of  about 
1,100  yards. 


PROBLEMS    AND    EXAMPLES 
IN    PHYSICS. 


I.  EQUILIBRIUM. 

1.  'A  body  being  placed  successively  in  the  two  pans  of  a  balance,  requires  180 
grammes  to  hold  it  in  equilibrium  in  one  pan,  and  181  grammes  in  the  other;  required 
the  weight  of  the  body  to  a  milligramme. 

From  the  formula  x  =•  *J p  p,  we  have 

x  =   /y/i8o  x  181   =   iSo*1",  499. 

2.  What  resistance  does  a  nut  offer  when  placed  in  a  pair  of  nutcrackers  at  a 
distance  of  f  of  an  inch  from  the  joint,  if  a  pressure  of  5  pounds  applied  at  a  distance 
of  4  inches  from  the  joint  is  just  sufficient  to  crack  it?  Ans.  26%  pounds. 

3.  What  force  is  required  to  raise  a  cask  weighing  6  cwt.  into  a  cart  o'8  metre 
high  along  a  ladder  275  metres  in  length  ?  Ans.  195*  pounds. 

4.  If  a  horse  can  move  30  cwt.  along  a  level  road,  what  can  it  move  along  a  road, 
the  inclination  of  which  is  i  in  80,  the  coefficient  of  friction  on  each  road  being  ^  ? 

Ans.  26§  cwt. 

5.  The  piston  of  a  force-pump  has  a  diameter  of  8  centimetres,  and  the  arms  of 
the  lever  by  which  it  is  worked  are  respectively  12  and  96  centimetres  in  length  ;  what 
force  must  be  exerted  at  the  longer  arm  if  a  pressure  of  12-36  pounds  on  a  square  cen- 
timetre is  to  be  applied?  Ans.  77 -69  pounds. 

II.  GRAVITATION. 

6.  A  stone  is  thrown  from  a  balloon  with  a  velocity  of  50  metres  in  a  second.   How 
soon  will  the  velocity  amount  to  99  metres  in  a  second,  and  through  what  distance 
will  the  stone  have  fallen  ? 

To  find  the  time  requisite  for  the  body  to  have  acquired  the  velocity  of  99  metres  in 
a  second,  we  have 

v=   V  -f  gt  • 

in  which  V  is  the  initial  velocity,  g  the  acceleration  of  gravity  which,  with  sufficient 
approximation,  is  equal  to  9*8  metres  in  a  second,  and  t  the  time.  Substituting  these 
values,  we  have 

/  -  99_-So  =    49    „   -seconds. 

9'8  9*8 

For  the  space  traversed  we  have 

s  =   Vt  +  ±gf*  =  50  x  5  +  4-9  x  25  =372-5  metres. 

7.  A  projectile  was  thrown  vertically  upwards  to  a  height  of  5iom -22.     Disregard- 
ing the  resistance  of  the  air,  what  was  the  initial  velocity  of  the  body  ? 

The  velocity  is  the  same  as  that  which  the  body  would  have  acquired  on  falling 
from  a  height  of  510-22  metres. 

From  the  formula  v  =   \/2  gs  we  get 

v  =   \/2  x  9-8  x  510-22  =   s/ibooo  «   zoo  metres. 

8.  A  stone  is  thrown  vertically  upwards  with  an   initial  velocity  of  100  metres. 
After  what  time  would  it  return  to  its  original  position  ? 


93°  Problems  and  Examples  in  Physics. 

The  time  of  rising  and  falling  is  the  same,  but  the  time  of  falling  is  —  (from  the 

g 

formula  v=gt)  or  —  =io'2,  which  is  half  the  time  required  ;  therefore  /=2o'4  sec. 
9-8 

9.  A  stone  is  thrown  vertically  upwards  with  an  initial  velocity  of  100  metres  ;  after 
x  seconds  a  second  stone  is  thrown  with  the  same  velocity.     The  second  stone  is  rising 
87  seconds  before  it  meets  the  first.     What  interval  separated  the  throws? 

The  rising  stone  will  have  the  velocity  v  =  V  —  gt,  whence  v  =  100  —  9*8  x  87. 
On  the  other  hand,  the  falling  stone,  at  the  moment  the  stones  meet,  will  have  the  velocity 
given  by  the  equation  v  =  gt'  in  which  t'  is  the  time  during  which  the  stone  falls 

before  it  meets  the  second  one.    This  time  is  equal  to  87  seconds  +  x  —  I?°.    Hence 

9'8 
its  velocity  is  / 

.  =  9-8   (87  +  .  -    '-). 

Equating  the  two  values  of  v  and  reducing,  we  obtain  x  =  3  seconds. 

10.  A  body  moving  with  a  uniformly  accelerated  motion  traverses  a  space  of  1000 
metres  in  10  seconds.     What  would  be  the  space  traversed  during  the  eighteenth 
second  if  the  motion  continued  in  the  same  manner  ? 

The  formula  s  =  \  gf*  gives  for  the  accelerating  force  g  =  20  metres  per  second. 
The  space  traversed  during  the  eighteenth  second  will  be  equal  to  the  difference  of 
the  space  traversed  in  18  seconds  and  that  traversed  at  the  end  of  the  seventeenth. 


^ 

11.  A  cannon-ball  has  been  shot  vertically  upwards  with  a  velocity  of  250  metres  in 
a  second.   After  what  interval  of  time  would  its  velocity  have  been  reduced  to  54  metres 
under  the  retarding  influence  of  gravity,  and  what  space  would  have  been  traversed  by 
the  ball  at  the  end  of  this  time  ? 

If  /  be  the  time,  then  at  the  end  of  each  second  the  initial  velocity  would  be  dimi- 
nished by  9ni  '8.     Hence  we  shall  have 

54  =   250  —  t  x  9  '8,  whence  t  =  20  seconds  ; 

and  for  the  space  traversed 

9  '8  x  20* 
—   ^^  ~  ^  —  -  =   3040  metres. 

12.  Required  the  time  in  which  a  body  would  fall  through  a  height  oi  2000  metres. 
neglecting  the  resistance  of  the  air. 

From  s  =  £  gfi  and  substituting  the  values,  we  have 

2000  =  ?—  f2,  whence  /  =   20  '2  seconds. 
2 

13.  A  body  falls  in  air  from  a  height  of  4000  metres.     Required  the  time  of  its  fall 
and  its  velocity  when  it  strikes  the  ground. 

From  the  formula  s  =  £  gt2  we  have  for  the  time  t  =       /  —  ;    and,  on  the  other 


hand,  from  the  formula  for  velocity  v  =  gt  we  have  t  =      =  —  =  20-4. 

cr      ~  -Q 

"Hence  -  =      /  — ,  from  which  v  =   «J  2.  sg,  and  substituting  the  values  for  s  and 

^       V    g 
g,  v  =  280  metres. 

14.  A  stone  is  thrown  into  a  pit  150  metres  deep  and  reaches  the  bottom  in  4 
seconds.     With  what  velocity  was  it  thrown,  and  what  velocity  had  it  acquired  on 
reaching  the  ground  ?    Ans.  The  stone  was  thrown  with  a  velocity  of  17-9,  and  on 
reaching  the  ground  had  acquired  the  velocity  57'!. 

15.  A  stone  is  thrown  downwards  from  a  height  of  150  metres  with  a  velocity  of  10 
metres  per  second.     How  long  will  it  require  to  fall  ? 

The  distance  through  which  the  stone  falls  is  equal  to  the  sum  of  the  distances 


Gravitation.  93  1 

through  which  it  would  fall  in  virtue  of  its  initial  impulse  and  of  that  which  it  would 
traverse  under  the  influence  of  gravity  alone  ;  that  is,  150  =   io/  +  9      -. 
Taking  the  positive  value  only  we  get  /  =  4-61  seconds. 

16.  How  far  will  a  heavy  body  fall  in  vacuo  during  the  time  in  which  its  velocity 
increases  from  40*25  feet  per  second  to  88-55  feet  P61"  second  ? 

A  ns.  Taking  the  value  of  g  at  32*2  feet,  the  body  falls  through  96*6  feet. 

17.  Required  the  time  of  oscillation  of  a  single  pendulum  whose  length  is  0-9938, 
and  in  a  place  where  the  intensity  of  gravity  is  9*81. 

From  the  general  formula  /  =  n      /  -,  in  which  t  expresses  the  time  of  one  oscil- 
lation, /  the  length  of  the  pendulum,  and  g  the  intensity  of  gravity,  we  have 


/  =  3-1416      /°'99384  =    x  secondi 

18.  What  is  the  intensity  of  gravity  in  a  place  in  which  the  length  of  the  seconds 
pendulum  is  o1"-^!  ? 

In  this  case  t  =  n     /      ;  and  also  t  =   n    /      ;  and  therefore          =    -,    frcm 
V   /  V   g' 

which  g'  =  •?-.     Substituting  in  this  latter  equation  the  values  of  g'  ,  I  and  /',  we 

have^'  =  9™  "782. 

19.  In  a  place  at  which  the  length  of  the  seconds  pendulum  is  0-99384,  it  is  required 
to  know  the  length  of  a  pendulum  which  makes  one  oscillation  in  5  seconds. 

In  the  present  case,  as  g  remains  the  same  in  the  general  formula,  and  /  varies,  the 
length  /  must  vary  also.       We  shall  have,  then, 


from  which,  reducing  and  introducing  the  values,  we  have 

r  =  5?  x  0-99384  =  24-846. 

20.  A  pendulum,  the  length  of  which  is  i'D'95,  makes  61,682  oscillations  in  a  day. 
Required  the  length  of  the  seconds  pendulum.  Arts.  0-99385  metres. 

21.  A  pendulum   clock  loses  5  seconds  in  a  day.     By   how  much  must    it   be 
shortened  to  keep  correct  time  ? 

Let  s  =  the  number  of  seconds  in  one  day,  and  /  the  number  indicated  by  the 
clock,  then  s  :  /  =  «  :  ri  =  t'  :  /=  V  I'  '•  \//  .*.  86400  :  86395=  i  :  \/xx.-.  x=  -9998843. 
Hence  1  —  ^  =  0-0001157  A  us. 

22.  What    is   the  normal  acceleration  of  a  body  which  traverses  a  circle  of  4-2 
metres  diameter  with  a  rectangular  velocity  of  3  metres?  Ans.  4*286  metres. 

23.  An  iron  ball  falls  from  a  height  of  68  cm.   on  a  horizontal  iron  plate,   and 
rebounds  to  a  height  of  27  cm.     Required  the  coefficient  of  elasticity  of  the  iron. 

If  an  imperfectly  elastic  ball  with  the  velocity  v  strikes  against  a  plate,  it  rebounds 
\\ith  the  velocity  vt  =   —  k  v,  from  which,  disregarding  the  sign,  k  =  V'.     Now  we 

have   the  velocity  vt  =   ^/z  ght  and  v  =   x/  2^/1,  from  which  k  =  —  '.    Substitut- 

*J  '  h 
ing  the  corresponding  values,  we  get  k  —   0-63. 

24.  Two  inelastic  bodies,  weighing  respectively  100  and  200  pounds,  strike  against 
each  other  with  velocities  of  50  and  20  feet  ;  what  is  their  common  velocity  after  the 
impact.?    Ans.  30,  or  3  -3,  according  as  they  move  in  the  same  or  in  opposite  directions 
betore  impact. 


932  Problems  and  Examples  in  Physics. 


III.     ON  LIQUIDS  AND  GASES. 

25.  The  force  with  which  a  hydraulic  press  is  worked  is  20  pounds  ;  the  arm  of  the 
lever  on  which  this  force  acts  is  5  times  as  long  as  that  of  the  resistance  ;  lastly,  the 
area  of  the  large  piston  is  70  times  that  of  the  smaller  one.     Required  the  pressure 
transmitted  to  the  large  piston. 

If  F  be  the  power,  and  p  the  pressure  transmitted  to  the  smaller  piston,  we  have 
from  the  principle  of  the  lever/  x  i  =  F  x  5.  Moreover,  from  the  principle  of  the 
equality  of  pressure 

P  x  i   =  /  x  70  =  5  x  20  x  70  =  7000  pounds. 

26.  The  force  with  which  a  hydraulic  press  is  worked  being  30  kilos,  and  the  arm 
of  the  lever  by  which  this  force  is  applied  being  10  times  as  long  as  that  of  the  resist- 
ance, and  the  diameter  of  the  small  piston  being  two  centimetres  ;  find  the  diameter  of 
the  large  piston,  in  order  that  a  pressure  of  2000  kilos,  may  be  produced. 

Ans.  5 -164  centimetres. 

27.  One  of  the  limbs  of  a  U-shaped  glass  tube  contains  mercury  to  a  height  of 
°m'I75  I  the  other  contains  a  different  liquid  to  a  height  of  om'42  ;  the  two  columns 
being  in  equilibrium,  required  the  density  of  the  second  liquid  with  reference  to  mer- 
cury and  to  water. 

If  d  is  the  density  of  the  liquid  as  compared  with  mercury  and  d,  the  density  com- 
pared with  water,  then  i  x  0*175  =  0*42  x  d ;  and  13-6  x  0-175  =  0*42  x  dt\ 
whence  d  =  0-416  and  d,  =  5'66. 

28.  What  force  would  be  necessary  to  support  a  cubic  decimetre  of  platinum  in 
mercury  at  zero?     Density  of  mercury  13-6  and  that  of  platinum  21 '5. 

From  the  formula  P  =  VD  the  weight  of  a  cubic  decimetre  of  platinum  is 
i  x  21 '5  =  2ik'5  and  that  of  a  cubic  decimetre  of  mercury  is  i  x  13 '6  =  i3k'6. 
From  the  principle  of  Archimedes,  the  immersed  platinum  loses  part  of  its  weight 
equal  to  that  of  the  mercury  which  it  displaces.  Its  weight  in  the  liquid  is  therefore 
21-5  —  13-6  =•  7-9,  and  this  represents  the  force  required. 

29.  Given  a  body  A  which  weighs  7-55  grammes  in  air,   5 '17  gr.  in  water,   and 
6-35  gr.  in  another  liquid,  B  ;  required  from  these  data  the  density  of  the  body  A  and 
that  of  the  liquid  B. 

The  weight  of  the  body  A  loses  in  water  7*55  —  5^17  =  2-38  grammes  ;  this  repre- 
sents the  weight  of  the  displaced  water.  In  the  liquid  B  it  loses  7 '55  —  6*35  =  i'2  gr. ; 
this  is  the  weight  of  the  same  volume  of  the  body  B,  as  that  of  A  and  of  the  displaced 
water.  The  specific  gravity  of  A  is  therefore 

755  =  3.172>  and  that  of  £  I2°  =  0-504. 
238  238 

30.  A  cube  of  lead,  the  side  of  which  is  4  cm.,  is  to  be  supported  in  water  by 
being  suspended  to  a  sphere  of  cork.    What  must  be  the  diameter  of  the  latter,  the 
specific  gravity  of  cork  being  0*24,  and  that  of  lead  n'35  ? 

The  volume  of  the  lead  is  64  cubic  centimetres  ;  its  weight  in  air  is  therefore 
64  x  1 1 '35,  and  its  weight  in  water  64  x  11-35  —  64  =  662-4  gr. 

If  r  be  the  radius  of  the  sphere  in  centimetres,  its  volume  in  cubic  centimetres  will 

be  4  ir_?Lf  and  its  weight  in  grammes  is  ^  ff       x  °  2^.     Now,  as  the  weight  of  the 

3  3 

displaced  water  is  obviously  -  w  r5  in  grammes,  there  will  be  an  upward  buoyancy 

represented  by  4  »  ?  1  4  «  r8  x  0^4  =  4 -^  x  076  wh-ch  must  be  equal  to  the 

weight  of  the  lead  ;  that  is,  4—  -—     °  ?6  =  662-5,  from  which  r  =  5cm'925  and  ,the 
diameter  =    n'8^. 


On  Liquids  and  Gases.  933 

31.  A  cylindrical  steel  magnet  15  cm.  in  length  and  1*2  mm.  in  diameter,  is  loaded 
at  one  end  with  a  cylinder  of  platinum  of  the  same  diameter  and  of  such  a  length  that 
\\hen  the  solid  thus  formed  is  in  mercury,  the  free  end  of  the  steel  projects  10  mm. 
above  the  surface.      Required  the  length  of  this  platinum,  specific  gravity  of  steel 
being  7 '8  and  of  platinum  21-5. 

The  weight  of  the  steel  in  grammes  will  be  15  *  rz  x  7*8  and  of  the  platinum 
A  r*  x  21-5. 

These  are  together  equal  to  the  weight  of  the  displaced  mercury,  which  is 

w  r-  (14  +  x)  1 3 '6,  from  which  x  =  9*29  cm. 

32.  A  cylindrical  silver  wire  om*ooi5  in  diameter  weighs  3*2875  grammes  ;  it  is  to 
be  covered  with  a  layer  of  gold  ora*ooo2  in  thickness.  Required  the  weight  of  the  gold  ; 
the  specific  gravity  of  silver  being  10*47  and  that  of  gold  19*26. 

If  r  is  the  radius  of-  the  silver  wire  and  R  its  radius  wfien  covered  with  gold,  then 
r  =  oc'O75  and  R  =  cfog^.  The  volume  of  the  silver  wire  will  be  T  r'- 1  and  its 
\\vight  n-  r2  /  io'47,  from  which  /  =  1^-768. 

The  volume  of  the  layer  of  gold  is 

*  (R*  -  r*)  17768, 
and  its  weight 

IT  (o*0952  —  o'0757)  x  17768  x  19*26  =  3*656  nearly. 

33.  A  kilogramme  of  copper  is  to  be  drawn  into  wire  having  a  diameter  of  0*16 
centimetre.     What  length  will  it  yield  ?    Specific  gravity  of  copper  8*88. 

The  wire  produced  represents  a  cylinder  /  cm.  in  length,  the  weight  of  which  is 
«•  /•-  /8'88,  and  this  is  equal  to  1000  grammes.  Hence  /  =  56m*oo85. 

3i.  The  specific  gravity  of  cast  copper  being  8*79,  and  that  of  copper  wire  being 
8  88,  what  change  of  volume  does  a  kilogramme  of  cast  copper  undergo  in  being 

drawn  into  wire?  Ans. 

86617 

35.  Determine  the  volumes  of  two  liquids,  the  densities  of  which  are  respectively 
I -3  and  07,  and  which  produce  a  mixture  of  three  volumes  having  the  density  0*9. 

If  x  and  y  be  the  volumes,  then  from  P  =  VD,  1*3*  +  077  =  3  x  0*9  and 
x  +  y  =  3,  from  which  .r  =  i  and  y  =  2. 

36.  The  specific  gravity  of  zinc  being  7  and  that  of  copper  9,  what  weight  of  each 
metal  must  be  taken  to  form  50  grammes  of  an  alloy  having  the  specific  gravity  8  2,  it 
being  assumed  that  the  volume  of  the  alloy  is  exactly  the  sum  of  the  alloyed  metals  ? 

Let  x  =  the  weight  of  the  zinc,  and  y  that  of  the  copper,  then  x  +  y  =  50,  and 

7} 

from  the  formula  P  =   VD,  which  gives  V  =      ,  the  volumes  of  the  two  metals  and  of 

the  alloy  are  respectively  X-  +  ^  =  ^°  .     From  these  two  equations  we  get  x  =   17*07 
andjy  =  32*93. 

37.  A  platinum  sphere  3  cm.  in  diameter  is  suspended  to  the  beam  of  a  very  ac- 
curate balance,  and  is  completely  immersed  in  mercury.    It  is  exactly  counterbalanced 
by  a  copper  cylinder  of  the  same  diameter  completely  immersed  in  water.     Required 
the  height  of  the  cylinder.      Specific  gravity  of  mercury  13*6,   of  copper  8*8,  and  of 
platinum  21*5.  Ans.  2*025  centimetres. 

38.  To  balance  an  ingot  of  platinum  27  grammes  of  brass  are  placed  in  the  other 
pan  of  the  balance.     What  weight  would  have  been  necessary  if  the  weighing  had  been 
effected  in  vacuo?    The  density  of  platinum  is  21*5,  that  of  brass  8*3,  and  air  under 

a  pressure  of  760  mm.  and  at  the  temperature  o°  has  —  the  density  of  water. 

770 

The  weight  of  brass  in  air  is  not  27  grammes,  but  this  weight  minus  the  weight  of 
a  volume  of  air  equal  to  its  own. 

Since  P  =    VD  .• .  V  =        and  the  weight  of  the  air  is P         =          2? 

D  D  x  770         8-3  x  770' 

By  similar  considerations,  if  x  is  the  weight  of  platinum  in  vacuo,  its  weight  in  air 


934  Problems  and  Examples  in  Physics. 

will  be  x  minus  the  weight  of  air  displaced,  that  is  x  —  and  this  weight 

21-5  x  770' 

is  equal  to  that  of  the  true  weight  of  the  brass  ;  and  we  have 

=  27  — ;  from  which  x  =  26  '996. 


21-5  x  770  8-3  x  770 

39.  A  body  loses  in  carbonic  acid  1*15  gr.  of  its  weight.     What  would  be  its  loss 
of  weight  in  air  and  in  hydrogen  respectively? 

Since  a  litre  of  air  at  o°  and  760  mm.  weighs  i  293  gramme,  the  same  volume  of 
carbonic  acid  weighs  1*293  x  1*524  =  1*97  gramme.  We  shall,  therefore,  obtain  the 
volume  of  carbonic  acid  corresponding  to  1*15  gr.  by  dividing  this  number  by  1-97, 
which  gives  0*5837  litre.  This  being  then  the  volume  of  the  body,  it  displaces  that 
volume  of  air,  and  therefore  its  loss  of  weight  in  air  is  0*5837  x  1*293  =  °7547  grammes, 
and  in  hydrogen  0*5837  x  1-293  x  0-069  =  0-052076. 

40.  Calculate  the  ascensional  force  of  a  spherical  balloon  of  oiled  silk  which,  when 
empty,  weighs  62*5  kilos,  and  which  is  filled  with  impure  hydrogen,  the  density  of 

which  is    -  that  of  air.     The  oiled  silk  weighs  0*250  kilo,  the  square  metre. 
13 

The  surface  of  the  balloon  is  5  _  250  square  metres.  This  surface  being  that  of 

0*25 

a  sphere,  is  equal  104*-  R~,  whence  4  n-^3  =  250  and  R  =  4*459  ;  therefore  V  —  4-7r-_ 

=  371*52  cubic  metres. 

The  weight  of  air  displaced  is  371*52  x  1*293  kilo  =  480*375  kilos  ;  the  weight  of 
the  hydrogen  is  36*88  kilos,  and  therefore  the  ascensional  force  is 

480*375  -  (36-88  +  62<5)   =  38°'995- 

41.  A  balloon  4  metres  in  diameter  is  made  of  the  same  material  and  filled  with 
the  same, hydrogen  as  above.     How  much  hydrogen  is  required  to  fill  it,  and  what 
weight  can  it  support? 

The  volume       ^  n  Rz  =  33*51  cubic  metres,  and  the  surface  4  *  R'2  =  50*265  square 

metres.  The  weight  of  the  air  displaced  is  33*51  x  1*293  =  43*328  kilos,  and  that  of 
the  hydrogen  is  from  the  above  data  3*333  kilos,  while  the  weight  of  the  material  is  12*566 
kilos.  Hence  the  weight  which  the  balloon  can  support  is 

43*328  -  (12*566  +  3*333)   =  27*429  kil. 

42.  Under  the  receiver  of  an  air-pump  is  placed  a  balance,  to  which  are  suspended 
two  cubes;  one  of  these  is  3  centimetres  in  the  side, and  weighs  26'324gr.  ;  and  the  other 
is  5  centimetres  in  the  side,  and  weighs  26*2597  grammes.     When  a  partial  vacuum  is 
made  these  cubes  just  balance  each  other.     What  is  the  pressure?         Ans.  om*374. 

43.  A  soap  bubble  8  centimetres  in  diameter  was  filled  with  a  mixture  of  one 
volume  of  hydrogen  gas  and  15  volumes  air.     The  bubble  just  floated  in  the  air ;  re- 
quired the  thickness  of  the  film. 

The  weight  of  the  volume  of  air  displaced  is  ^  «•  r5  x  0*001293  gramme,  and  that 

of  the'  mixture  of  gases    4  »  r5  x  0*001293  x   *-$ ?_°_93  .  an(j   tne  difference    of 

3  16 

these  will  equal  the  weight  of  the  soap  bubble. 

This  weight  is  that  of  a  spherical  shell,  which,  since  its  thickness  /  is  very 
small,  is  with  sufficient  accuracy  4  n  r2 1  s  in  grammes,  where  s  is  the  specific  gravity 
==i*t.  Hence 


4  TT  r5  (  '001293  —  '001293  x    I^0  93s)    _  4  n  ri  t  j.j 
3  \  io     / 

Dividing  each  side  by  4  «•  r-,  and  putting  r  =  4,  we  get 
4  x   -001293  (  i  -  I5- 


On  Liquids  and  Gases.  935 

•001293  x  '9W  =  3-3  /  : 
whence/  =    '000091166290111. 

44.  In  a  vessel  whose  capacity  is  3  litres,  there  are  introduced  2  litres  of  hydrogen 
under  the  pressure  of  5  atmospheres  ;  3  litres  of  nitrogen  under  the  pressure  of  half  an 
atmosphere,  and  4  litres  of  carbonic  acid  under  the  pressure  of  4  atmospheres.     What  is 
the  final  pressure  of  the  gas,  the  temperature  being  supposed  constant  during  the 
experiment  ? 

The  pressure  of  the  hydrogen,  from  Dalton's  law,  will  be  —  i-^,  that  of  the  nitro- 
gen will  remain  unchanged,  and  that  of  the  carbonic  acid  will  be  — — — .  Hence  the 
total  pressure  will  be 

—  +  -  +   —   =  9^  atmospheres. 
323 

45.  A  vessel  containing  10  litres  of  water  is  first  exposed  in  contact  with  oxygen 
under  a  pressure  of  78  cm.  until  the  water  is  completely  saturated.     It  is  then  placed 
in  a  confined  space  containing  100  litres  of  carbonic  acid  under  a  pressure  of  72  cm. 
Required  the  volumes  of  the  two  gases  when  equilibrium  is  established.    The  coeffi- 
cient of  absorption  of  oxygen  is  0*042,  and  that  of  carbonic  acid  unity. 

The  volume  of  oxygen  dissolved  is  0-42.  Being  placed  in  carbonic  acid  it  will 
act  as  if  it  alone  occupied  the  space  of  the  carbonic  acid,  and  its  pressure  will  be 

78   x     °  *2     =  ©'326  cm. 

IOO-42 

Similarly  the  10  litres  of  water  will  dissolve  10  litres  of  carbonic  acid  gas,  the  total 
volume  of  which  w'll  be  no,  of  which  100  are  in  the  gaseous  state  and  10  are  dissolved. 
Its  pressure  is  therefore  72  x  KO  =  65-454  cm. 

Hence  the  total  pressure  when  equilibrium  is  established  is 

0^326  +  65-454  =  65-78  cm.  ; 
and  the  volume  of  the  oxygen  dissolved  reduced  to  the  pressure  6578  is 

ollt>42  x  —         =  ollt '00208,  and  that  of  the  carbonic  acid  10  x     ^  ^^  =  9-95. 

46.  In  a  barometer  which  is  immersed  in  a  deep  bath  the  mercury  stands  743 
mm.  above  the  level  of  the  bath.     The  tube  is  lowered  until  the  barometric  space, 
which  contains  air,  is  reduced  to  one-third,  and  the  mercury  is  then  at  a  height  of  701 
mm.    Required  the  atmospheric  pressure  at  the  time  of  observation.    Ans.  =  764mm. 

47.  What  is  the  pressure  on  the  piston  of  a  steam  boiler  of  8  decimetres  diameter 
if  the  pressure  in  the  boiler  is  3  atmospheres  ?  Ans.  ^0385.85  kilos. 

48.  What  is  the  pressure  of  the  atmosphere  at  that  height  at  which  an  ascent  of  21 
metres  corresponds  to  a  diminution  of  imnj  in  the  barometric  height?  Ans.  378'9mm. 

49.  What  would  be  the  height  of  the  atmosphere  if  its  density  were  everywhere 
uniform?  Ans.  7954-1  metres,  or  nearly  5  miles. 

50.  How  high  must  we  ascend  at  the  sea  level  to  produce  a  depression  of  i  mm. 
in  the  height  of  the  barometer? 

Ans.  Taking  mercury  as  10,500  times  as  heavy  as  air,  the  height  will  be  10-5  metres. 

51.  Mercury  is  poured  into  a  barometer  tube  so  that  it  contains  15  cc.  of  air  under 
the  ordinary  atmospheric  pressure.     The  tube  is  then  inverted  in  a  mercury  bath  and 
the  air  then  occupies  a  space  of  25  cc.  ;  the  mercury  occupying  a  height  of  302  mm. 
What  is  the  pressure  of  the  atmosphere  ? 

Let  x  be  the  amount  of  this  pressure,  the  air  in  the  upper  part  of  the  tube  will  have 
a  pressure  represented  by  i^fi,  and  this,  together  with  the  height  of  the  mercurial 
column  302,  will  be  the  pressure  exerted  in  the  interior  of  the  tube  on  the  level  of  the 


Problems  and  Examples  in  Physics. 


mercury  in  the  bath,  which  is  equal  to  the.  atmospheric  pressure  ;  that  is  T~  *   +  302 

=  x,  from  which  x  =  755  mm. 

•  52.  What  effort  is  necessary  to  support  a  cylindrical  bell-jar  full  of  mercury 
immersed  in  mercury  ;  its  internal  diameter  being  6  centimetres,  its  height  ob  above 
the  surface  of  the  mercury  (fig.  i)  18  centimetres,  and  the  pressure  of  the  atmosphere 
077  centimetre? 

The  bell-jar  supports  on  the  outside  a  pressure  equal  to  that  of  a  column  of  mercury 
the  section  of  whose  base  is  cd,  and  the  height  that  of  the  barometer.     This  pressure  is 

equal  to 

ir  R-  x  077  x  13 '6. 

The  pressure  on  the  inside  is  that  of  the  atmosphere  less  the  weight  of  a  column 
of  mercury  whose  base  is  cd  and  height  ob.  This  is  equal  ton-  J?1*  x  (077  — o'i8)  x  13-6; 
and  the  effort  necessary  is  the  difference  of  these  two  pres- 
sures. Making  R  =  3  cm.,  this  is  found  to  be  69-216  kilo- 
grammes. 

53.  A  barometer  is  placed  within  a  tube  which  is  after- 
wards hermetically  closed.  At  the  moment  of  closing,  the 
temperature  is  15°  and  the  pressure  750  mm.  The  ex- 
ternal space  is  then  heated  to  30°.  What  will  be  the  height 
of  the  barometer  ? 

The  effect  of  the  increase  of  temperature  would  be  to 

raise  the  mercury  in  the  tube  in  the  ratio  i 


+     -3° 
5550 


to  i  + 


5550 


,  and  the  height  h  would  therefore  be 


75 


3°: 
5550, 


5550 

and   since  in  the  closed  space,   the  elastic  force  of  the  air  increases  in  the  ratio 
i  +   30  a  :  i    +   15  a  we  shall  have  finally  h  =   301*74  mm. 

54.  The  heights  of  two  barometers  A  and  B  have  been  observed  at  —  10°  and 
+  15°,  respectively,  to  be  A   =  737  and  B  =  763.     Required  their  corrected  heights 
at  o°.  Ans.  A    =   738-33.     B  =  760-94. 

55.  A  voltaic  current  gives  in  an  hour  840  cubic  centimetres  of  detonating  gas 
under  a  pressure  of  760  and  at  the  temperature  12° -5  ;  a  second  voltaic  current  gives 
in  the  same  time  960  cubic  centimetres  under  a  pressure  of  755  and  at  the  temperature 
T5°'S-     Compare  the  quantities  of  gas  given  by  the  two  currents.     Ans.  i  :  1-129. 

56.  The  volume  of  air  in  the  pressure  gauge  of  an 
apparatus  for  com  pressing  gases  is  equal  to  152  parts. 
By  the  working  of  the  machine  this   is  reduced   to 
7  parts,    and   the  mercury  is  raised   through   0-48 
metre.     What  is  the  pressure  of  the  gas  ? 

Here  AB  =  152,  AC  =  37 parts,  and  BC  =  om-48. 
The  pressure  of  air  therefore  in  AC  is,  from  Boyle's 
law, 

37 
The  pressure  in  the  receiver  is  therefore 

3-122  +  0-48  =  3m'6o2, 
which  is  equal  to  474  atmospheres. 

57.  An  air-tight  bladder    holding    two  litres  of 
air  at    the   standard  pressure    and   temperature  is 
immersed  in  sea  water  to   a  depth  of   100   metres 
where  the  temperature  is  4°.     Required  the  volume 

Fig.  2.          •  of  the  gas. 


Air  pump.  937 

The  specific  gravity  of  sea  water  being  1-026,  the  depth  of  100  metres  will  repre- 
sent a  column  of  pure  water  102 '6  metres  in  height.  As  the  pressure  of  an  atmo- 
sphere is  equal  to  a  pressure  of  10*33  metres  of  pure  water,  the  pressure  of  this  column 

=   I02:6!  =  9-94  atm. 

10-33 
Hence,  adding  the  atmospheric  pressure,  the  bladder  is  now  under  a  pressure  of  10-94 

atmospheres,  and  its  volume  being  inversely  as  the  pressure  will  be  +-'-        =  0-183  litre, 

if  the  temperature  be  unaltered.    But  the  temperature  is  increased  by  4°,  and  therefore 
the  volume  is  increased  in  the  ratio  277  to  273,  and  becomes 

0*183  x  277  =  0-18568  litre. 

58.  To  what  height  will  water  be  raised  in  the  tube  of  a  pump  by  the  first  stroke  of  the 
piston,  the  length  of  stroke  of  which  is  0-5111. ,  the  height  of  the  tube  6  metres,  and  its  section 
rxo  that  of  the  piston  ?    At  starting  the  air  in  the  tube  is  under  a  pressure  of  10  metres. 

If  we  take  the  section  of  the  tube  as  unity,  that  of  the  body  of  the  pump  is  10  ;  and 
the  volumes  of  the  tube  and  of  the  body  of  the  pump  are  in  the  ratio  of  6  to  5.  Then 
if  x  is  the  height  to  which  the  water  is  raised  in  the  pipe,  the  volumes  of  air  in  the 
pump  before  and  after  the  working  of  the  pump  are  6  at  the  pressure  10,  and  5  +  6  -  x 
at  the  pressure  10  —  x. 

Forming  an  equation  from  these  terms,  and  solving,  we  have  two  values,  x'  =  i8m  26 
and  x"  =  274.  The  first  of  these  must  be  rejected  as  being  physically  impossible  ; 
and  the  true  height  is  x  =  2*75  metres. 

59.  A  receiver  with  a  capacity  of  10  litres  contains  air  under  the  pressure  76  cm. 
It  is  closed  by  a  valve,  the  section  of  which  is  32  square  centimetres,  and  is  weighted 
with  25  kilogrammes.     The  temperature  of  the  air  is  30°  ;  its  density  at  o°  and  76  cm. 

pressure  is  -i-  that  of  water.     The  coefficient  of  the  expansion  of  gases  is  0-00366. 

Required  the  weight  of  air  which  must  be  admitted  to  raise  the  valve. 

The  air  already  present  need  not  be  taken  into  account  as  it  is  under  the  pressure 
of  the  atmosphere.  Let  x  be  the  pressure  in  centimetres  of  mercury  of  that  which  is 
admitted,  x  *  I3_  will  represent  in  kilogrammes  its  pressure  on  a  square  centi- 

IOOO 

metre  ;  and  therefore  the  internal  pressure  on  the  valve,  and  which  is  equal  to  the  ex- 
ternal pressure  of  25  kilogrammes,  is  x  x         '  ^-2?  =  25  k.    From  which  x  =  57-44. 

IOOO 

For  the  weight  we  shall  have 

p  _       10  x  0-001293      x  57-44  =  8-8055  grammes, 
i  +  0-00366  x  30       76*00 

60.  A  bell-jar  contains  3-17  litres  of  air  ;  a  pressure  gauge  connected  with  it  marks 
zero  when  in  contact  with  the  air  (fig.  3).     The  jar  is 

closed  and  the  machine  worked  ;  the  mercury  rises 
to  65  cm.  A  second  barometer  stands  at  76  cm. 
during  the  experiment.  Required  the  weight  of  air 
withdrawn  from  the  bell-jar  and  the  weight  of  that 
which  remains. 

At  o°  and  76  cm.  the  weight  of  air  in  the  bell-jar  is 
1-293  x  3-I7  =  4'0988i. 

At  o°  and  under  the  pressure  76  —  65  the  weight 
of  the  residual  air  is 

IH^JL".  0-393..  • 

and  therefore  the  weight  of  that  which  is  withdrawn  is 

4-0988  -  0-5932  =  3-5056  gr.  

61.  The  capacity  of  the  receiver  of  an  air-pump 


938  Problems  and  Examples  in  Physics. 

is  7 '53  I  it  is  ^u^  °f  air  under  the  ordinary  atmospheric  pressure  and  at  o°.  Re- 
quired the  weight  of  air  when  the  pressure  is  reduced  to  o'2i  ;  the  weight  with- 
drawn by  the  piston  ;  and  the  weight  which  would  be  left  at  15°. 

The  weight  of  7*53  litres  of  air  under  the  ordinary  conditions  is  9736  grammes. 

Under  a  pressure  of  o'2i  it  will  be  2*69  grammes,  and  at  the  temperature  15°  it  will 

be £5£ „  =  0-255  gramme. 

i  +  ©'00366  x  i 5 

62.  In  a  theoretically  perfect  air-pump,  how  great  is  the  rarefaction  after  10  strokes, 
if  the  volumes  of  the  barrel  and  the  receiver  are  respectively  2  and  3  ? 

Ans.   =  4'59mm  ;  or  about    x    of  an  atmosphere. 
1 66 

63.  What  must  be  the  capacity  of  the  barrel  of  an  air-pump  if  the  air  in  a  re- 
ceiver of  4  litres  is  to  be  reduced  to  J  the  density  in  two  strokes  ?  Ans.  2-9. 

64.  The  reservoir  of  an  air-gun,  the  capacity  of  which  is  40  cubic  inches,  contains 
air  whose  density  is  8  times  that  of  the  mean  atmospheric  pressure.     A  shot  is  fired 
when  the  atmospheric  pressure  is  741  mm.  and  the  gas  which  escapes  occupies  a  volume  of 
80  cubic  inches.  What  is  the  elastic  force  of  the  residual  air?  Ans.  6 '05 atmospheres. 

65.  Suppose  that  at  the  limit  of  the  atmosphere  the  pressure  of  the  attenuated 

air  is  the      I      of  a  millimetre  of  mercury  and  the  temperature  —  135°,  and  that  in  a 

1000 

place  at  the  sea  level,  in  latitude  45°,  the  pressure  of  the  atmosphere  is  76omm  and  its 
temperature  15°  C.  Determine  from  these  data  the  height  of  the  atmosphere. 

From  the  formula  18400  {  i  +  o'oo2  { T  +  /}  j-  log  --,  we  get  for  the  height  in  metres 
82237,  which  is  equal  to  51 'i  miles. 

66.  If  water  is  continually  flowing  through  an  aperture  of  3  square  inches  with  a 
velocity  of  10  feet,  how  many  cubic  feet  will  flow  out  in  an  hour  ?  Ans.  750  cubic  feet. 

67.  With  what  velocity  does  water  issue  from  an  aperture  of  3  square  inches,  if 
37'5  cubic  feet  flow  out  every  minute?  Ans.  30  feet. 

68.  What  is  the  ratio  of  the  pressure  in  the  above  two  cases?  Ans.  i  :  9. 

69.  What  is  the  theoretical  velocity  of  water  from  an  aperture  which  is  9  feet 
below,  the  surface  of  water  ?  Ans.  24  feet. 

70.  In  a  cylinder,  water  stands  2  feet  above  the  aperture  and  is  loaded  by  a  piston 
which  presses  with  a  force  of  6  pounds  on  the  square  inch.     Required  the  velocity  of 
the  effluent  water.  Ans.  32  feet. 

71.  How  deep  must  the  aperture  of  the  longer  leg  of  a  syphon,  which  has  a  sec- 
tion of  4  square  centimetres,  be  below  the  surface  of  the  water  in  order  that  25  litres 
may  flow  out  in  a  minute?  Ans.  5-535  cm. 

72.  Through  a  circular  aperture  having  an  area  of  ©'196  square  cm.  in  the  bottom 
of  a  reservoir  of  water  which  was  kept  at  a  constant  level,  55  cm.  above  the  bottom, 
it  was  found  that  98-5  grammes  of  water  flowed  in  22  seconds.     Required  the  coeffi- 
cient of  efflux. 

Since  the  velocity  of  efflux  through  an  aperture  in  the  bottom  of  a  vessel  is  given  by 
the  formula  v  =  Sigh,  it  will  readily  be  seen  that  the  weight  in  grammes  of  water 
which  flows  in  a  given  time,  t,  will  be  given  by  the  formula  w  =  a  a  t\/  zgh,  where  a  is 
the  area  in  square  centimetres,  o  the  coefficient  of  efflux,  t  the  time  in  seconds,  and  h 
the  height  in  centimetres.  Hence  in  this  case  a  =  0*699. 

73.  Similarly  through  a  square  aperture,  the  area  of  which  was  almost  exactly  the 
same  as  the  above,  and  at  the  same  depth,  104-4  grammes  flowed  out  in  21 '6  seconds. 
In  this  case  a  =  0-78. 


Sound.  939 


IV.    ON  SOUND. 

74.  A  stone  is  dropped  into  a  well,   and  4  seconds  afterwards  the  report  of  its 
striking  the  water  is  heard.     Required  the  depth,  knowing  that  the  temperature  of  the 
air  in  the  pit  was  io°'74. 

From  the  formula  v  =  333  \f  \  +  at  we  get  for  the  velocity  of  sound  at  the  tem- 
perature in  question  339 '05  metres. 

Let  /  be  the  time  which  the  stone  occupies  in  falling ;  then  \gfl  =  x  will  represent 
the  depth  of  the  well ;  on  the  other  hand,  the  time  occupied  by  the  report  will  be  4  —  /, 
and  the  distance  will  be  (4  —  t]  v  =  x  (i)  ;  thus  (4  —  t)  v  =  \gfl  (ii),  from  which, 
substituting  the  values, 

(4  -  t}  339-5  =  4-9  fl 

1   ~  3793  seconds,  and  substituting  this  value  in  either  of  the  equations  (i)  or  (ii), 
we  have  the  depth  =  72-6  metres  nearly. 

75.  A  bullet  is  fired  from  a  rifle  with  a  velocity  of  414  metres,  and  is  heard  to  strike 
a  target  4  seconds  afterwards.     Required  the  distance  of  the  target  from  the  marks- 
man, the  temperature  being  assumed  to  be  zero. 

_*    +     *    =  4;  x  =  738-2. 
4H       333 

76.  At  what  distance  is  an  observer  from  an  echo  which  repeats  a  sound  after  3 
seconds,  the  temperature  of  the  air  being  io°? 

In  these  3  seconds  the  sound  traverses  a  distance  of  3  x  339  =  1017  metres  ;  this 
distance  is  twice  that  between  the  observer  and  the  reflecting  surface  ;  hence  the  dis- 
tance is 

™*7-  =  5o8.5  metres. 

77.  Between  a  flash  of  lightning  and  the  moment   at  which   the  corresponding 
thunder  is  first  heard,  the  interval  is  the  same  as  that  between  two  beats  of  the  pulse. 
Knowing  that  the  pulse  makes  80  beats  in  a  minute,  and  assuming  the  temperature 
of  the  air  to  be  15°  C.,  what  is  the  distance  of  the  discharge?       Ans.  454*1  metres. 

78.  A  stone  is  thrown  into  a  well  with  a  velocity  of  12  metres,  and  is  heard  to 
strike  the  water  4  seconds  afterwards.  Required  the  depth  of  the  well. 

Ans.     About  no  metres. 

79.  What  is  the  velocity  of  sound  in  coal  gas  at  o°,  the  density  being  0-5  ? 

Ans.  470-9  metres. 

80.  What  must  be  the  temperature  of  air  in  order  that  sound  may  travel  in 

the  same  velocity  as  in  hydrogen  at  o°  ?  Ans.  About  3680°  C. 

81.  What  must  be  the  temperature  of  air  in  order  that  the  velocity  of  sound  may 
be  the  same  as  in  carbonic  acid  at  o°  ?  Ans.  —  io5°5  C. 

82.  Kendall,  in  a  North  Pole  Expedition,  found  the  velocity  of  sound  at  —40° 
was  314  m.     How  closely  does  this  agree  with  that  calculated  from  the  value  we  have 
assumed  for  o°  ?  Ans.  6-64  metres  too  much. 

83.  The  report  of  a  cannon  is  heard  15  seconds  after  the  flash  is  seen.     Required 
the  distance  of  the  cannon,  the  temperature  of  the  air  being  22°. 

From  the  formula  for  the  velocity  of  sound  we  have 

X5  x  333  -s/i  +  0*003665  x  22  =  5190  metres. 

84.  If  a  bell  is  struck  immediately  at  the  level  of  the  sea,  and  its  sound,  reflected 
from  the  bottom,  is  heard  3  seconds  after,  what  is  the  depth  of  the  sea  ? 

Ans.  7140  feet. 
S  S  2 


940  Problems  and  Examples  in  Physics. 

85.  A  person  stands  150  feet  on  one  side  of  the  line  of  fire  of  a  rifle  range  450  feet 
in  length  and  at  right  angles  to  a  point  150  feet  in  front  of  the  target.     What  is  the 

velocity  of  the  bullet  if  the  person  hears  it  strike  the  target  -  of  a  second  later  than 

the  report  of  the  gun?    The  temperature  is  assumed  to  be  i6°'5.       Ans.  2038  feet. 

86.  An  echo  repeats  five  syllables,  each  of  which  requires  a  quarter  of  a  second  to 
pronounce,  and  half  a  second  elapses  between  the  time  the  last  syllable  is  heard  and 
the  first  syllable  is  repeated.     What  is  the  distance  of  the  echo,  the  temperature  of 
the  air  being  10°  C.  ?  Ans.  297-47  metres. 

87.  The  note  given  by  a  silver  wire  a  millimetre  in  diameter  and  a  metre  in 
length  being  the  middle  C,  what  is  the  tension  of  the  wire?     Density  of  silver  10-47. 

Ans.  22-67  kilogrammes. 

88.  The  density  of  iron  being  7*8  and  that  of  copper  8  -8,   what  must  be  the 
thickness  of  wires  of  these  materials,  of  the  same  length  and  equally  stretched,  so  that 
they  may  give  the  same  note  ? 

From  the  formula  for  the  transverse  vibration  of  strings  we  have  for  the  number  of 

vibrations  n  —  --      /  --     As  in  the  present  case,  the  tensions,  the  length  of  the 
strings,  and  the  number  of  vibrations  are  the  same,  we  have 

1      fL.  =  -1     /Z",  from  which  Z      A  =    *     /7  ; 
rl  V    ir  d        r,l  V    *  d,  r  V    d        rt  V    dt 

**         d'j 

d         7-8 


.whence     -   =         =         ;  hence  r  =       /8^   =   1-062. 

r,        \/  7-8 


89.  A  wire  stretched  by  a  weight  of  13  kilos,  sounds  a  certain  note.     What  must 
be  the  stretching  weight  to  produce  the  major  third  ? 

The  major  third  having  5  the  number  of  vibrations  of  the  fundamental  note,  and  as, 

all  other  things  being  the  same,  the  numbers  of  vibrations  are  directly  as  the  square 
roots  of  the  stretching  weight,  we  shall  have  x  =  20-312  kilos. 

"9O.  The  diameters  of  two  wires  of  the  same  length  and  material  are  0-0015  and 
0-0038™.  ;-  and  their  stretching  weights  400  and  1600  grammes  respectively.  Required 
the  ratio  of  the  numbers  of  their  vibrations.  Ans.  n  :  n,  =  1-266  :  i. 

91.  A  brass  wire  i  metre  in  length  stretched  by  a  weight  of  2  kilogrammes,  and  a 
silver  wire  of  the  same  diameter,  but  3-165  metres  in  length,  give  the  same  number  of 
vibrations.     What  is  the  stretching  weight  in  the  latter  case? 

Since  the  number  of  vibrations  is  equal,  we  shall  have 

£       //»      ..      I        /-*V 

rl\/  ntt        rl,  V    n  d/ 
from  which,  replacing  the  numbers,  we  get  x  =  25  kilos. 

92.  A  brass  and  a  silver  wire  of  the  same  diameter  are  stretched  by  the  weights  of  2 
and  25  kilogrammes  respectively,  and  produce  the  same  note.  What  are  their  lengths, 
knowing.that  the  density  of  brass  is  8-39,  and  of  silver  10*47? 

ANS.  The  length  of  the  silver  wire  is  3-16  times  that  of  the  brass. 

93.  A  copper  wire  1-25  mm.   in  diameter  and  a  platinum  one  of  0-75  mm.  are 
stretched  by  equal  weights.     What  is  the  ratio  of  their  lengths,  if,  when  the  copper 
wire  gives  the  note  C  the  platinum  gives  F  on  the  diatonic  scale? 

Ans-.  The  length  of  the  copper  is  to  the  length  of  the  platinum   =   1-264  :  I- 

94.  An  organ  pipe  gives  the  note  C  at  a  temperature  o°  ;  at  what  temperature 
will  it  yield  the  major  third  of  this  note?  Ans.   153°  C. 

95.  A  brass  wire  a  metre  in  length,  and  stretched  by  a  weight  of  a  kilogramme, 
yields,  the  same  note  as  a  silver  wire  of  the  same  diameter  but  2-5  metres  in  length  and 

-stretched  by  a  weight  of  7-5  kilogrammes.    Required  the  specific  gravity  of  the  silver. 

Ans.  io'o68. 

96.  How  many  beats  are  produced  in  a  second  by  two  notes,  whose  rates  of  vibra- 
tion are  respectively  340  and  354  ?  Ans.  14. 


Heat.  941 


V.   ON  HEAT. 

97.  Two  mercurial  thermometers  are  constructed  of  the  same  glass  ;  the  internal 
diameter  of  one  of  the  bulbs  is  7IDn>>5  and  of  its  tube  2-5  ;  the  bulb  of  the  other  i* 
6-2  in  diameter  and  its  tube  1*5.     What  is  the  ratio  of  the  length  of  a  degree  of  the 
first  thermometer  to  a  degree  of  the  second? 

Let  A  and  B  be  the  two  thermometers,  D  and  D  the  diameters  of  the  bulbs,  .and 
d  and  <f  the  diameters  of  the  tubes.  Let  us  imagine  a  third  thermometer.  C  with  the 
same  bulb  as  B  and  the  same  tube  as  A,  and  let  /,  f,  and  /"  denote  the  length  of  a 
degree  in  each  of  the  thermometers  respectively.  Since  the  stems  of  A  and  C 
have  the  equal  diameters,  the  lengths  /  and  /"  are  directly  as  the  volumes  of  the 
tubes,  or  what  is  the  same,  as  the  cubes  of  their  diameters  ;  and  as  B  and  C  have 
the  same  bulk,  the  lengths  F  and  /"  are  inversely  proportionate  to  the  sections  of 
the  stems,  or  what  amounts  to  the  same,  to  the  squares  of  their  diameters.  We 
have  then 

/         Z*        .    f        f* 

r  -  -&  and  r    =  **' 

introducing  the  values  and  solving,  we  have 
l-  =  0-638. 

98.  At  what  temperature  is  the  number  on  the 
Centigrade  and  Fahrenheit  thermometers  the  same  ? 

Ans.  -  40°. 

99.  The  same  question  for  the  Fahrenheit  and 
Reaumur  scales.  Ans.  —  25 '6. 

100.  A  capillary  tube  is  divided  into  180  parts 
of  equal  capacity,   25  of  which  weigh  1*2  gramme. 
What  must  be  the  radius  of  a-  spherical  bulb  to  be 
blown  to  it  so  that  180  divisions  correspond  to  150 
degrees  Centigrade? 

Since    25    divisions-    of    the  tube    contain    1*2 

gramme,  180  divisions  contain  *—*  l8<?-    =    8-64. 

2S 
And  since  these  180  divisions  are  to  represent  150  degrees,  the  weight  of  mercury 

corresponding  to  a  single  degree  is     — *.     But  as  the  expansion    corresponding    to 

I5° 

one  degree  is  only  the  apparent  expansion  of  mercury  in  glass,  the  weight     -*  is 

150        0400 

of  the  mercury  in  the  reservoir,  which  is- 1  T^5.    From  this  R  =  i  '8755  centimetre. 

101.  By  how  much  is  the  circumference  of  an.  iron  wheel,  whose  diameter  is  6  feet, 
increased  when  its  temperature  is  raised  400  degrees?    Coefficient  of  expansion  of 
iron  =  0-0000122.  Ans.  By  0-092  foot. 

102.  What  must  be  the  length  of  a  wire  of  this  metal  which  for  a  temperature  of 
i°  expands  by  one  foot?  Ans.  81967  feet. 

103.  A  pendulum  consists  of  a  platinum  rod,  on  a  flattening  at  the  end  of  which 
rests  a  spherical  zinc  bob.     The  length  of  the  platinum  is  /  at  o°.     What  must  be  the 
diameter  of  the  bob,  so  that  its  centre  is  always  at  the  same  distance  from  the  point  of 
suspension  whatever  be  the  temperature?     Coefficient   of  expansion   of    platinum 
o -0000088  and  of  zinc  0-0000294. 

Ans.  The  diameter  of  the  bob  must  be  |  of  the  length  of  the  platinum. 

104.  Two  walls,  which  when  perpendicular   are  30  feet  apart,  have  bulged  out- 
wards to  the  extent  of  2-4  inches.     They  are  to  be  made  perpendicular  by  the  contrac- 


942  Problems  and  Examples  in  Physics. 

tion  of  an  iron  bar.    By  how  much  must  its  temperature  be  raised  above  that  of  the  air, 
which  is  taken  at  o°?  Ans.  532°. 

105.  An  iron  wire  4  sq.  mm.  in  cross  section  is  stretched of  its  length  by  a 

81200 

weight  of  i  kilogramme.     What  weight  must  be  applied  to  a  bar  9  sq.  mm.  in  cross 
section,  when  it  is  heated  from  o°  to  20°,  in  order  to  prevent  it  from  expanding  ? 

Ans.  44*5  kilo. 

106.  At  the  temperature  zero  a  solid  is  immersed  0*975  of  its  total  volume  in 
alcohol.     At  the  temperature  25°  the  solid  is  wholly  immersed.     The  coefficient  of 
expansion  of  the  solid  being  o '000026,   required  the  coefficient  of  expansion  of  the 
alcohol.  Ans.  0-001052. 

107.  Into  a  glass  globe,  the  capacity  of  which  at  o°  is  250  cc.,  are  introduced 
25  cc.  of  air  measured  at  o°  and  76  cm.     The  flask  being  closed  and  heated  to  100°, 

required  the  internal  pressure.     Coefficient  of  cubical  expansion  of  glass  — - — . 

38700 

At  100°  the  capacity  of  the  flask  is  250  f  i  +  —  —  j  ;  again  atioo°the  volume  of 
the  free  air  under  the  pressure  76  is  25  (i  +  100  x  0-00366).  But  its  real  volume  is 
250  x  3 — .  under  a  pressure  x.  Hence 

387  88 

76    :  x  =  250  x  3       ;  25  x  1*366,  from  which  x  =   10*3548  cm. 

387  . 

108.  The  specific  gravity  of  mercury  at  o°  being  13*6,  required  the  volume  of  3 

kilogrammes  at  85°.     Coefficient  of  expansion . 

555° 

The  volume  at  o°  will  be  -3°    and  at  85°  -&L    x  (i  +  -85 ^  =  2*239  litres. 
13-6  13-6      V         5550  / 

109.  A  hollow  copper  sphere  20  cm.  in  diameter  is  filled  with  air  at  o°  under  a 
pressure  of  i£  atmosphere  ;  what  is  the  total  pressure  on  the  interior  surface  when  the 
enclosed  air  is  heated  to  a  temperature  of  600°  ?  Ans.  6226-5  kilogrammes. 

110.  Between  the  limits  of  pressure  700  to  780 mm.  the  boiling  point  of  water  varies 
o">*0375  C.  for  each  mm.  of  pressure.     Between  what  limits  of  temperature  does  the 
boiling  point  vary,  when  the  height  of  the  barometer  is  between  735  and  755  mm.  ? 

Ans.  Between  99°"o625  and  990-8i25. 

111.  Liquid  phosphorus  cooled  down  to  30°,  is  made  to  solidify  at  this  tempera- 
ture.    Required  to  know  if  the  solidification  will  be  complete,  and  if  not,  what  weight 
will  remain  melted  ?  The  melting  point  of  phosphorus  is  44*2  ;  its  latent  heat  of  fusion 
5 '4,  and  its  specific  heat  o'2. 

Let  x  be  the  weight  of  phosphorus  which  solidifies ;  in  so  doing  it  will  give  out  a 
quantity  of  heat  =  5-4  x  ;  this  is  expended  in  raising  the  whole  weight  of  the  phos- 
phorus from  30  to  44 '2.  Hence  we  have  5*4  x  =  i  x  (44*2  —  30)  0*2,  from  which 

x  —  2    4  =  0*526,  so  that  0-474  °f  phosphorus  will  remain  liquid. 
5 '4 

112.  A  pound  of  ice  at  o°  is  placed  in  two  pounds  of  water  at  o°  ;  required  the 
weight  of  steam  at  100°  which  will  melt  the  ice  and  raise  the  temperature  of  the  mix- 
ture to  30°.    The  latent  heat  of  the  liquefaction  of  ice  is  79*2,  and  that  of  the  vaporisa- 
tion of  water  536.  Ans.   '279  pound. 

113.  65*5  grammes  of  ice  at  —  20°  having  been  placed  in  x  grammes  of  oil  of 
turpentine  at  3-3°,  the  final  temperature   is  found  to  be  3-1°.     The  specific  heat  of 
turpentine  is  0*4,  and  it  is  contained  in  a  vessel  weighing  25  grammes,  whose  specific 
heat  is  o'i.     The  specific  heat  of  ice  is  0*5.     Required  the  value  of  x. 

Ans.  x  =  382*0  grammes. 

114.  In  what   proportion  must  water  at  a  temperature  of  30°  and  linseed  oil 
(sp.  heat  =  0-5)  at  a  temperature  of  50°  be  mixed  so  that  there  are  20  kilogrammes  of 
the  mixture  at  40°?  Ans.  Water  =  6 '66  kilos,  and  linseed  oil  =   13*34. 


943 

115.  3y  how  much  will  mercury  at  o°  be  raised  by  an  equal  volume  of  water  at 
iooj?  Ans.  68°'9  C. 

116.  The  specific  heat  of  gold  being  0-03244,  what  weight  of  it  at  45°  will  raise  a 
kilogramme  of  water  from  i2°'3  to  15°  -7? 

Let  x  be  the  weight  sought  ;  then  x  kilogrammes  of  gold  in  sinking  from  45°  to 
i5°7  will  give  out  a  quantity  of  heat  represented  by  x  (45°  —  i5°7)  0-0324,  and  this  is 
rqual  to  the  heat  gained  by  the  water,  that  is  to  i  (15-7  —  12*3)  =  3-4,  that  is  x  =  3-58. 

117.  The  specific  heat  .of  sulphide  of  copper  is  0-1212,  and  that  of  sulphide  of.silver 
0-0746.    5  kilos,  of  a  mixture  of  these  two  bodies  at  40°,  when  immersed  in  6  kilos,  of 
water  at  7-669  degrees,  raises  its  temperature  to  10°.    How  much  of  each  sulphuret  did 
the  mixture  contain  ? 

The  weight  of  the  copper  sulphuret  =  2,  and  that  of  the  silver  sulphuret  3. 

118.  Into  a  mass  of  water  at  o°,  100  grammes  of  ice  at  —  12°  are  introduced  ;  a 
weight  of  7 '2  grammes  of  water  at  o°  freezes  about  the  lump  immersed,  while  its 
temperature  rises  to  zero.     Required  the  specific  heat  of  ice.     Latent  heat  of  water 
79-2.  Ans.  0-4752. 

119.  Four  pounds  of  copper  filings  at  130°  are  placed  in  20  pounds  of  water  at  20°, 
the  temperature  of  which  is  thereby  raised  2  degrees.     What  is  the  specific  heat,  c,  of 
copper?  Ans.  c  =  0-0926. 

120.  Two  pieces  of  metal  weighing  300  and  350  grammes,  heated  to  a  temperature 
x,  have  been  immersed,  the  former  in  940-8  grammes  of  water  at  10°,  and  the  latter  in 
546  grammes  at  the  same  temperature.    The  temperature  in  the  first  case  rises  to  20°, 
and  in  the  second  to  30°.     Required  the  original  tempferature  and  the  specific  heat  of 
the  metal.  Ans.  x  the  temperature  =  1980°;  c  the  specific  heat  =   '1038. 

121.  In  what  proportions  must  a  kilogramme  of  \vater  at  50°  be  divided  in  order  that 
th3  heat  which  one  portion  gives  out  in  cooling  to  ice  at  zero  may  be  sufficient  to  change 
the  other  into  steam  at  100°  ?  Ans.  x  =  0-830. 

122.  Three  mixtures  are  formed  by  mixing  two  and  two  together,  equal  quantities 
of  ice,  salt,  and  water  at  o°.     Which  of  these  mixtures  will  have  the  highest  and  which 
the  lowest  temperature  ?    Ans.  The  mixture  of  ice  and  salt  will  produce  the  lowest 
temperature,  while  that  of  ice  and  water  will  produce  no  lowering  of  temperature. 

123.  In  25-45  kilogrammes  of  water  at  i20-5  are  placed  6*17  kilos,  of  a  body  at  a 
temperature  of  80°  ;  the  mixture  acquires  the  temperature  14°-!.    Required  the  specific 
heat  of  the  body. 

If  c  is  the  specific  heat  required,  then  me  (f  —  0)  represents  the  heat  lost  by  the  body 
in  cooling  from  80°  to  14° 'i ;  and  that  absorbed  by  the  water  in  rising  from  12° -5  to 
14°-!  is  m'  (0  —  t).  These  two  values  are  equal.  Substituting  the  numbers,  we  have 

C    =    O'lOII. 

124.  Equal  lengths  of  the  same  thin  wire  traversed  by  the  same  electrical  current  are 
placed  respectively  in  i  kilogramme  of  water  and  in  3  kilogrammes  of  mercury.     The 
water  is  raised  10°  in  temperature,  by  how  much  will  the  mercury  be  raised  ? 

Ans.   100° '04. 

125.  How  many  cubic  feet  of  air  under  constant  pressure  are  heated  through  i°  C. 
by  one  thermal  unit  ?  Ans.  5105  cubic  feet. 

126.  Given  two  pieces  of  metal,  one  x  weighing  2  kilos,  heated  to  80°,  and  the  other 
y  weighing  3  kilos,  and  at  the  temperature  50°.     To  determine  their  specific  heats 
they  are  immersed  in  a  kilogramme  of  water  at  10°,  which  is  thereby  raised  to  26°'3. 

The  experiment  is  repeated,  the  two  metals  being  at  the  temperature  100°  and  40° 
respectively,  and,  as  before,  they  are  placed  in  a  kilogramme  of  water  at  10°,  which 
this  time  is  raised  to  28°  4.  Required  the  specific  heats  of  the  two  metals. 

Ans.  x  =  0-115  5  y  =  0-0555. 

127.  For  high  temperatures  the  specific  heat  of  iron  is  0-1053  *  ° '000071  /.  What 
is  the  temperature  of  a  red-hot  iron  ball  weighing  a  kilogramme,  which,  plunged  in  16 


944  •      Problems  and  Examples  in  Physics. 

kilogrammes  of  water,  raises  its  temperature  from  12°  to  24°?    What  was  the  tempe- 
rature of  the  iron  ? 

(o'io53  4-  o*ooooi7/)  (/  —  24)   =   16  (24  —  12), 
°r  '000017  ft  +  "1048892  t  —  2*5272  =   192 ; 

transposing  and  dividing  by  the  coefficient  of  /2,  we  get 

/*  +  6176  /  =   11442776, 
/8  +  6170  /  +  (3085)2  =  20960001  ; 
hence  t  +  3085  =  4578 '3  nearly  ;    .'.  /  =   1493-3. 

128.  A  kilogramme  of  the  vapour  of  alcohol  at  80°  passes  through  a  copper  worm 
placed  in  10*8  kilogrammes  of  water  at  12°,  the  temperature  of  which  is  thereby  raised 
to  36°.     The  copper  worm  and  copper  vessel  in  which  the  water  is  contained  weigh 
together  3  kilogrammes.     Required  the  latent  heat  of  alcohol  vapour.    Ans.  23877. 

129.  Determine  the  temperature  of  combustion  of  charcoal  in  burning  to  form  car- 
bonic acid. 

We  know  from  chemistry  that  one  part  by  weight  of  carbon  in  burning  unites 
with  2§  parts  by  weight  of  oxygen  to  form  3!  parts  by  weight  of  carbonic  acid. 
Again  the  number  of  thermal  units  produced  by  the  combustion  of  a  pound  of  charcoal 
is  8080  ;  the  whole  of  this  heat  is  contained  in  the  3$  parts  of  carbonic  acid  produced, 
and  if  its  specific  heat  were  the  same  as  that  of  water,  its  temperature  would  be 

o—  =  2204°  C. ;  but  since  the  specific  heat  of  carbonic  acid  is  0*2163  that  of  an  equal 

weight  of  water,  the  temperature  will  be  .-204    =  IOI89°  C. 

0-2163 

ISO.  A  glass  globe  measuring  60  cubic  centimetres  is  found  to  weigh  19  -515 
grammes  when  filled  with  air  under  a  pressure  of  752-3'"m  and  at  a  temperature  of  10°  C. 
Some  ether  is  introduced  and  vaporised  at  a  temperature  of  60°,  whereupon  the  flask 
is  sealed  while  quite  full  of  vapour,  the  pressure  being  753  "4mm.  Its  weight  is  now 
found  to  be  19-6786  grammes.  Required  the  density  of  the  ether  vapour  compared 
with  that  of  hydrogen.  Ans.  54-4. 

131.  Calculate  the  density  of  alcohol  vapour  as  compared  with  air  by  Gay-Lussac's 
method  from  the  following  data  : — 

Weight  of  alcohol  o- 1047  grm.;  vol.  of  vapour  at  110°  C.  =82*55  c.c.  '<  height  of 
mercury  above  the  level  in  the  bath,  98  mm.  ;  barometric  height,  752-3  mm.  ;  tempera- 
ture of  the  room,  15°  C.  Ans.  1*6. 

132.  In  a  determination  of  the  vapour  density  by  Gay-Lussac's  method,  0*1163 
gramme  of  substance  was  employed.     The  volume  observed  was  5079  cc,  the  height 
of  the  mercury  above  the  level  of  that  in  the  bath  was  8o'omm,  the  height  of  the  oil 
column  reduced  to  millimetres  of  mercury  16-9;   the  temperature  215°  C.,  and  the 
height  of  the  barometer  at  the  time  of  observation  755 -5mm.     Required  the  specific 
gravity  of  the  vapour  as  compared  with  that  of  hydrogen.  Ans.  50' i. 

133.  Through  a  U-tube  containing  pumice  saturated  with  sulphuric  acid  a  cubic 
metre  of  air  at  15°  is  passed,  and  the  tube  is  found  to  weigh  3-95  grammes   more. 
Required  the  hygrometric  state  of  the  air. 

The  pressure  of  aqueous  vapour  at  15°  is  12*699;  hence  the  weight  of  a  cubic 
metre  of  aqueous  vapour  saturated  at  15°  is  I293  x  I2'699J^_5  _  I2-79  grammes 

O«3)  76ox8 

and  the  hygrometric  state  is  JL§$    =  0*309. 
12-79 

134.  The  quantity  of  water  given  out  by  the  lungs  and  skin  may  be  taken  at 
30  ounces  in  24  hours.   How  many  cubic  inches  of  air  already  half  saturated  at  10°  will 
be  fully  saturated  by  the  moisture  exhaled  from  the  above  two  sources  by  one  man  ? 
Tension  of  aqueous  vapour  in  inches  =  0-532.    Pressure  of  the  atmosphere  =  30  inches. 

Ans.  328782*5  c.i.  =  a  cube  5*752  feet  in  the  side. 


Heat.  945 

135.  A  mass  of  air  extending  over  an  area  of  60,000  square  metres  to  a  height  of 
300  metres  has  the  dew  point  at  15°,  its  temperature  being  20°.  How  much  rain  will 
fall  if  the  temperature  sinks  to  io°? 

The  weight  of  vapour  condensed  from  one  cubic  metre  under  these  circumstances 
will  be  3*1435  grammes,  and  therefore  from  18,000,000  cubic  metres  it  will  be  56,583 
kilogrammes,  which  is  equal  to  a  rainfall  0-0943  mm.  in  depth. 

136.  When  3  cubic  metres  of  air  at  10°  and  5  cubic  metres  at  18°,  each  saturated 
with  aqueous  vapour  at  those  temperatures,  are  mixed  together,  is  any  water  precipi- 
tated ?    And  if  so,  how  much  ? 

The  weight  of  water  contained  in  the  two  masses  under  the  given  conditions  are 
respectively  28 -i8a»d  76 -59  grammes  ;  the  weight  required  to  saturate  the  mixture  at  the 
temperature  of  15°  is  102-39  grammes,  and  therefore  2-38  grammes  will  be  precipitated. 

137.  The  temperature  of  the  air  at  sunset  being  10°,  what  must  be  the  lowest  hygro- 
metric  state,  in  order  that  dew  may  be  deposited,  it  being  assumed  that  in  conse- 
quence of  nocturnal  radiation  the  temperature  of  the  ground  is  7°  below  that  of  the  air  ? 

Ans.  The  hygrometric  state  must  be  at  least  0-608  of  total  saturation. 

138.  It  is  stated  as  a  practical  rule  that  when  the  tension  of  aqueous  vapour  present 
in  the  atmosphere,  as  indicated  by  the  dew  point,  is  equal  to  x  mm.  of  mercury,  the 
weight  of  water  present  in  a  cubic  metre  of  that  air  is  x  grammes.     What  is  the  error 
in  this  statement  for  a  pressure  of  10  mm.  and  the  temperature  15°  C.  ? 

Ans.  ©'172  gr. 

139.  A  raindrop  falls  to  the  ground  from  a  height  of  a  mile  ;  by  how  much  would 
its  temperature  be  raised,  assuming  that   it  imparts  no   heat   to  the  air  or  to  the 
ground?  Ans.  3° -8  C. 

140.  A  lead  bullet  falls  through  a  height  of  10  metres  ;  by  what  amount  will  its 
temperature  have  been  raised. when  it  reaches  the  ground,  if  all  the  heat  is  expended  in 
raising  the  temperature  of  the  bullet?  Ans.  o'75i5°  C. 

141.  From  what  height  must  a  lead  bullet  fall  in  order  that  its  temperature  may 
be  raised  n  degrees  ? — and  what  velocity  will  it  have  acquired'?    ft  is  assumed  that  all  the 
heat  is  expended  in  raising  the  temperature  of  the  bullet,  the  specific  heat  of  lead  is 
taken  at  0-0314,  and  Joule's  equivalent  in  metres  at  424. 

Ans.  13-31- x  n  metre   ;  v  =  28-8  Vn. 

142.  How  much  heat  is  disengaged  if  a  bullet  weighing  50  grammes  and  having 
a  velocity  of  50  metres  strikes  a  target  ? 

Ans.  Sufficient  to  raise  one  gramme  of  water  through  15°  C. 

143.  How  much  heat  is  produced  in  the  room  of  a  manufactory  in  which  1*2  horse- 
power of  the  motor  is  consumed  each  second  in  overcoming  the  resistance  of  friction  ? 

Ans.  A  quantity  sufficient  to  raise  41024  pounds  of  water  one  degree  Centigrade. 

144.  What  is  the  ratio  between  the  quantities  of  heat  which  are  respectively  pro- 
duced, when  a  bullet  weighing  50  grammes  and    having  a  velocity  of  500  metres, 
and  a  cannon-ball  weighing  40  kilogrammes  with  a  velocity  of  400  metres,  strike  a 
target?  Ans.   i  :  512. 

145.  The  specific  heat  of  lead  is  0-031,  and  its  latent  heat  5*37.     What  is  the 
mechanical  equivalent  of  the  heat  necessary  to  raise  5  pounds  of  lead  from  a  tempera- 
ture of  270°  C.  to  its  melting-point  335°  C.,  and  then  to  melt  it  ? 

Ans.  51326  foot-pounds. 

146.  Assuming  that  the  temperature  at  which  heat  leaves  a  perfect  engine  is  16°  C., 
at  what  temperature  must  it  be  taken  in  in  order  to  obtain  a  theoretical  useful  effect  of  J  ? 

A  MS.  160-5°  C. 

147.  Assuming  that  in  a  perfect  engine  heat  is  taken  in  at  a  temperature  of  144°, 
and  is  given  out  at  a  temperature  of  36^  :  what  is  the  greatest  theoretical  useful  effect  ? 

Ans.  o'26i. 


553 


946  Problems  and  Examples  in  Physics. 


VI.    LIGHT. 

148.  How  many  candles  are  required  to  produce  at  a  distance  of  2-5  metres,  the 
same  illuminating  effect  as  one  candle  at  a  distance  of  0-45  m.  ?  Ans.  31. 

149.  Two  sources  of  light  whose  intensities  are  as  i  :  2  are  two  metres  apart.     At 
what  position  is  a  space  between  them  equally  illuminated  ? 

Ans.  0-828  metre  from  the  less  intense  light. 

150.  A  candle  sends  its  rays  vertically  against  a  plane  surface.  When  the  candle  is 
removed  to  thrice  the  distance  and  the  surface  makes  an  angle  of  60°  with  the  original 

position,  what  is  the  ratio  of  the  illuminations  in  the  two  cases  ?  Ans.  i  :  - 

151.  An  observer,  whose  eye  is  6  feet  above  the  ground,  stands  at  a  distance  of  18 
feet  from  the  near  edge  of  a  still  pond,  and  sees  there  the  image  of  the  top  of  a  tree, 
the  base  of  which  is  at  a  distance  of  100  yards  from  the  place  at  which  the  image  is 
formed.     Required  the  height  of  the  tree.  Ans.  100  feet. 

152.  What  is  the  height  of  a  tower,  which  casts  a  shadow  56-4  m.  in  length  when  a 
vertical  rod  0*95  m.  in  height  produces  a  shadow  1-38  m.  in  length?          Ans.  38-8. 

153.  A  minute  hole  is  made  in  the  shutter  of  a  dark  room,  and  at  a  distance  of 
2 '5  metres  a  screen  is  held.     What  is  the  size  of  the  image  of  a  tree  which  is  15*3 
metres  high  and  is  at  a  distance  of  40  metres?  Ans.  0*95625  metre. 

154.  What  is  the  length  of  the  shadow  of  a  tree  50  feet  high  when  the  sun  is  30° 
above  the  horizon?  What  when  it  is  45°,  and  60° ?    Ans.  86'6  ;  50,  and  28-867  feet- 

155.  Under  what  visual  angle  does  a  line  of  30  feet  appear  at  a  distance  of  18  feet  ? 

Ans.  79° '36. 

156.  The  apparent  diameter  of  the  moon  amounts  to  31'  3".     What  is  its  real  dia- 
meter if  its  distance  from  the  earth  is  taken  at  239000  geographical  miles  ? 

Ans.  2166  geographical  miles. 

157.  For  an  ordinary  eye  an  object  is  visible  with  a  moderate  illumination  and  pure 
air  under  a  visual  angle  of  40  seconds.     At  what  distance,  therefore,  can  a  black  circle 
(6  inches  in  diameter)  be  seen  on  a  white  ground  ?  Ans.  2578  feet. 

158.  At  what  distance  from  a  circle  with  a  diameter  of  one  foot  is  the  visual  angle  a 
second?  Ans.  206265  feet. 

159.  At  what  distance  would  a  circular  disc  i  inch  in  diameter,  of  the  same  bright- 
ness as  the  sun's  surface,  illuminate  a  given  object  to  the  same  extent  as  a  vertical  sun 
in  the  tropics,  the  light  absorbed  by  the  air  being  neglected  ? 

Ans.  Taking  the  sun's  angular  diameter  at  30',  x  =  38  inches. 

160.  What  is  the  minimum  deviation  for  a  glass  prism  (n  =  i  -53),  whose  refracting 
angle  is  60°  ?  Ans.  39°  50'. 

161.  What  is  the  minimum  deviation  for  a  prism  of  the  same  substance  when  the 
refracting  angle  is  45°  ?  Ans.  63°  38'. 

162.  The  refracting  angle  of  a  prism  of  silicate  of  lead  has  been  found  by  measure- 
ment to  be  2i°'i2,  and  the  minimum  deviation  to  be  240-46.     Required  the  refractive 
index  of  the  substance.  Ans.  2-122. 

163.  Construct  the  path  of  a  ray  which  falls  on  an  equiangular  crown-glass  prism 
at  an  angle  of  30°  ;  and  find  its  deviation.  Ans.  70° -45. 

164.  WThat  are  the  angles  of  refraction  upon  a  ray  which  passes  from  air  into  glass 
at  an  angle  of  40°  ;  from  air  into  water  at  an  angle  of  65°  ;  and  from  air  into  diamond 
at  an  angle. of  80° ?  Ans.  250-20  ;  44° -5  ;  23° -12. 

165.  The  focal  distance  of  a  concave  mirror  is  8  metres.     What  is  the  distance  of 
the  image  from  the  mirror  when  the  object  is  at  a  distance  of  12,  5,  and  7  metres 
respectively?  Ans.  24;  —  13-3  and  —  56. 


Light.  947 

166.  An  object  at  a  distance  of  10  feet  produces  a  distinct  image  at  a  distance  of  3 
feet.     What  is  the  focal  distance  of  the  mirror?  Ans.  2^3077  feet. 

167.  Required  the  focal  distance  of  a  crown-glass  meniscus,  the  radius  of  curvature 
of  the  concave  face  being  45  mm.,  and  that  of  the  convex  face  30  mm.  ;  the  index  of 
refraction  being  1-5.  Ans.  f  =   180  mm. 

168.  What  is  the  principal  focal  distance  of  a  double-convex  lens  of  diamond,  the 
radius  of  curvature  of  each  of  whose  faces  is  4  mm.,  and  the  refractive  index  of  dia- 
mond 2^487?  Ans.  1*34  mm. 

169.  A  watch-glass  with  ground  edges,  the  curvature  of  which  was  4*5  cm.,  was 
filled  with  water  and  a  glass  plate  slid  over  it.     The  focus  of  the  plano-convex  lens 
thus  formed  was  found  to  be  13-5  cm.     Required  the  refractive  index  of  the  water. 

Ans.  n   =   1-33. 

170.  What  is  the  focal  distance  of  a  double-convex  lens  when  the  distances  of  the 
image  and  object  are  respectively  5  and  36  centimetres?  Ans.  4-4  centimetres. 

171.  The  radii  of  curvature  of  a  double-convex  lens  of  crown  glass  are  six  and 
eight  inches.     What  is  the  focal  distance?  A ns.  6-85  inches. 

172.  The  focal  distance  of  a  double-convex  lens  is  4  inches  ;  the  radius  of  cur- 
vature of  one  of  its  faces  is  3  inches.     What  is  that  of  the  second?   Ans.  6  inches. 

173.  The  radius  of  curvature  of  a  plano-convex  lens  is  12  inches.     Required  its 
focal  distance.  Ans.  24  inches. 

174.  If  the  focal  distance  of  a  double-convex  lens  is  i  centimetre,  at  what  distance 
must  a  luminous  object  be  placed  so  that  its  image  is  formed  at  2  centimetres  dis- 
tance from  the  lens  ?  Ans.  2  centimetres. 

175.  A  candle  at  a  distance  of  120  centimetres  from  a  lens  forms  an  image  on  the 
other  side  of  the  lens  at  a  distance  of  200  feet.     Required  the  nature  of  the  lens  and 
its  focal  distance.  Ans.  It  is  a  convex  lens,  and  its  focal  distance  is  75  cm. 

176.  A  plano-convex  lens  was  found  to  produce  at  a  distance  of  62  cm.  a  sharp 
image  of  an  infinitely  distant  object.     In  front  of  the  same  lens,  at  a  distance  of  84  cm., 
a  millimetre  scale  was  placed,  and  a  sharp  image  was  formed  at  a  distance  of  250  cm. 
It  was  thus  found  that  10  millimetres  in  the  object  corresponded  to  29  in  the  image. 
From  these  observations  determine  the  focal  distance  of  the  lens.     Ans.    The  mean 
of  the  results  is  62-4. 

177.  The  image  of  a  distant  tree  was  sharply  formed  at  a  distance  of  31  cm.  from 
the  centre  of  a  concave  mirror. 

In  another  case  the  image  of  an  object  18  mm.  in  length  at  a  distance  of  405  mm. 
from  the  mirror  was  formed  at  1350  mm.  from  the  mirror  and  had  a  length  of  61  mm. 
In  another  experiment  the  distances  of  object  and  image  and  the  size  of  the  image  were 
respectively  2200,  355,  and  3  mm. 

Deduce  from  these  several  data  the  focal  distance  of  the  mirror.     Ans.  31*2  ;  3o'5. 

178.  What  must  be  the  radii  of  curvature  of  the  faces  of  a  lens  of  best  form  made 
of  glass  (//  =  1*5)  if  its  focal  distance  is  to  be  6  inches?    Ans.  3^5  inches  and  21  inches. 

179.  A  diffraction  grating,  with  lines  0-05  mm.  apart,  is  held  in  front  of  a  Bunsen's 
burner  in  which  common  salt  is  volatilised,  and  when  viewed  through  a  telescope  it  is 
found  that  the  angular  distances  of  the  first,  second,  fourth,  and  sixth  bright  bands  from 
the  central  one  are  respectively  o°  41',   i°  21',  2°  42',  and  4°  3'.     Required  the  wave- 
length of  sodium  light. 

The  formula  \  =  _S1_"    ',  where  K  is  the  wave-length,  <J>  the  angular  distance  of 
n 

any  bright  line  of  order  n  from  the   central  one,  gives  as  the  mean  of  the  4  observa- 
tions :  Ans.  o'ooo59o88  mm. 


948  Problems  and  Examples  in  Physics. 


VII.     MAGNETISM  AND  FRICTIONAL  ELECTRICITY. 

ISO.  A  compass  needle  at  the  magnetic  equator  makes  15  oscillations  in  a  minute  ; 
how  many  will  it  make  in  a  place  where  the  horizontal  force  of  the  earth's  magnetism  is 
~  as  great?  Ans.  12. 

25 

181.  A  compass  needle  makes  9  oscillations  a  minute  under  the  influence  of  the 
earth's  magnetism  alone  ;  how  many  will  it  make  when  re-magnetised  so  as  to  be 
half  as  strong  again  as  before?  Ans.  n. 

182.  A  small  magnetic  needle  makes  loo  oscillations  in  7  min.  42  sees,  under  the 
influence  of  the  earth's  force  only  ;  when  the  south  pole  of  a  long  bar  magnet  A  is 
placed  10  inches  north  of  it,  it  makes  too  oscillations  in  4  min.  3  sees.  ;  and  with  the 
south  pole  of  another  magnet  B  in  the  same  place,  it  makes  100  oscillations  in  4  min. 
48  sees.     What  are  the  relative  strengths  of  the  magnets  A  and  B  ? 

Ans.  A  =  1*404  B. 

183.  On  a  table  where  the  earth's  magnetism  is  counteracted,  the  north  pole  of  a 
compass  needle  makes  20  oscillations  in  a  minute  under  the  attraction  of  a  south  pole 
4  inches  distant ;  how  many  will  it  make  when  the  south  pole  is  3  inches  distant  ? 

Ans.  26 '6. 

184.  If  the  oscillating  magnet  be  re-magnetised  so  as  to  be  twice  as  strong  as 
before,  how  many  oscillations  in  a  minute  will  it  make  in  the  two  positions  respectively  ? 

Ans.  28-28  and  50-27. 

185.  At  one  end  of  a  light  glass  thread,  carefully  balanced  so  as  to  oscillate  in  a 
vertical  plane,  is  a  pith  ball.     Over  this  and  in  contact  with  it  is  a  fixed  pith  ball  of  the 
same  dimensions.     Both  balls  being  charged  with  the  same  electricity  it  is  found  that 
to  keep  them  i  -4  inch  apart,  a  weight  of  -9  mgr.  must  be  placed  at  the  free  end  of  the 
glass  thread.     What  weight  must  be  placed  there  to  keep  the  balls  1-05  inch  apart  ? 

Ans.   i '6  mgr. 

186.  A  small  insulated  sphere  A  charged  with  the  quantity  of  +  electricity  2  is 
at  a  distance  of  25  mm.  from  a  second  similar  sphere  B  charged  with  the  quantity  5  ; 
the  latter  is  momentarily  touched  with  an  unelectrified  sphere  B,  of  the  same  size,  and 
the  distance  altered  to  20  mm.     What  is  the  ratio  of  the  repulsive  forces  in   the  two 
cases?  Ans.  32  :  25. 

187.  Two  insulated  spheres  A  and  B,  whose  diameters  are  respectively  as  7  :  10, 
have  equal  quantities  of  electricity  imparted  to  them.    In  what  ratio  are  their  electrical 
densities?  Ans.   100  :  49. 

188.  Two  such   spheres  whose  diameters   are   as  3  :  5   contain  respectively  the 
quantities  of  electricity  7  and  10.     In  what  ratio  are  their  densities  ?       Ans.  35  :  18. 

189.  Three  insulated  conducting  spheres,  A,  B,  and  C,  whose  radii  are  respectively 
i,  2,  and  3,  are  charged  with  electricity,  so  that  their  respective  potentials  are  as  3  :  2  :  i, 
and  are  then  connected  by  wires,  whose  capacity  may  be  neglected.     What  is  the  total 
quantity  and  potential  of  the  system  ?  Ans.  Q  =  io  ;  V  =  r66. 

190.  Supposing  each  of  the  spheres  discharged  separately,  what  would  be  the  total 
work  they  would  produce,  as  compared  with  that  produced  by  the   discharge  of  the 
whole  system?  Ans.  30  :  25. 


Voltaic  Electricity.  949 


VIII.     VOLTAIC  ELECTRICITY. 

191.  A  galvanometer  offering  no  appreciable  resistance  is  connected  by  short  thick 
wires  with  the  poles  of  a  cell,  and  deflects  20°.  By  how  much  will  it  be  deflected  if  two 
exactly  similar  cells  are  connected  with  the  first  side  by  side  ?  Ans.  47°'3o. 

192.  By  how  much  if  the  three  cells  are  connected  in  series  ?  Ans.  20°. 

193.  Two  cells  each  of  i  ohm  resistance  are  connected  in  series  by  a  wire  the 
resistance  of  which  is  also  i  ohm.     If  each  of  these  when  connected  singly  by  short 
thick  wires  to  a  galvanometer  of  no  appreciable  resistance  deflects  it  25°,  how  much 
will  the  combination  deflect  it,  the  connections  being  made  by  short  thick  wires? 

Ans.  I7°'i6. 

A  Siemens  unit  is  equal  to  the  resistance  of  a  column  of  pure  mercury  a  metre  in 
length  and  a  square  mm.  in  cross  section.  It  is  equal  to  0-9536  of  an  ohm  or  BA 
unit;  or  a  BA  unit  equals  1*0485  Siemens  unit,  or  equals  a  column  of  mercury  i'O485 
metre  in  length  and  a  square  mm.  in  cross  section. 

194.  A  single  thermo-electric  couple  deflects  a  galvanometer  of  100  ohms  resist- 
ance o°  30';  how  much  will  a  series  of  30  such  couples  deflect  it,  the  connections  being 
made  by  short  thick  wires?  Ans.  i4°'4o. 

195.  Suppose  a  sine  galvanometer  had  been  used  in  the  last  question,   and  the 
first  reading  had  been  6°'3o',  what  would  the  second  be?  Ans.  i5°'io. 

196.  The  internal  resistance  of  a  cell  is  half  an  ohm  ;  when  a  tangent  galvano- 
meter of  i  ohm  resistance  is  connected  with  it  by  short  thick  wires  it  is  deflected  15°  ; 
by  how  much  will  it  be  deflected  if  for  one  of  the  thick  wires  a  thin  wire  of  i£  ohm 
resistance  is  substituted  ?  Ans.  7°'37. 

197.  \Vhat  will  be  the  deflection  if  each  of  the  wires  is  replaced  by  a  thin  wire  of 
\\  ohm  resistance  ?  Ans.  6°  10'. 

198.  A  cell  of  one-third  of  an  ohm  resistance  deflects  a  tangent  galvanometer  of 
unknown  resistance  45°,  the  connection  being  made  by  two  short  thick  wires.  If  a  wire 
of  3  ohms  resistance  be  substituted  for  one  of  the  short  wires  the  deflection  is  30°.  What 
is  the  resistance  of  the  galvanometer?  Ans.  375  ohms. 

199.  What  would  be  the  deflection  if  for  the  cell  in  the  last  question  three  exactly 
similar  cells  in  series  were  substituted  (a)  when  the  galvanometer  alone  is  in  circuit  ; 
(b]  when  both  the  galvanometer  and  the  thin  wire  are  in  circuit? 

Ans.  a  67° -48.  b  =  57° '41. 

200.  A  galvanometer  offering  no   sensible  resistance  is  deflected  50°  by  a  cell 
connected  with  it  by  short  thick  wires.     If  a  resistance  of  3  ohms  be  put  in  the  circuit, 
the  deflection  is  20°.     Find  the  internal  resistance  of  the  cell.  Ans.  1*32. 

201.  Suppose  the  results  in  the  last  question  were  produced  by  two  exactly  similar 
cells  in  series,  find  the  internal  resistance  of  each.  Ans.  o'659. 

202.  Suppose  they  were  produced  by  two  exactly  similar  cells  placed  side  by  side, 
find  the  internal  resistance  of  each.  Ans.  2-639. 

203.  If  the  resistance  of  130  yards  of  a  particular  copper  wire  —  -    of  an  inch   in 

16 

diameter  is  an  ohm,  express  in  that  unit  the  resistance  of  8242  yards  of  copper  wire  — 
of  an  inch  in  diameter.  Ans.  35-66. 

204.  One  form  of  fuse  for  firing  mines  by  voltaic  electricity  consists  of  a  platinum 
wire  |  of  an  inch  long,  of  which  a  yard  weighs  2  grains.     Required  its  resistance  in 
terms  of  a  Siemens  unit.     Specific  gravity  of  platinum  22,  and  its  conducting  power 
1 1  "25  that  of  mercury.  Ans.  0-131. 

205.  Express  in  ohms  the  resistance  of  one  mile  of  copper  wire  £  of  an  inch  in 
diameter  of  the  same  quality  as  that  referred  to  in  203.  Ans.  0-8461. 


9 SO  Problems  and  Examples  in  Physics. 

206.  The  whole  resistance  of  a  copper  wire  going  round  the  earth  (24800  miles)  is 
221650  ohms.     Find  its  diameter  in  inches.  Ans.  o'O738. 

207.  What  length  of  platinum  wire  0*05  of  an  inch  in  diameter  must  be   taken  to 
get  a  resistance  equal  to  i  ohm,  the  specific  resistance  of  platinum  being  taken  at  5-55 
that  of  copper  ?  Ans.  14-25  metres. 

208.  660  yards  of  iron  wire  0-0625  of  an  inch  in  diameter  have  the  same  electrical 
resistance  as  a  mile  of  copper  wire  0-0416  of  an  inch  in  diameter.     Find  the  specific 
resistance  of  iron,  that  of  copper  being  unity.  Ans.  6-15. 

209.  Ten  exactly  similar  cells  in  series  produce  a  deflection  of  45°  in  a  tangent 
galvanometer,  the  external  resistance  of  the  circuit  being  10  ohms.     If  arranged  so 
that  there  is  a  series  of  5  cells,  of  two  abreast,  a  deflection  of  33°  '42  is  produced  ; 
find  the  internal  resistance  of  the  cell.  Ans.  %  ohm. 

210.  On  the  bobbins  of  the  new  Post  Office  pattern  of  a  single  needle  instrument 
are  coiled  225  yards  of  No.  35  copper  wire  0-0087  inch  in  diameter,  the  resistance  of 
which  is  about  92  ohms.     Required  the  conducting  power  of  the  wire   in  terms  of 
mercury.  Ans.  46. 

211.  Ten  exactly  similar  cells  each  of  f  of  an  ohm  resistance  give,  when  arranged 
in  five  series  of  2  each,  a  deflection  of  23°'S7  '<  but  when  arranged  in  2  series  of  5  each 
a  deflection  of  33° '42.     Required  the  external  resistance  of  the  circuit  including  that 
of  the  galvanometer.  A  us.  3*,. 

212.  A  cell  in  a  certain  circuit  deflects  a  tangent  galvanometer  18°  26' ;  two  such 
cells  abreast  in  the  same  circuit  deflect  it  23°  57' ;  two  such  cells  in  series  in  the  same 
circuit  diminished  by  i  ohm  deflect  it  29° '2.     Find  the  internal  resistance  of  one  cell ' 
and  that  of  the  circuit.  Ans.  R  =  r  =  i'66. 

213.  What  is  the  best  arrangement  of  6  cells,   each  of  f  of  an  ohm  resistance, 
against  an  external  resistance  of  2  ohms  ? 

Ans,  Indifferent  whether  in  6  cells  of  i  each  or  in  3  cells  of  2  each. 

214.  What  is  the  best  arrangement  of  20  cells,  each  of  o"8  ohm  resistance,  against 
an  external  resistance  of  4  ohms  ?  Ans.  10  cells  of  2  each. 

215.  In  a  circuit  containing  a  galvanometer  and  a  voltameter,  the  current  which 
deflects  the  galvanometer  45°  produces  10-32  cubic  centimetres  of  mixed  gas  in  a 
minute.     The  electrodes  are  put  farther  apart,  and  the  deflection  is  now  20°  ;  find 
how  much  gas  is  now  produced  per  minute.  Ans.  3-757  cc. 

216.  100  inches  of  copper  wire  weighing  100  grains  has  a  resistance  of  0-1516  ohm. 
Required  the  resistance  of  50  inches  weighing  200  grains.  Ans.  0-01895. 

217.  A  knot  of  nearly  pure  copper  wire  weighing  one  pound  has  a  resistance  of 
1200  ohms  at  i5°'5  C.  ;  what  is  the  resistance  at  the  same  temperature  of  a  knot  of  the 
same  quality  of  wire  weighing  125  pounds?  Ans.  9-6  ohms, 

218.  Find  the  length  in  yards  of  a  wire  of  the  same  diameter  and  quality  as  the 
knot  pound  in  217,  having  a  resistance  of  2  ohms.  Ans.  3-38  yards. 

219.  Find  the  length  in  yards  of  a  wire  of  the  same  quality  and  total  resistance  as 
the  knot  pound  in  217,  but  of  three  times  the  diameter.  Ans.  18261  yards. 

220.  The  specific  gravity  of  platinum  is  2^  times  that  of  copper  ;  its  resistance  5^ 

9 

as  great.     What  length  of  platinum  wire  weighing  100  grains  has  the  same  resistance 
as  zoo  inches  of  copper  wire  also  weighing  100  grains?  Ans.  27. 

221.  A  cell  with  a  resistance  of  an  ohm  is  connected  by  very  short  thick  wires  with  the 
binding  screws  of  a  tangent  galvanometer,  the  resistance  of  which  is  half  an  ohm,  and 
the  deflection  is  45°  ;  if  the  screws  of  the  galvanometer  be  also  connected  at  the  same 
time  by  a  wire  of  i  ohm  resistance,  find  the  deflection.  Ans.  36°  52'. 

222.  The  resistance  of  a  galvanometer  is  half  an  ohm,  and  the  deflection  when 


Voltaic  Electricity.  951 

the  current  of  a  cell  is  passed  through  it  is  30°.     When  a  wire  of  2  ohms  resistance  is 
introduced  into  the  circuit  the  deflection  is  15°  ;  find  the  internal  resistance  of  the  cell. 

Ans.  1-23. 

223.  When  the  current  of  a  cell,  the  resistance  of  which  is  §  of  an  ohm,  is  passed 
through  a  galvanometer  connected  with  it  by  very  short  thick  wires,  the  deflection  is 
45° ;  when  the  binding  screws  are  also  connected  by  a  shunt  having  a  resistance  of  i 
the  deflection  is  33°'42.     Find  the  resistance  of  the  galvanometer.  Ans.  2. 

224.  A  cell  whose  internal  resistance  is  2  ohms  has  its  copper  pole  connected  with 
the  binding    screw  A  of  a  galvanometer  formed  of  a  thick  band  of  copper.     From 
the  other  screw  B  a  wire  of  20  ohms  resistance  passes  to  the  zinc  pole,  and  the  deflection 
read  off  is  7°'8.     Find  the  deflection  when  B  is  at  the  same  time  connected  with  the 
zinc  pole  by  a  second  wire  of  30  ohms  resistance.  Ans.  n°-&'. 

225.  What  would  be  the  deflection  in  212  if  the  second  wire  instead  of  passing 
from  B  to  the  zinc  pole  passed  directly  from  the  zinc  pole  to  the  copper  pole  ? 

Ans.  2-437. 

226.  A  Leclanche*  cell  deflects  a  galvanometer  30°  when  200  ohms  resistance  are 
introduced  into  the  circuit,   15°  when  570  ohms  are  introduced ;  a  standard  Daniell 
cell  deflects  it  30°  when  100  ohms  are  in  circuit  and  15°  when  250  additional  ohms  are 
introduced.     Required  the  electromotive  force  of  the  Leclanche"  in  terms  of  that  of  the 
Daniell.  Ans.  1-48. 

227.  A  Bunsen  and  a  Daniell  cell  are  placed  in  the  same  circuit  in  the  first  case 
so  that  the  carbon  of  the  first  is  united  to  the  zinc  of  the  Daniell ;  and  in  the  second 
case  so  that  their  currents  oppose  each  other.     The  currents  are  respectively  30° '2, 
and  in  the  second  io°'6.     Required  the  electromotive  force  of  the  Bunsen  in  terms  of 
the  Daniell.  Ans.  1-89. 

228.  A  telegraph  line  constructed  of  copper  wire,  a  kilometre  of  which  weighs  30*5 
kilogrammes,  is  to  be  replaced  by  iron  wire  a  kilometre  of  which  weighs  135 '6  kilo- 
grammes.    In  what  ratio  does  the  resistance  alter?    Ans.  The  resistance  of  the  iron 
wire  will  be  i'i8  times  that  of  the  copper  wire  for  which  it  is  substituted. 

229.  A  telegraph  line  which  has  previously  consisted  of  copper  wire  weighing  30*5 
kilogrammes  to  the  kilometre  is  to  be  replaced  by  an  iron  wire  of  the  same  diameter 
which  shall  offer  the  same  resistance.     What  must  be  the  section  of  the  latter,  and 
what  its  weight  per  kilometre? 

Ans.  The  section  of  the  copper  wire  is  3^4357  sq.  mm.,  that  of  the  iron  by  which 
it  is  replaced  is  2o'6  sq.  mm.,  and  its  weight  per  kilometre  is  160-4  kilogrammes. 

230.  When  the  poles  of  a  voltaic  cell  are  connected  by  a  conductor  of  resist- 
ance i,  a  current  of  strength  1-32  is  produced  ;  and  when  they  are  connected  by  a 
conductor  of  resistance  5  the  strength  of  the  current  is  0-33.     Find  from  these  data 
the  internal  resistance  and  the  electromotive  force  of  the  cell.     Ans.  £=%  -£  =  176. 

231.  A  silver  wire  is  joined  end  to  end  to  an  iron  wire  of  the  same  length,  but  of 
double  the  diameter,  and  six  times  the  specific  resistance  ;  the  other  ends  are  joined 
to  the  battery,  the  current  of  which  is  transmitted  for  five  minutes,  during  which  time 
a  total  quantity  of  45  units  of  heat  is  generated  in  the  two  wires.  How  is  it  shared 
between  them  ?  Ans.  Ag :  Fe— 18  :  27. 

232.  A  window  casement  of  iron  faces  the  south,  and  the  hinges  which  support  it 
are  on  the  east.     What  electrical  phenomena  are  observed  (a)  when  the  window  is 
opened,  and  (£)  when  it  is  closed  ? 

233.  Two  points  135°  apart  in  a  uniform  circular  conducting  ring  are  connected 
with  the  opposite  poles  of  a  voltaic  battery.     Compare  the  strength  of  the  current  in 
the  two  portions  of  the  ring. 

234.  A  mile  of  cable  with  a  resistance  of  3-59  ohms  was  put  in  water,  with  the 
end  B  insulated  ;  its  core  having  been  pricked  with  a  needle  the  resistance  tested  from 
the  end  A  was  found  to  be  2'8i  ohms.     A  being  insulated,  a  test  from  B  showed  the 
resistance  to  be  2*76.     Required  the  distance  from  A  to  the  injured  spot. 

Ans.  867  yards. 


INDEX. 


(THE  NUMBERS  REFER  TO  THE  ARTICLES.) 


ABE 

\ BEL'S  electric  fuse,  794 
Aberration,       chromatic,       583 ; 
spherical,  533 

Absolute  expansion  of  mercury,  322 
Absolute  measure  of  electrical  resistance, 

947 

Absorbent  power  of  aqueous  vapour,  973 
Absorbing  power,  424 
Absorption,  of  gases,    144 ;   of  gases  by 

liquids,  184;  of  heat  by  liquids,  434; 
,'  vapours,   435  ;  heat  produced  by, 

2 

Acceleration  of  a  force,  27,  78 

Accidental  haloes,  627  ;  images,  626 ; 
magnetic  variations,  694 

Accommodation  (of  the  eye),  620 

Achromatism,  584  ;  of  the  microscope, 
592 

Achromatopsy,  632 

Acidometer,  127 

Acierage,  855 

Aclinic  1  nes,  698 

Acoustic  foci,  237  ;  attraction  and  repul- 
sion, 290 

Acoustics,  220-287 

Actinic  rays,  436,  573 

Action  and  reaction,  39 

Adhesion,  87 

Aerial  meteors,  964 

Aerolite?,  480 

yEsculine,  582 

Affinity,  86 

Agents,  6 

Agonic  line,  692 

Air,  aspirating  action  of  currents  of,  197  ; 
causes  which  modify  temperature  of, 
963,  994 ;  heating  by,  491  ;  ther- 
mometer, 334  ;  resistance  of,  48 

Air-balloons,  186;  chamber,  207 

Air-pump,  467 ;  Bianchi's,  193  ;  con- 
densing, 190;  Deleuil's,  194;  gauges, 


AQU 

191  ;  rarefaction  in,  190  j  receiver  of, 

IQO  ;  Sprengel's,  195  ;  uses  of,  200 
Ajutage,  214 
Alarum,  electric,  894 
Alcarrazas,  373 
Alcoholic  value  of  wines,  378 
Alcoholometer,  129  ;  Gay-Lussac's,  129  ; 

centesimal,  129 
Alcohol  thermometer,  306 
Alloys,  340 
Amalgam,  754 
Amalgamated  zinc,  816 
Amber,  723 
Amici's  microscope,  591  ;  camera  lucida, 

603 
Ampere's  memoria  tcchnica,  820  ;  theory 

of  magnetism,  877 
Amplitude  of  vibration,  55 
Analogous  pole,  732 
Analyser,  656 

Analysis,  spectral,  575  ;  of  solar  light,  430 
Anelectrics,  724,  748 
Anelectrotonus,  828 
Anemometer,  963,  964 
Aneroid  barometer,  182 
Angle  of  deviation,  544,  990;  optic,  617  ; 

of  polarisation,  654  ;  of  reflection  and 

incidence,   511,   536;    of  repose,  39; 

of  refraction,  536  ;  visual,  617 
Angular  currents,  laws  of,  858  ;  velocity, 

53 

Animal  heat,  485 
Anione,  841 
Annealing,  91 
Annual  variations,  693 
Anode,  841 
Antilogous  pole,  732 
Anvil,  918 

Aqueous  humour,  612 
Aqueous  vapour,  its  influence  on  climate, 

973;  tension  of,  355,  356,  357 


954 


Index. 


ARA 

Arago's  experiment,  175 

Arbor  Dianre,  851  ;  Saturni,  851 

Arc  of  vibration,  55  ;  voltaic,  833 

Archimedes'  principle,  114;  applied  to 
gases,  185 

Area,  unit  of,  22 

Armatures,  718  ;  Siemens',  912 

Arms  of  levers,  40 

Armstrong's  hydro-electric  machine,  758 

Artesian  wells,  112 

Artificial  magnets,  680 

Ascent  of  liquids  in  capillary  tubes,  133  ; 
between  surfaces,  134 

Aspirating  ac.tion  of  air  currents,  197 

Astatic  currents,  871  ;  needle  and  system, 
700  ;  circuits,  871 

Astronomical  telescope,  595 

Athermancy,  434 

Atmosphere,  its  composition,  151  ;  crush- 
ing force  of,  153  ;  amount  of,  determi- 
nation of,  157  ;  electricity  in  the,  981, 
982  ;  moisture  of,  400 

Atmospheric  electricity,  causes  of,  980, 
983;  pressure,  152,  961 

Atomic  heat,  458  ;  weight  deduced  from 
specific  heat,  458 

Atoms,  3 

Attraction,  capillary,  135  ;  and  repulsion 
produced  by  capillarity,  135  ;  mole- 
cular, 84  ;  universal,  67 

Attractions,  magnetic  laws  of,  703  ; 
electrical,  laws  of,  734 

Atwood's  machine,  78 

Aura,  764 

Aurora  borealis,  694,  991 

Aurum  musivum,  754 

Austral  pole,  689 

Avoirdupois,  23 

Axis  of  crystal,  640 ;  electric,  732  ; 
lenses,  551  ;  optic,  617  ;  of  a  magnet, 
68 1  ;  of  oscillation,  80 

Azimuthal  circle,  695 


BABINET'S  stopcock,  192 
Bad  conductors.  404 

Bain's  electro-chemical  telegraph,  892 

Balance,  72  ;  beam  of,  73  ;  compensat- 
ing, 320  ;  delicacy  of,  74  ;  hydrostatic, 
121  ;  knife-edge  of,  72  ;  physical  and 
chemical,  75  ;  torsion,  90,  704,  733 

Ballistic  pendulum,  82 

Balloons,  186-189;  construction  and 
management  of,  187  ;  Mongolfier,  186; 
weight  raised  by,  189 

Bands  of  spectrum,  576 

Barker's  mill,  217 


BOI 

Barometers,  158  ;  aneroid,  182  ;  Bun- 
ten's,  161  ;  cistern,  159;  corrections 
in,  164  ;  determination  of  heights  by, 
172;  fixed,  169;  Fortin's,  160;  Gay- 
Lussac's,  161  ;  glycerine,  170  ;  pre- 
cautions with,  162  ;  wheel,  168  ;  va- 
riations of  height  of,  165 

Barometric  formula,  Laplace's,  172  ; 
gradients,  9670;  height  of,  corrected 
for  heat,  327  ;  manometer,  180  ;  va- 
riations, 1 66 

Baroscope,  185 

Battery,  Bunsen's,  810  ;  Callan's,  810  ; 
chemical  effects  of,  840 ;  Daniel's, 
808  ;  electric,  774 ;  gas,  848  ;  gravity, 
8 12  ;  Grove's,  809  ;  Leclanche's,  843  ; 
Leyden,  constant,  807  ;  charged  by 
coil,  919  ;  local,  875  ;  luminous  ef- 
fects, 833;  magnetic,  717;  measure- 
ment of  charge,  777 ;  mechanical 
effects  of,  838;  Menotti's,  812;  Marie 
Davy's,  812;  postal,  875;  Smee's, 
811  ;  sulphate  of  mercury,  812;  ten- 
sion of,  815;  thermo-electric,  938; 
voltaic,  804,  805;  Walker's,  811  ; 
Wollaston's,  805 

Beam  of  a  balance,  73  ;  of  a  steam-en- 
gine, 467 

Beats,  262 

Beaume's  hydrometer,  128 

Becquerel's  pyrometer,  943  ;  thermo- 
electric battery,  938  ;  electrical  ther- 
mometer, 942 

Bell  of  a  trumpet,  237 

Bell's  telephone,  924  ;  photophone,  930 

Bellows,  243  ;  hydrostatic,  102 

Bennett's  electroscope,  751 

Berthollet's  experiment,  183 

Bertin's  commutator,  868 

Bianchi's  air-pump,  193 

Biaxial  crystals,  double  refraction  in, 
644  ;  optic  axis  of,  644  ;  rings  in,  667 

Bifurcation,  639 

Binnacle,  697 

Binocular  vision,  621 

Biot's  apparatus,  676 

Black's  experiments  on  latent  heat,  461 

Bladder,  swimming,  119 

Block  and  tackle,  45 

Blood-globules,  15 

Blue  cloud.  974 

Bodies,  properties  of,  7>  I23 

Bohnenberger's  electroscope,  818 

Boiler,  466 

Boiling,  350  ;  by  cooling,  367  ;  laws  of, 

363 
Boiling-point,  influence  of  dissolved  sub- 


Index. 


955 


BOR 

stances  on,  365  ;  of  nature  of  vessel, 
366 ;  of  pressure  on,  367  ;  in  a  ther- 
mometer, 302 ;  measure  of  heights  by, 

.     369 

Boreal  pole,  689 

Boutigny's  experiments,  385 

Boyle's  law,  174-176 

Bramah's  hydraulic  press,  109 

Branch  currents,  954 

Breaking  weight,  92 

Breezes,  land  and  sea,  966 

Breguet's  thermometer,  309 

Bridge,  \Vheatstone's,  949 

British  imperial  yard,    22  ;  and  French 

system  of  weights  and  measures,  126 
Browning's  regulator,  836 
Brush  discharge,  787 
Bull's  eye,  591 
Bunsen's  filter  pump,  196  ;  battery,  811  ; 

burner,    576  ;    ice    calorimeter,    452 ; 

photometer,  509 

Bunsen  and  KirchhofTs  researches,  578 
Bunten's  barometer,  161 
Buoyancy  of  liquids,  101 
Burning  mirrors,  420 


CJ-.SIUM,  578 
Cagniard-Latour's  syren,  242  ;  ex- 
periments   on    formation    of    vapour, 
370 

Cailletet's  and  Pictet's  researches,  382 

Cnllan's  batter)-,  811 

Calorescence,  433 

Caloric,  448 

Calorific  effects  of  electrical  discharge, 
790 ;  of  current  electricity,  829,  830 ; 
of  Ruhmkorft's  coil,  919  ;  of  the  spec- 
trum, 573 

Calorimeter,  450;  Bunsen's  ice,  451; 
Black's,  451  ;  Favreand  Silbermann's, 
463;  Lavoisier  and  Laplace's,  451 

Calorimetry,  447 

Camera  lucida,  594;  Amici's,  603;  ob- 
scura,  602;  Porta's  obscura,  514 

Campani's  eyepiece,  592 

Capacity,  electrical,  739;  specific  induc- 
tive, 748 

Capillarity,  132  ;  attraction  and  repul- 
sion produced  by,  135;  correction  for, 
163 

Capillary  phenomena,  132-139  ;  electro- 
meter, 839;  tubes,  133;  ascent  and 
depression  in,  133 ;  between  parallel  or 
inclined  surfaces,  134 

Capsule  of  the  eye,  612 

Cardan's  suspension,  160 


COA 

Carre's  mode  of  freezing,  374;  dielectri- 
cal  machine,  760 

Carriage  lamps,  535 

Cartesian  diver,  117 

Cascade,  charging  by,  776 

Cathetometer,  89 

Catoptric  telescopes,  598 

Caustics,  533,  534 

Celsius'  scale,  303 

Centesimal  alcoholometer,  129 

Centigrade  scale,  303 

Centimetre,  126 

Centre,  optical,  555;  of  gravity,  69;  ol 
parallel  forces,  37 ;  of  pressure,  103 

Charge  of  a  Leyden  jar,  penetration  of, 
773 ;  measurement  of,  787 ;  laws  of, 
778;  residual,  773 

Charging  by  cascade,  776 

Chatterton's  compound,  883 

Chemical  affinity,  86;  combination,  483  ; 
effects  of  the  battery,  793  ;  of  electrical 
discharge,  793 ;  of  voltaic  currents, 
821;  of  Ruhmkorffs  coil,  919;  har- 
monicon,  278;  hygrometer,  394;  pro- 
perties of  the  spectrum,  573 

Chemistry,  I 

Chevallier's  microscope,  591 

Cheval-vapeur,  473 

Chimes,  electrical,  763 

Chimney,  487 

Chladni's  experiments,  284 

Chlorophylle,  580 

Chords,  major  and  minor,  247  ;  physical 
constitution  of,  264;  tones  dominant 
and  subdominant,  248 ;  vocal,  259 

Choroid,  612 

Chromatic  scale.  250 ;  aberration,  583 

Chromium,  magnetic  limit  of,  720 

Ciliary  processes,  612 

Circle,  azirnuthal,  685 

Circular  polarisation,  669 

Cirrocumulus,  969 

Cirrostratus,  969 

Cirrus,  969 

Cistern  barometer,  159 

Cfamond's  thermo-electric  battery,  939 

Clarke's  magneto-electrical  machine,  909 

Cleavage,  electricity  produced  by,  731 

Clement  and  Desorme's  experiment,  197 

Climate,  996 ;  constant,  996 ;  influence 
of  aqueous  vapour  on,  973 

Climatology,  992-999 

Clocks,  82 ;  electrical,  895 

Clouds,  969;  electricity  of,  984;  forma- 
tion of,  970 

Coatings,  769  ;  Leyden  jar  with  movable, 
771 


956 


Index. 


COB 

Cobalt,  720 
T  Coefficients    of    linear    expansion,    313, 

3!5,  3i6 

Coercive  force,  687 
Cohesion,  85 
Coil,  primary,   877;   RuhmkorfPs,   912; 

effects  produced  by,  912;  secondary, 

877 

Cold,  apparent  reflection  of,  422;  pro- 
duced by  evaporation,  373  ;  expansion 
of  gases,  494;  by  nocturnal  radiation, 
495  ;  sources  of,  493 

Colladon  and  Sturm's  experiments,  234 

Collecting  plate,  779 

Collimation,  595 

Collision  of  bodies,  59 

Colloids,  141 

Coloration  produced  by  rotatory  polari- 
sation, 675 

Colour,  7  ;  of  bodies,  592 ;  of  heat,  436 ; 
of  thin  plates,  650 

Colour  disease,  632 

Colours,  contrast  of,  627;  mixed,  570; 
simple,  566;  comp  ementary,  570; 
produced  by  polarised  light,  662-668 ; 
by  compressed  glass,  668 

Combustion,  483 ;  heat  disengaged  dur- 
ing, 484 

Comma,  musical,  248 

Common  reservoir,  726 

Communicator,  883 

Commutator,  884,  886,  910,  918;  Ber- 
lin's, 868 

Compass,  correction  of  errors,  696 ;  de- 
clination, 695  ;  manner's,  697  ;  incli- 
nation, 698  ;  sine,  824 ;  tangent,  823 

Compensating  cube,  438 

Compensation  pendulum,  320 ;  balance, 
320;  gridiron,  320;  strips,  320 

Complementary  colours,  570 

Component  forces,  32 

Composition  of  velocities,  52 

Compound  microscope,  56 
<"Compressed  glass,  colours  produced  by, 
668 

Compressibility,  7,  16;  of  gases,  174; 
of  liquids,  96 

Concave  mirrors,  419,  52^ 

Concert  pitch,  251 

Concordant  tones,  247 

Condensation  of  vapours,  375 

Condensed  gas,  145 ;  wave,  225 

Condenser,  467,  759,  765 ;  limits  to 
charge  of,  768 ;  of  Ruhmkorff's  coil, 
918;  Liebig's,  377 

Condensing  engine,  472;  air-pump,  199; 
force,  calculation  of.  767 ;  electro- 


CUR 

scope,   779>  plate,  779;  hygrometers, 

395 
^Conduction  of  heat,  403 ;  of  electricity, 

725  ;  lightning,  989 

Conductivity  of  bodies  for  heat,  404 ;  co- 
efficient of,  404,  405 ;  of  gases,  409 ; 
of  liquids,  407;  for  electricity,  948, 

951 

Conductors,  725 ;  equivalent,  949 ;  good 
and  bad,  404;  lightning,  989;  prime, 
753  ;  resistance  of,  946 

Congelation,  343 

Conical  pendulum,  57 

Conjugate  mirrors,  420;  focus,  525,  552 

Connecting  rod,  467 

Conservation  of  energy,  66 

Constant  currents,  807 

Contact  theory  of  electricity,  799 

Contractile  force,  319 

Convection,  408 
""Con-vex    meniscus,    132  ;    mirrors,    526, 

529 

Cooling,  method  of,  455 ;  Newton's  law 
of,  417 

Cornea,  612 

Corpuscular  theory,  499 

Corti's  fibres,  260 

Cosine,  law  of  the,  414,  508 

Coulomb's  law,  703 

Couple,    36;  terrestrial   magnetic,    690; 

voltaic,  801 ;  thermo-electric,  936 
\    Couronne  des  tasses,  805 
I    Cowper's  writing  telegraph,  887 

Cox  well's  balloon,  186 

Crab,  42 

Critical  angle,  540 ;  temperature,  370 

Crookes's  radiometer,  445  ;  vacuum,  446; 
experiments,  921 

Cross-wire,  595 

Crutch  of  a  clock,  82 

Cryohydrate,  348 

Cryophorus,  373 

Crystal,  hemihedral,  732 
!    Crystalline,  612 
I    Crystallisation,  344 
i    Crystalloids,  141 

_  Crystals,  343;  expansion  of,  315;  doubly 
refracting,  639,  652,  663;  uniaxial, 
642  ;  positive  and  negative,  643 

Cube,  Leslie's,  423 

Cumulostratus,  968 

Cumulus,  968 

Current  electricity,  800 
-Currents,  action  on  currents,  860,  86 1  ; 
action    of    magnets,    864 ;    action   of 
earth  on,    870,  871 ;    action  on   sole- 
noids,  872,   877 ;    constant,    807  ;  di- 


Index. 


957 


CUR 

vided,  954 ;  detection  and  measurement 
of  voltaic,  819  ;  diaphragm,  838  ; 
direct  and  inverse,  897,  898,  905 ; 
effects  of  enfeeblement  of,  806 ;  extra, 
904,  905 ;  of  inclination,  956 ;  inten- 
sity of,  825  ;  induction  by,  897  ;  laws 
of  angular,  858  ;  laws  of  sinuous,  859  ; 
local,  816 ;  magnetisation  by,  869 ; 
motion  and  sounds  produced  by,  88 1  ; 
muscular,  955  ;  in  active  muscle,  958 ; 
in  nerve,  959  ;  rotation  of  magnets  by, 
854  ;  secondary,  806  ;  terrestrial,  878  ; 
thermal  effects  of,  830,  831  ;  transmis- 
sions by,  843 

Curvature   of  liquid   surfaces,    136;   in- 
fluence  of,    on   capillary   phenomena, 

137 

Curves,  magnetic,  704 
Cushions,  753 
Cyanogen  gas,  380 
Cyclones,  967^ 
Cylinder,  467  ;  electrical  machine,  757 


-pvAGUERREOTYPE,  608 
L/     Daltonism,  632 
Dalton's  laws  on  gases  and  vapours,  383  ; 

method  of  determining  the  tension  of 

aqueous  vapour,  356 
Damper,  279,  902 
Danielt's  batter)',  808  ;  hygrometer,  396 ; 

pyrdmeter,  311 
Dark   lines   of  the   spectrum,    574 ;    of 

solar  spectrum,  579 
Davy's  battery,  812 
Davy's  experiment,  421 
Day,  apparent,  21 
Decimetre,  24,  126 
Declination    compass,    695  ;    errors    of, 

696  ;  magnetic,   691  ;  of  needle,  691  ; 

variations  in,  692  ;  of  a  star,  600 
Decomposition,  chemical,  840  ;  of  white 

light,  564  ;  of  salts,  842 
Deflagrator,  Hare's,  805,  829 
Degrees  of  a  thermometer,  303 
De  la  Rive's  floating  battery,  865  ;    ex- 
periments, 922 
De    la   Rue   and   M  tiller's   experiments, 

9220 

Deleuil's  air-pump,  194 
Delezenne's  circle,  903 
Delicacy  of  balance,  74  ;  of  thermometer, 

307 

Densimeter,  131 

Density,  24  ;  of  the  earth,  68  ;  electric, 
736  ;  of  gases,  335-337  ;  maximum  of 
water,  330  ;  of  vapours,  Gay-Lussac's 


DIV 

method,  386  ;    Dumas',  388 ;    Deville 
and  Troost's,  389 ;  Hofmann's,  387 

Depolarisation,  665 

Depolarising  plate,  663 

Depression  of  liquids  in  capillary  tube, 
133  ;  between  surfaces,  134 

Derived  currents,  954 

Descartes'  laws  of  refraction,  537 

Despretz's  experiment,  404 

Developer,  609 

Deviation,  angle  of,  544 
1    Deville  and  Troot's  method,  389 

Dew,  975  ;  point,  395 

Diabetic  urine,  analysis  of,  678 

Dial  telegraphs,  885 

Dialyser,  141 

Dialysis,  141 

Diamagnetism,  932 

Diapason,  257 

Diaphanous  bodies,  500 

Diaphragm,  591 ;  currents,  838 

Diathermancy,  434 

Diatonic  scale,  248 

Dielectrical  machine,  Carre's,  760 

Dielectrics,  748 

Differential  barometer,  180 

Differential  galvanometer,  821  ;  thermo- 
meter, Leslie's,  308  ;  Matthiessen's, 
308  ;  tone,  263 

Diffraction,  503  ;  spectra,  648 ;  fringes, 
646 

Diffusion  of  heat,  437  ;  of  liquids,  141 

Digester,  Papin's,  371 

Dionoea  muscipula,  827 

Dioptric  telescopes,  598 

Diplopy,  631 

Dip,  magnetic.  698 

Dipping  needle,  698 

Disc,  Newton's,  567 

Discharge,  electrical.  766  ;  effects  of  the, 
783 ;  lateral,  989  ;  slow  and  instanta- 
neous, 766  ;  universal,  775 

Discharging  rod,  766 

Dispersion,  544  ;  abnormal,  581 
'•    Dispersive  power,  564 

Displacement,  46 

Dissipation  of  energy,  498 

Distance,  estimation  of,  618  ;  adaptation 
of  eye  to,  620 

Distillation,  376 

Distribution  of  free  electricity,  735  ;  of 
magnetism,  722  ;  of  temperature,  997 ; 
of  land  and  water,  999 

Diurnal  variations,  693 
;    Diver,  Cartesian,  117 
•    Divided  currents,  954 
|    Dividing  machine,  1 1 


953 


Index. 


DIV 

Divisibility,  7,  12 

Dobereiner's  lamp,  482 

Dominant  chords,  248 

Doppler's  principle,  233 

Double-action  steam-engine,  467,  468 

Double  refraction,  652 

Doublet,  Wollaston,  586 

Dove's  law  of  storms,  967 

Draught  of  fire-places,  488 

Driving  wheels,  470 

Drummond's  light,  606 

Dry  piles;  817 

Duboscq's  microscope,    606  ;    regulator, 

835 

Ductility,  7,  93 

Duhamel's  graphic  method,  245 
Dulong    and    Arago's     experiments    on 
Boyle's   law,    1 75  ;    method  of  deter- 
mining the  tension  of  aqueous  vapour, 

Dulong  and  Petit's  determination  of  ab- 
solute expansion  of  mercury,  322 ; 
method  of  cooling,  455  ;  law,  458 

Dumas'  method  for  vapour  density,  388 

Duplex  telegraphy,  890 

Duration  of  electric  spark,  795 

Dutroche's  endosmometer,  140 

Dynamical  theory  of  heat,  429 

Dynamic  radiation  and  absorption,  442 

Dynamo-magnetic  machine,  914 


T?  AR,  the,  7 

L_^     Earnshaw  on  velocity  of  sound.  230 

Earth,  its  action  on  currents,  869-871  ; 
action  of  solenoids,  876 ;  current,  891  ; 
flattening  of,  by  rotation,  83  ;  magnetic 
poles  of  the,  698  ;  magnetisation  by,  714 

Earth's  magnetism,  701 

Ear  trumpet,  239 

Ebullition,  350  ;  laws  of,  363 

Eccentric,  467,  468 

Echelon  lenses,  607 

Echoes,  237  ;  monosyllabic,  trisyllabic, 
multiple,  237 

Edison's  phonograph,  291  ;  tasimeter, 
927  ;  telephone,  928 

Efflux,  velocity  of,  21 1  ;  quantity  of, 
213  ;  influence  of  tubes  on,  214 

Effusion  of  gases,  143 

Elastic  bodies,  59 

Elastic  force,  146;  of  vapours,  351 

Elasticity,  7,  17  ;  limit  of,  17,  89;  of 
traction,  89  ;  modulus  of,  89  ;  of  tor- 
sion, 90;  of  flexure,  91 

Electric  alarum,  894;  axis,  732>  bat- 
teries, bottle,  774.  789  ;  charge,  778  ; 


EME 

chimes,  763  ;  clocks,  895  ;  density, 
736 ;  discharge,  783  ;  egg,  788  ;  fish, 
960 ;  fuse,  794 ;  glow,  787  ;  light, 
831-833;  stratification  of  the,  920 
pendulum,  724 ;  pistol,  793  ;  poles, 
732  ;  residue,  773  ;  shock,  77°>  785  ; 
spark,  762  ;  telegraphs,  883-896  ;  ten- 
sion, 736  ;  tube,  789  ;  whirl,  764 

Electrical  attractions  and  repulsions, 
734;  potential,  738;  capacity,  739; 
measurement  of,  740  ;  resistance,  unit 
of,  947  ;  conductivity,  951  ;  quantity, 
733. 

Electrical  machines,  752-761  ;  precau- 
tions in,  754 

Electricity,  6,  723 ;  application  of,  to 
medicine,  961  ;  atmospheric,  980- 
989  ;  current,  800  ;  communication  of, 
749  ;  development  of,  by  friction,  724  ; 
by  pressure  and  cleavage,  731  ;  dis- 
tribution of,  735 ;  dynamical,  797- 
954 ;  disengagement  of,  in  chemical 
actions,  793,  799 ;  factional,  730  ; 
loss  of,  743  ;  mechanical  effects,  792  ; 
power  of  points,  742  ;  produced  by 
induction,  744 ;  velocity  of,  796 ; 
theories  of,  728  ;  work  required  for 
production  of,  761 

Electrified  bodies,  motion  of,  729,  750 

Electro-capillary  phenomena,  839 

Electrochemical  telegraph,  892 ;  series, 
841 

Electrodes,  803  ;  polarisation  of,  806 

Electrodynamics,  856 

Electrogilding,  853 

Electrolysis,  841  ;  laws  of,  845 

Electrolyte,  841 

Electromagnetic  force,  880 ;  machines, 
896 

Electromagnets,  88 1 

Electrometallurgy,  852-854 

Electrometer,  751  ;  Lane's,  777;  quad- 
rant, 756  ;  Thomson's,  780 

Electromotive  series,  801  ;  force,  802, 
814,  825,  952  ;  determination  of,  952  ; 
force  of  elements,  814 

Electromotor,  883 

Electrophorus,  752 

Electropyrometer,  943 

Electroscope,  724  ;  Bohnenberger's,  818; 
Volta's  condensing,  779  ;  gold  leaf,  751 

Electrosilvering,  854 

Electrotonus,  828 

Elements,  electronegative  and  electro- 
positive, 841 

Elliptical  polarisation,  672 

Emergent  rays,  542 


Index. 


959 


EMI 

Emission  theory,  499 

Emissive  power,  425 

Endosmometer,  136 

Endosmose,  140 ;  electrical,  838  ;  of 
gases,  142 

Endosmotic  equivalent,  140   . 

Energy',  63  ;  conservation  of,  66  ;  dissi- 
pation of,  498  ;  transformations  of,  65  ; 
varieties  of,  64 

Engines,  gas,  475 ;  steam,  465  ;  double- 
action,  467  ;  low  and  high  pressure, 
472;  single  action,  469;  locomotive, 
454 ;  fire,  209  ;  transformation  of,  65 

Eolipyle,  471 

Equator,  68 1  ;  magnetic,  698 

Equilibrium  of  forces,  35 ;  of  floating 
bodies,  116;  of  heavy  bodies,  70;  of 
liquids,  107,  108  ;  mobile  of  tempera- 
ture, 414;  neutral,  71;  stable,  71; 
unstable,  71 

Equivalent,  endosmotic,  140 ;  conduc- 
tors, 948 

Escapement,  82  ;  wheel,  82 

Ether,  429  ;  luminiferous,  499 

Eustachian  tube,  260 

Evaporation,  350  ;  causes  which  accele- 
rate it,  362  ;  cold  due  to,  373  ;  latent 
heat  of,  372 

Evaporation  and  ebullition,  364 

Exchanges,  theory  of,  415 

Exhaustion,  produced  by  air-pump,  193; 
by  Sprengel's  pump,  195 

Exosmose,  140 

Expanded  wave,  225 

Expansibility  of  gases,  146 

Expansion,  296;  apparent  and  real,  321  ; 
absolute,  of  mercury,  322  ;  apparent, 
of  mercury,  323  ;  of  liquids,  326  ;  of 
solids,  313  ;  of  gases,  331-333  ;  linear 
and  cubical,  coefficients  of,  313  ; 
measurement  of  linear,  314 ;  of  crystals, 
318  ;  applications  of,  319 ;  force  of,  329 

Expansion  of  gases,  cold  produced  by, 
494  ;  problems  on,  332 

Expansive  force  of  ice,  346 

Experiment,  Berthollet's,  183  ;  Frank- 
lin's, 368  ;  Florentine,  98  ;  Pascal's, 
156  ;  Torricellian,  155 

Extension,  7,  9 

Extra  current,  904,  905  ;  direct,  905  ; 
'  inverse,  905 

Eye,  612  ;  accommodation  of,  620  ;  not 
achromatic,  628 ;  refractive  indices  of 
media  of,  613  ;  path  of  rays  in,  615  j 
dimensions  of  various  parts  of,  614 
Eye-glass,  544,  630  ;  lens,  592  ;  piece, 
583>  590,  592  5  Campani's,  592 


FOR 

TTAHRENHEIT'S  hydrometer,  124 
r          scale,  303 
Falling  bodies,  laws  of,  77 
Faraday's  experiments,  745  ;  wheel,  625  ; 
theory  of  induction,  747;  voltameter, 

845 

Favre  and  Silbermann's  calorimeter,  463; 
determination  of  heat  of  combustion, 

483 

Field  lens  and  glass,  592 

Field  of  a  microscope,  591  ;  of  view,  593; 
magnetic,  707 

Figures,  Lichtenberg's,  772 

Filter  pump,  196 

Finder,  595 

Fire  engine,  209  ;  places,  487  ;  works, 
217 

Fish,  electrical,  960 

Fishes,  swimming  bladder  of,  118 

Fizeau's  experiments,  316,  507 

Flame,  483 

Flask,  specific  gravity,  122 

Flattening  of  the  earth.  83 

Flexure,  elasticity  of,  91 

Float,  466 

Floating  bodies,  1 1 6 

Florentine  experiment,  13,  98 

Fluid,  4;  imponderable,  6;  elastic,  149; 
magnetic,  683 

Fluidity,  7 

Fluorescence,  582 

Flute,  280 

Fluxes,  340 

Fly-wheel,  467 

Focal  distance,  419 

Foci,  acoustic,  237;  of  convex  mirrors, 
526;  in  double  convex  lenses,  552 

Focus,  419,  525  ;  conjugate,  determina- 
tion of  the  principal,  527 ;  of  a  sphe- 
rical concave  mirror,  525 

Focussing  the  microscope,  587 
i    Fogs,  968 

\     Foot,  22 

(    Foot-pound,  60,  473 

j  Force,  26;  conservation  of,  66;  coer- 
cive, 687  ;  direction  of,  30;  elastic,  of 
gases,  146 ;  lines  of  magnetic,  707  ; 
of  expansion  and  contraction,  319; 
electromotive,  802,  814 ;  representa- 
tion of,  30;  parallelogram  of,  33;  of 
liquids,  529  ;  portative,  719 
Forces,  6;  along  the  same  line,  31; 
equilibrium  of,  38 ;  impulsive,  6 1  ; 
magnetic,  708 ;  molecular,  84 ;  mo- 
ments of,  38 ;  polygon  of,  35  ;  triangle 
of,  35 
Formulae  for  expansion,  318;  barome- 


960 


Index. 


FOR 

trie,   168;  for  sound,  231;  for  spheri- 
cal mirrors,  530,  531 ;  for  lenses,  559 

Fortin's  barometer,  1 60 

Foucault's  determination  of  velocity  of 
light,  506;  experiment,  834,  923 

Fountain  in  vacuo,  200 ;  at  Giggleswick, 
204 ;  intermittent,  202 ;  Hero's,  201 

Franklin's  experiment,  368,  980;  plate, 
769  ;  theory  of  electricity,  728 

Fraunhofer's  lines,  574,  575 

Freezing,  apparatus  for,  374 

Freezing  mixtures,  347,  348  ;  point  in  a 
thermometer,  302 

French  weights  and  measures,  1 24 ; 
boiler,  466 

Fresnel's  experimentum  crucis,  645; 
rhomb,  671 

Friction,  26,  47;  heat  of,  477  ;  hydrau- 
lic, 214  ;  internal,  of  gases,  446  ;  deve- 
lopment of  electricity  by,  720 

Friction  wheels,  78 

Frigorific  rays,  422 

Fringes,  646 

Frog,  rheoscopic,  957 

Frost,  975 

Frozen  mercury,  373,  380,  384 

Fulcrum,  44 

Fulgurites,  987 

Fulminating  pane,  769 

Fuse,  Abel's,  794  ;  Chatham,  829,  830 

Fusing  point,  338 

Fusion,  laws  of,  338 ;  vitreous,  338 ; 
latent  heat  of,  461 ;  of  ice,  450 


ALILEAN  telescope,  597 
Galleries,  whispering,  237 

Gallon,  126 

Galvani's  experiment,  797 

Galvanometer,  821  ;  differential,  821  ; 
Sir  W.  Thompson's,  822 

Galvanoscope,  821 

Galvano-thermometer,  830 

Gas  battery,  848  ;  engines,  475 

Gaseous  state,  4 

Gases,  absorption  of,  by  liquids,  184  ; 
application  of  Archimedes'  principle 
to,  185  ;  cold  produced  by  expansion 
of,  494  ;  compressibility  of,  148,  174  ; 
conductivity  of,  409;  diamagnetism 
of,  931  ;  density  of,  335,  337  ;  dyna- 
mical theory  of,  293  ;  expansion  of, 
147,  331-334  ;  endosmose  of,  142  ; 
effusion  and  transpiration  of,  143 ; 
Gay-Lussac's  method,  331  ;  index  of 
refraction  of,  550  ;  law?  of  mixture  of, 
183  ;  and  vapours,  mixtures  of,  383  ; 


HAI 

permanent,    380 ;    problems   in,    332, 

383;    liquefaction   of,    380;    physical 

properties   of,    146 ;    pressure   exerted 

by,  150;  radiation  of,  441;  Regnault's 

method,   336  ;    specific  heat  of,    460  ; 

velocity  of  sound  in,   230,    231,  232  ; 

viscosity  of,  446  ;  weight  of,  149 
Gassiott's  battery,  815 
Gauge,  air-pump,  191 ;  rain,  971 
Gay-Lussac's  alcoholometer,  129  ;  baro-j 

meter,  161  ;  determination  and  expan-; 

sion  of  gases,  331  ;  of  vapour-density,  ] 

385  ;  stopcock,  382 
Geissler's  tubes,  195,  578,  921 
Generating  plate,  80 1 
Geographical  meridian,  691 
Geometrical  shadows,  503 
Giffard's  injector,  197 
Gilding  metal,  853 
Gimbals,  697 
Glacial  pole,  997 
Glaciers,  979 
Glashier's  balloon  ascents,   1 86  ;  factors,; 

398 
Glass,   expansion  of,    325  ;    magnifying,] 

583  ;    object,    588  ;    opera,    397  ;    un- 

annealed,  668 

Glasses,  periscopic,  629;  weather,  168 
Globe  lightning,  985 
Glow,  electrical,  787 
Glycerine  barometer,  1 70 
Gold-leaf  electroscope,  75 1 
Goniometers,  534 
Good  conductors,  404 
Gramme,  24,  126 
Gramme's  magneto-electrical  machine,  9 1 
Graphic  method,   Duhamel's,   245  ;  Fos 

ter's,  831 
Gratings,  647 
Gravesand's  ring,  295 
Gravitation,   6,    83 ;  terrestrial,   68  ;  ac 

celerative  effect  of,  27 
Gravity,  battery,  812 
Gravity,  centre  of,  69 
Gregorian  telescope,  599 
Gridiron  pendulum,  320 
Grimaldi's  experiment,  645 
Grotthiiss'  hypothesis,  844 
Grove's  battery,  809 ;  gas,  848 
Guericke's  air-pump,  190 
Gulf  Stream,  994 
Guthrie's  researches,  348 


HADLEY'S  reflecting  sextant,  521 
Hail,  977 
Hair  hygrometer,  399 


hidex. 


96 1 


HAL 

HaMat's  apparatus,  102 
Hall's  experiment,  878 
Hallstronvs  experiments,  329 
Haloes,  627 
Hammer,  279,  918 
Hardening,  91 
Hardness,  7  ;  scale  of,  94 
I  Lire's  deflagrator,  805,  829,  830 
Harmonicon,  chemical,  278 
Harmonics,  254,  273 
Harmonic  triad,  247;  grave,  263 
Harp,  281 

I  [arris's  unit  jar,  778 

Heat,  292 ;  animal,  485  ;  absorption  of, 
by  vapours,  &c.,  435,  439  ;  diffusion 
of,  437  ;  developed  by  induction,  923; 
dynamical  theory  of,  429 ;  hypothesis 
on,  292  ;  influence  of  the  nature  of, 
435  ;  latent,  341 ;  mechanical  equi- 
valent of,  497  ;  polarisation  of,  679  ; 
produced  by  absorption  and  imbibi- 
tion, 482  ;  radiated,  403 ;  radiant, 
411;  reflection  of,  418  ;  scattered,  424 ; 
sources  of,  477-496 ;  specific,  448 ; 
transmission  of,  403;  terrestrial,  481 

Heaters,  466 

I 1  eating,   486  ;  by  steam,   490  ;  by  hot 
air,  491 ;  by  hot  water,  492 

Height  of  barometer,  159,  165  ;  varia- 
tions in,  165 

Heights  of  places,  determination  of,  by 
barometer,  172,  173  ;  by  boiling  point, 

369 

Heliograph,  523 

Heliostat,  534 

Helix,  45,  879 

Helmholtz's  analysis  of  sound,  255  ;  re- 
searches, 258 

Hemihedral  crystal,  732 

Hemispheres,  Magdeburg,  154 

Henley's  electrometer,  756;  discharger, 
792 

Henry's  experiment,  906 

Herepath's  salt,  656 

Hero's  fountain,  201 

Herschelian  rays,  430 ;  telescope,  601 

Hirn's  experiments,  474 

Hoar  frost,  975 

Hofmann's  density  of  vapours,  387 

Holmes's  magneto-electrical  machine,  91 1 

Holtz's  electrical  machine,  759 

Homogeneous  light,  572 ;  medium,  502 

Hope's  experiments,  330 

Horizontal  line,  68  ;  plane,  68 

Horse  power,  473 

Hotness,  297 

Hour,  21 


IND 

Howard's  nomenclature  of  clouds,  969 

Hughes's  microphone,  925 ;  induction 
balance,  926 

Humour,  aqueous,  612 

Huyghens' barometer,  171 

Hyaloid  membrane,  612 

Hydraulic  press,  109  ;  friction,  214  ; 
tourniquet,  217 

Hydraulics,  96 

Hydrodynamics,  96 

Hydro-electric  machine,  758 

Hydrometers,  120 ;  Nicholson's  121  ; 
Fahrenheit's,  124;  with  variable 
volume,  127;  Beaume's  128;  of  con- 
stant volume,  127  ;  specific  gravities, 
1 20  ;  uses  of  tables  of,  1 26 

Hydrostatic  bellows,  102;  paradox,  104; 
balance,  121 

Hydrostatics,  96-99 

Hygrometers,  393 ;  of  absorption,  399  ; 
chemical,  394  ;  condensing,  395  ;  wet- 
bulb,  398;  Mason's,  398;  Regnault's, 

397 

Hygrometric  state,  392 ;  substances,  39 1 
Hygrometry,  391 ;  problem  on,  401 
Hygroscope,  399 
Hypothesis,  5 
Hypsometer,  369 


ICE,  978  ;  method  of  fusion  of,  450 
Ice    calorimeter,     450  ;     Bunsen's, 
451;    expansive   force   of,    346;    ma- 
chine, 494 

Iceland  spar,  659 

Idio-electrics,  724 

Image  and  object,  magnitudes  of,  561 

Images,  accidental,  626 ;  condition  of 
distinctness  of,  587 ;  formation  of,  in 
concave  mirrors,  528;  in  convex  mir- 
rors, 529;  in  plane  mirrors,  513;  of 
multiple,  516;  magnitude  of,  532; 
produced  by  small  apertures,  504 ; 
virtual  and  real,  514;  inversion  of,  616 

Imbibition,  144;  heat  produced  by,  482 

Impenetrability,  7 

Imperial  British  yard,  22 

Imponderable  matter, 

Impulsive  forces,  58 

Inch,  126 

Incident  ray,  536 

Inclination,  708  ;  compass,  699 

Inclined  plane,  43  ;  motion  on,  50 

Index  of  refraction,  538  ;  measurement 
of,  in  solids,  548  ;  in  liquids,  549 ;  in 
gases,  550 

Indicator,  883,  885,  886 


XT 


962 


Index. 


IND 

Indices,  refractive,  table  of,  550 

Indium,  578 

Induced  currents,  897-909 

Induction,  apparatus  founded  on,  909  ; 
by  the  earth,  903  ;  by  currents,  897  ; 
of  a  current  on  itself,  904  ;  electrical, 
744  ;  in  telegraph  cables,  888 ;  limit 
to,  746 ;  Faraday's  theory  of,  747  ; 
heat  developed  by,  923  ;  by  magnets, 
901  ;  magnetic,  686  ;  vertical,  715 

Inductive  capacity,  specific,  748 

Inductorium,  917 

Inelastic  bodies,  59 

Inertia,  19  ;  applications  of,  20 

Influence,  magnetic,  686  ;  electrical,  744. 

Ingenhaus's  experiment,  404 

Injector,  197 

Insects,  sounds  produced  by,  242 

Insolation,  635,  636 

Instruments,  optical,  585 ;  polarising, 
656 ;  mouth,  270 ;  reed,  272 ; 
stringed,  279  ;  wind,  271,  280 

Insulating  bodies,  726 ;  stool,  762 

Insulators,  725 

Intensity  of  the  current,  825  ;  of  the 
electric  light,  837  ;  illumination,  508  ; 
of  reflected  light,  519  ;  of  a  musical 
tone,  246  ;  of  radiant  heat.  414  ;  of 
sound,  causes  which  influence,  226; 
of  terrestrial  magnetism,  7O1  j  °f  ter- 
restrial gravity,  83 

Interference  of  light,  645  ;  of  sound,  261    \ 

Intermittent  fountain,  202 ;  springs,  204 ; 
syphon,  204 

Interpolar,  825 

Intervals,  musical,  247 

Intrapolar  region,  828 

Inversion  of  images,  616 

lones,  841 

Iris,  612 

Iron,    passive   state   of,    849 ;   electrical    \ 
deposition  of,  855 

Iron  ships,  magnetism  of,  715 

Irradiation,  627 

Irregular  reflection,  518 

Isobars,  967^ 

Isochimenal  line,  905 

Isoclinic  lines,  698 

Isodynamic  lines,  701 

Isogeothermic  lines,  995 

Isogonic  lines,  692 

Isotheral  lines,  995 

Isothermal  lines,  995  ;  zone,  995 


J 


ACOBl'S  unit,  947 
Jar,  Leyden,  770-780 


LEN 

Jar,  luminous,  785  ;  Harris's  unit,  777 
Jet,    lateral,   211;  height   of,   212;  form 

of,  216 

Jordan's  barometer,  170 
Joule's   experiment    on    heat    and  work, 

497  ;  equivalent,  497 
Jupiter,  505 
Jurin's  laws  of  capillarity,  133 

TV^ALEIDOPHONE,  625 

iS^     Kaleidoscope,  516 

Kamsin,  966 

Kathelectrotonus,  828 

Kathode,  841 

Katione,  841 

Keepers,  718 

Kerr's  electro -optical  experiments,  931 

Key,  884,  903,  910,  918;  note,  249 

Kienmayer's  amalgam,  754 

Kilogramme,  24,  126 

Kilogrammetre,  473 

Kinetic  energy,  63 

Kinnersley's  thermometer,  792 

Kirk's  ice  machine,  494 

Knife  edge,  72 

Konig's    apparatus,    256 ;      manometric 

flames,  288 

Kravogl's  machine,  896 
Kiilp's  method  of  compensation,  719 
Kundt's  velocity  of  sound,  277 

LABYRINTH  of  the  ear,  260 
Lactometer,  130 

Ladd's  dynamomagnetic  machine,  914 

Land  and  water,  999 

Lane's  electrometer,  777 

Lantern,  magic,  604 

Laplace's  barometric  formula,  172 

Laryngoscope,  563 

Larynx,  259 

Latent  heat,  341  ;  of  fusion,  461  ;  of 
vapours,  372,  462 

Latitude,  influence  on  the  air,  993 ; 
parallel  of.  83 

Lavoisier  and  Laplace's  calorimeter,  450  ; 
method  of  determining  linear  expan- 
sion, 314 

Law,  5 

Lead  tree,  851 

Leclanche's  elements,  813,  814 

Ledger  lines,  252 

Leidenfrost's  phenomenon,  385 

Lemniscate,  667 

Length,  unit  of,  22  ;  of  undulation,  225 

Lenses,  551-559;  achromatic,  582; 
aplanatic,  558;  centres  of  curvature 


Index. 


963 


LEN 

551 ;  combination  of,  560 ;  foci  in 
double  convex,  552 ;  in  double  con- 
cave, 553  ;  formation  of  images  in 
double  convex,  556;  in  double  con- 
cave, 557-;  formula?  relating  to,  559  ; 
lighthouse,  607;  optical  centre,  secon- 
dary axis  of,  555 

Lenz's  law,  898 

Leslie's  cube,  423 ;  experiment,  373, 
thermometer,  308 

Level,  water,  no;  spirit,  in 

Level  surface,  68 

Levelling  staff,  no 

Lever,  40 

Leyden  discharge,  inductive  action  of,  900 

Leyden  jars,  770  -780 ;  charged  by 
RuhmkorfFs  coil,  919  ;  potential  of, 
782  ;  work  by,  784 

Lichtenberg's  figures,  772 

Liebig's  condenser,  377 

Ligament,  saspensory,  612 

Light,  499 ;  diffraction  of,  646  ;  homo- 
geneous, 569,  572  ;  intensity  of,  508  ; 
interference  of,  645  ;  laws  of  reflection 
of,  511  ;  medium,  502  ;  oxyhydrogen, 
606  ;  polarisation  of,  652 ;  relative 
intensities  of,  510;  sources  of,  634; 
theory  of  polarised  light,  661  ;  un- 
dulatory  theory  of,  499,  637  ;  velocity 
of,  505-507 

Lighthouse  lenses,  607 

Lightning,  987  ;  ascending,  985 ;  effects 
of,  985 ;  conductor,  989 ;  globe,  987  ; 
heat,  985;  brush,  985;  flashes,  985; 
zigzag,  985 

Limit,  magnetic,  720;  to  induction,  746; 
of  perceptible  sounds,  244 

Line,  aclinic,  698  ;  of  collimation,  595  ; 
isoclinic,  698 ;  agonic,  692 ;  isogonic, 
692  ;  isodynamic,  701  ;  of  sight,  595 

Linear  expansion,  coefficients  of,  313,  315 

Lippmann's  capillary  electrometer,  839 

Liquefaction  of  gases,  380,  381  ;  of 
vapours,  375 

Liquids,  ioo;  active  and  inactive,  667  ; 
buoyancy  of,  IOI  ;  compressibility  of, 
98  ;  conductivity  of,  407 ;  calculation 
of  density  of,  108  ;  diffusion  of,  141  ; 
diamagnetism  of,  932  ;  expansion  of, 
321  ;  equilibrium  of,  105  ;  manner  in 
which  they  are  heated,  408  ;  pressure 
on  sides  of  vessel,  103  ;  refraction  of, 
549 ;  rotatory  power  of,  676 ;  sphe- 
roidal form  ot",  85  ;  spheroidal  state  of, 
385 ;  specific  heat  of,  456 ;  volatile 
and  fixed,  349 :  tensions  of  vapours  of, 
359 ;  of  mixed  liquids,  360 

T 


MAG 

Lissajous's  experiments,  284  286 

Lithium,  578 
i    Litre,  24,  126 

i    Local  action,  806;  attraction,  715;  bat- 
tery, 886  ;  currents,  816 

Locatelli's  lamp,  428 

Locomotives,  470,  471 

Lodestone,  680 

Long  sight,  629 

Loops  and  nodes,  269 

Loss  of  electricity,  743  ;  of  weight  in  air, 
correction  for,  402 

Loudness  of  a  musical  tone,  246 

Luminiferous  ether,  499 

Luminous  bodies,  500 ;  effects  of  the 
electric  discharge,  773,  833  ;  of  the 
electric  current,  919  ;  of  RuhmkorflPs 
coil,  919;  jar,  789;  meteors,  981  ; 
pane,  789  ;  pencil,  501  ;  ray,  501  ; 
tube,  789  ;  square,  and  bottle,  789 

Luminous  radiation,  432  ;  heat,  434 


MACHINE,    Atwood's,    78;    elec- 
trical,  752-760  ;    Von    Ebner's, 

794;  electromagnetic,  883 
Mackerel-sky,  969 
!    Magazine,  717 
Magdeburg  hemispheres,  154 
Magic  lantern,  604 
Magnetic  attractions  and  repulsions,  702  ; 

battery,    717  ;    couple,    690  ;    curves, 

706;     declination,     695;     dip,     698; 

effects  of  the  electrical  discharge,  791  ; 

equator,  698 ;  field,   707 ;  fluids,  683  ; 

induction,  686;  influence,  686;  limit, 

720;  meridian,  691 ;  needle,  691,  692; 

oscillations     of,     705  ;     observatories, 

702;    poles,    698;     saturation,     716; 

storms,  694 
Magnetisation,  710;  by  the  action  of  the 

earth,    714;    by  currents,   879;  single 

touch,  711 
I    Magnetism,    6,   700 ;    determination   of, 

in  absolute  pressure,  709;  earth's,  701  ; 

of  iron  ships,  715;  Ampere's  theory  of, 

877;  remanent,  880;  theory  of,  683; 

terrestrial  distribution  of  free,  721 
Magneto-electrical       apparatus,        909  ; 

Gramme's,  915;  machines,  911-914 
I    Magneto  and  dynamo-  electrical  machines, 

916 
!    Magnets,    artificial    and    natural,     680; 

broken,  685 ;  action  of  earth  on,  689  ; 

equator  of,  68 1  ;  floating,   722  ;  north 

and  south  poles  of,  682 ;  portative  force 

of,  719;  saturation  of,  716;  influence 
T  2 


964 


Index. 


MAG 

of  heat,  720;  induction  by,  901;  in- 
ductive action  on  moving  bodies,  902  ; 
action  on  currents,  865 ;  on  solenoids, 
875 ;  rotation  of  induced  currents  by, 
922 ;  optical  effects  of,  926 ;  total  action 
of  two,  708 

Magnification, linear  and  superficial,  89; 
measure  of,  589;  of  a  telescope,  55,  65 
Magnifying  power,  594 
Magnitude,   9;    apparent,    of  an  object, 

588  ;  of  images  in  mirrors,  587 
Major  chord,  247 ;  triads,  248 
Malleability,  857 
Mance's  heliograph,  523 
Manganese,  magnetic  limit  of,  720 
Manhole,  466 
Manipulator,  885 

Manometer,    98,     177;    open-air,    178; 
with  compressed  air,  179;  Regnault's 
barometric,  181 
Manometric  flames,  288 
Mares'  tails,  969 
Marie  Davy  battery,  812 
Marine  galvanometer,  822 
Mariner's  card,  964 ;  compass,  697 
Mariotte  and  Boyle's  law,  174 
Mariotte's  tube,  174;  bottle,  219 
Marloye's  harp,  281 
Maskelyne's  experiment,  68 
Mason's  hygrometer,  398 
Mass,  measure  of,  23 ;  unit  of,  23 
Matter,  2 

Matteucci's  experiment,  900 
Matthiessen's  thermometer,  308;  table  of 
electromotive    forces,    934;    electrical 
conductivity,  951 

Maximum  current,  conditions  of,  826 
Maximum  and  minimum  thermometers, 

310;  of  tension,  755 
Mayer's  floating  magnets,  722 
Mean  temperature,  992 
Measure  of  force,  29;  of  work,  61 
Measure  of  magnification,   589,    594;  of 
mass,  23;  of  space,  22  ;  of  time,  21  ; 
of  velocity,  25 

Measurement  of  small  angles  by  reflec- 
tion, 522 
Mechanical    equivalent    of   heat,    497  ; 

effects  of  electrical  discharge,  792 
Melloni's   researches,    429;    thermomul- 

tiplier,  412,  940 
Melting  point,  influence  of  pressure  on, 

339 

Membranes,  vibrations  of,  283 
Memoria  technica,  820 
Meniscus,      133;     in     barometer,     163; 

Sagitta  of,  163 


MOR 

Menotti's  battery,  812 

Mercury,  frozen,  373,  381,  384;  pendu- 
lum, 320;  coefficient  of  expansion, 
323;  expansion  of,  322;  pump,  198 

Meridian,  21  ;  geographical  and  mag- 
netic, 691 

Metacentre,  116 

Metal,  Rose's  and  Wood's  fusible,  340 

Metals,  conductivity  of,  951 

Meteoric  stones,  480 

Meteorograph,  963 

Meteorology,  962 

Metre,  22,  126 

Mica,  664 

Micrometer  lines,  594;  screw,  II 

Microphone,  925 

Microscope,  12  ;  achromatism  of,  592  ; 
Amici's,  591  ;  compound,  590  ;  focus- 
sing, 587  ;  magnifying  powers  of,  5945 
photo-electric,  606 ;  simple,  586 ; 
solar,  605 

Microspectroscope,  580 

Mill,  Barker's,  217 

Millimetre,  126 

Mineral  waters,  988 

Mines,  firing  by  electricity,  795,  829 

Minimum  thermometer,  310;  deviation, 

547 

Minor  chord,  247 

Minute,  21 

Mirage,  541 

Mirrors,  512;  applications  of,  534;  bum- 
ing,  420  ;  concave,  419  ;  conjugate, 
420;  glass,  515;  parabolic,  535;  ro- 
tating, 520,  795  ;  spherical,  524 

Mists,  968 

Mixture  of  gases,  183;  of  gases  and 
liquids,  184 

Mixtures,  freezing,  347  ;  method  of,  452 

Mobile  equilibrium,  415 

Mobility,  7,  18 

Modulus  of  elasticity,  89 
i    Moisture  of  the  atmosphere,  400 

Molecular  forces,  3 ;  attraction,  84 ; 
state  of  bodies,  4  ;  velocity,  294 

Molecular  state,  relation  of  absorption  to, 

443 

Molecules,  3 
Moments  offerees,  38 
Momentum,  28 
|    Mongolfier's  balloon,  186 
Monochord,  266 
Monochromatic  light,  569 
Monosyllabic  echo,  237 
Moon,  510 

Morgagni's  humour,  610 
Morin  s  apparatus,  79 


Index. 


965 


MOR 

Morren's  mercury  pump,  198 

Morse's  telegraph,  886 

Moser's  images,  144. 

Motion,  1 8  ;  on  an  inclined  plane,  50  ; 
curvilinear,  25  ;  in  a  circle,  53,  54 ; 
rectilinear,  25  ;  resistance  to,  in  a 
fluid,  48  ;  uniformly  accelerated  rec- 
tilinear, 48 ;  quantity  of,  29  ;  of  a 
pendulum,  55  ;  of  projectile,  51 

Mouth  instrument,  271 

Multiple  battery,  826 

Multiple  echoes,  237  ;  images  formed  by 
mirrors,  515,  516,  517 

Multiplier,  821 

Muscular  currents,  955,  956,  957 

Music,  217  ;  physical  theory  of,  246- 
264 

Musical  boxes,  279 ;  intervals,  247  ; 
scale,  248  ;  temperament,  250  ;  tones, 
properties  of,  246  ;  intensity,  notation, 
252  ;  pitch  and  timbre,  246  ;  sound, 
223  ;  range,  252 

Myopy,  619,  629 


NAIRNE'S  electrical  machine,  757 
Nascent  state,  86 
Natterer's  apparatus,  381 
Nauman's  law,  458 
Needle,    dipping,    698  ;    astatic,    700 ; 

magnetic,  691 
Negative  plate,  801 
Negatives  on  glass,  609 
Nerve  currents,  959 
Neutral    line,     744;     equilibrium,    71; 

point,  744 

Newtonian  telescope,  600 
Newton's  disc,  568  :  law  of  cooling,  416  ; 

rings,  650,  651 ;  theory  of  light,  568 
Nicholson's  hydrometer,  121 
Nickel,    electrical    deposition    of,    855  ; 

magnetic  limit  of,  720 
Nicol's  prism,  660 
Nimbus,  969 
Nobili's  battery,  937  ;  rings,  850 ;  ther- 

momultipliers,     939;     thermo-electiic 

pile,  428,  431,  937 
Nocturnal  radiation,  495 
Nodal  points,  271,  645 
Nodes  and  loops,  269  ;  of  an  organ  pipe, 

274  ;  explanation  of,  276 
Noises,  221 
Nonconductors,  725 
Norremberg's  apparatus,  657 
Northern  light,  991 
Norwegian  stove,  410 
Notation,  musical,  252 


PEN 


Notes  in  music,  247  ;  musical,  of  women 

and  boys.  259  ;  wave-length  of,  253 
Nut  of  a  screw,  45 


OBJECT  glass,  590 
Objective,  590 
Obscure    radiation,     432 ;     rays,    433  ; 

transmutation  of,  433 
Observatories,  magnetic,  702 
Occlusion  of  gases,  145 
Octave,  249 

Oersted's  experiment,  820 
Ohm's  law,  825 
Opaque  bodies,  500 
Opera-glasses,  597 
Ophthalmoscope,  633 
Optic  axis,  607  ;  axis  of  biaxial  crystals, 

644  ;  angle,  607  ;  nerve,  612 
Optical  centre,  555  ;  effects  of  magnets, 

929 ;  instruments,  585 
Optics,  499 
Optometer,  619 

Organ  pipes,  274  ;  nodes  and  loops  of,  274 
Orrery,  electrical,  764 
Oscillations,  55  ;  axis  of,  80  ;  method  of, 

70S 

Otto  von  Guericke's  air-pump,  190 
Outcrop,  112 
Overshot  wheels,  218 
Oxyhydrogen  light,  606 
Ozone,  793,  987 


PALLET,  82 
Pane,  fulminating,  769 ;  luminous ; 
790 

Papin's  digester,  371 

Parabolic  mirrors,  535;  curve,  61,  211 

Parachute,  188 

Paradox,  hydrostatic,  104 

Parallel  of  latitude,  83  ;  forces,  36  ; 
centre  of,  27 

Parallel  rays,  501 

Parallelogram  offerees,  33 

Paramagnetic  bodies,  932 

Partial  current,  954 

Pascal's  law  of  equality  of  pressures,  99 
experiments,  156 

Passage  tint,  677 

Passive  state  of  iron,  849 

Pedal,  279 

Peltier's  cros?,  944 

Pendulum,  55;  application  to  clocks, 
82  ;  ballistic,  82  ;  corrcal,  57  ;  com- 
pensation, 320 ;  electrical,  698  ;  grid- 
iron, 320;  mercurial,  320;  length  of 


966 


Index. 


PEN 

compound,  80 ;  reversible,  80  ;  verifi- 
cation of  laws  of,  8 1 
Penumbra,  503 
Percussion,  heat  due  to,  479 
Periscopic  glasses,  629 
Permanent  gases,  380 
Persistence  of  impression  on  the  retina, 

625 

Perturbations,  magnetic,  692,  693 
Phenakistoscope,  625 
Phenomenon,  5 
Phial  of  four  elements,  107 
Phonautograph,  287 
Phonograph,  Edison's,  291 
Phosphorescence,  635,  636 
Phosphorogenic  rays,  573 
Phosphoroscope,  636 
Photo-electric  microscope,  606 
Photogenic  apparatus,  606 
Photographs   on   paper,    609 ;   on   albu- 

menised  paper  and  glass,  611 
Photography,  608-61 1 
Photometers,  509,  511 
Photophone,  930 
Physical    phenomena,     5 ;     agents,     6 ; 

shadows,  503 
Physics,  object  of,  I 

Physiological  effects  of  the  electric  dis- 
charge,  785;  of  the  current,  827;  of 
Ruhmkorffs  coil,  919 
Piezometer,  98 
Pigment  colours,  570 
Pile,  voltaic,  804-818 
Pipes,  organ,  274 
Pisa,  tower  of,  70 
Pistol,  electric.  793 
Piston  of  air-pump,  190;  rod,  467 
Pitch,    concert,    251  ;    of  a   note,  246  ; 

a  screw,  45 
Plane,    45  ;      electrical    inclined,     764 ; 

wave,  642 

Plante's  secondary  battery,  847 
Plants,  absorption  in,  144 
Plate  electrical  machine,  753 
Plates,  colours  of  thin,  650  ;  vibrations 

of,  282 

Plumb  line,  68 
Pluviometer,  971 
Pneumatic  syringe,  148,  479 
Poggendorffs  law,  793 
Point,  boiling,  366,  367 
Points,  power  of,  742 
Poiseuille's  apparatus,  215 
Polar  aurora,  991 

Polarisation,  847 ;  angle  of,  654  ;  cur- 
rent, 847  ;  of  electrodes,  806 ,  by 
double  refraction,  652  ;  by  reflection, 


PRO 

653  ;  by  single  refraction,  655  ;  ellip- 
tical and  circular,  669,  670,  672  ;  of 
heat,  679  ;  galvanic,  806,  847  ;  of  the 
medium,  747  ;  plane  of,  654  ;  plate, 
804  ;  rotatory,  674 

Polarised  light,  theory  of,  66 1  ;  colours 
produced  by  the  interference  of,  662, 
668  ;  rays,  662 

Polariser,  656 

Polarising  instruments,  656 

Polarity,  806  ;  boreal,  austral,  689 

Poles,  803  ;  analogous  and  antilogous, 
841  ;  of  the  earth,  698  ;  of  a  magnet, 
68 1  ;  mutual  action  of,  682  ;  precise 
definition  of,  684  ;  austral  and  boreal, 
689 

Polygon  of  forces,  35 

Polyprism,  544 

Ponderable  matter,  6 

Pores,  13 

Porosity,  7,  13  ;  application  of,  15 

Portative  force,  719 

Positive  plate,  80 1 

Positives  on  glass,  610 

Postal  battery,  886 

Potential  energy,  63  ;  of  electricity,  738  ; 
of  a  Leyden  jar,  782;  of  a  sphere,  741 

Pound,  126  ;  avoirdupois,  23,  29  ;  foot, 
60 

Powders,  radiation  from,  443 

Power  of  a  lever,  40  ;  of  a  microscope, 

594 

Presbytism,  619,  629 

Press,  hydraulic,  109 

Pressure,  centre  of,  103 ;  on  a  body  in  a 
liquid,  113  ;  atmospheric,  152  ;  amount 
of,  on  human  body.  157  ;  experiment 
illustrating,  200  ;  influence  on  melting 
point,  339  ;  heat  produced  by,  479 ; 
electricity  produced  by,  731 

Pressures,  equality  of,  99  ;  vertical  down- 
ward, IOO  ;  vertical  upward,  101  ;  in- 
dependent of  form  of  vessel,  102  ;  on 
the  sides  of  vessels,  103 

Prevost's  theory,  415 

Primary  coil,  890 

Primitive  current,  954 

Principal  current,  954 

Principle  of  Archimedes,  114 

Prisms,  543-547  ;  double  refracting,  659; 
Nicol's,  660  ;  with  variable  angle,  544 

Problems  on  expansion  of  gases,  332  ; 
on  mixtures  of  gases  and  vapours,  384  ; 
on  hygrometry,  401 

Projectile,  motion  of,  51 

Proof  plane,  735 

Propagation  of  light,  502 


Index. 


967 


PRO 

Protoplasm,  827 

Protuberances,  579 

Pulley,  41 

Pump  ,air,  190  ;  condensing,  199  ;  filter, 

196 
Pumps,  different  kinds  of,  205  ;  suction, 

206 ;  suction  and  force,  207 
Pupil,  612 

Psychrometer,  398,  963 
Pyroelectricity,   732 
Pyroheliometer,  480 
Pyrometers,  311  ;  electric,  943 


^vUADRANTAL  deviation,  715 
Quadrant  electrometer,  756 


RADIANT  heat,  515  ;  detection  and 
measurement  of,  412  ;  causes 
which  modify  the  intensity  of,  414  ; 
Melloni's  researches  on,  428  ;  relation 
of  gases  and  vapours  to,  438 

Radiated  heat,  .403,  411 

Radiating  power,  425  ;  identity  of  ab- 
sorbing and  radiating,  426 ;  causes 
which  modify,  &c.,  427  ;  of  gases,  441 

Radiation,  cold  produced  by,  495  ;  from 
powders,  443  ;  of  gases,  luminous,  and 
obscure,  432 ;  laws  of,  413 ;  solar, 
480 

Radiative  power,  973 

Radiometer,  445 

Rain,  971 ;  clouds,  971  ;  bow,  990;  fall, 
963>  971  J  gauge,  971  ;  drop,  velocity 
of,  48 

Ramsden's  electrical  machine,  753 

Rarefaction  in  air-pump,  190  ;  by  Spren- 
gel's  pump,  195 

Ray.  incident,  536 ;  luminous,  501  ; 
ordinary  and  extraordinary,  641 

Rays,  actinic,  or  Ritteric.  433  ;  diver- 
gent and  convergent,  501  ;  frigorific, 
422;  of  heat,  411,  429;  invisible, 
429  ;  obscure.  433  ;  path  of,  in  eye, 
615  ;  polarised,  662  ;  transmutation  of 
thermal,  434 

Reaction  and  action,  39 

Reaction  machines,  471 

Real  volume,  14  ;  foci,  552  ;  focus,  525; 
image,  528,  556 

Reaumur  scale,  303 

Receiver  of  air-pump,  190 

Recomposition  of  white  light,  567 

Reed  instruments,  272 

Reeds,  free  and  beating,  272 

Reflected  light,  intensity  of,  519 


RIN 

Reflecting  power,  423  ;  goniometer, 
534;  sextant,  521  ;  stereoscope,  623  ; 
telescope,  598 

Reflection,  apparent,  of  cold,  422  ;  of 
heat,  418  ;  from  concave  mirrors,  419; 
irregular,  518;  laws  of,  417;  verifi- 
cation of  laws  of,  420 ;  in  a  vacuum, 
421  ;  of  light,  511-541  ;  of  sound,  236 

Refracting   stereoscope,  624  ;  telescope, 

598 

Refraction,  536-545  ;  double,  639  ;  po- 
larisation by,  652  ;  explanation  of 
single,  638  ;  of  sound,  238 

Refractive  index,  538  ;  determination  of, 
562  ;  of  gases,  550 ;  of  liquids,  549  ; 
of  solids,  548  ;  table  of,  550  ;  indices 
of  media  of  eye,  613 

Refractory  substances,  338 

Refrangibility  of  light,  alteration  of,  582 

Regelation,  978 

Regnault's  experiments,  229  ;  determi- 
nation of  density  of  gases,  336;  mano- 
meter, 181  ;  methods  of  determining 
the  expansion  of  gases,  333  ;  of  specific 
heat,  454 ;  of  tension  of  aqueous  va- 
pour, 356,  358  ;  hygrometer,  397 

Regulator  of  the  electric  light,  835,  836 

Reis's  telephone,  882 

Relay,  886 

Remanent  magnetism,  880 

Repulsions,  magnetic,  705  ;  electrical 
laws  of,  731 

Reservoir,  common,  726 

Residual  charge,  773 

Residue,  electric,  773 

Resinous  electricity,  727,  728 

Resistance  of  a  conductor,  825  ;  of  an 
element,  950 

Resonance,  237  ;  box,  251  ;  globe,  255 

Rest,  1 8 

Resultant  of  forces,  32-34 

Retina,  612;  persistence  of  impression 
on,  625 

Return  shock,  988 

Reversible  pendulum,  80 

Reversion,  method  of,  696 

Rheometer,  821 

Rheoscope,  821 

Rheoscopic  frog,  957 

Rheostat,  945 

Rhomb,  Fresnel's,  671 

Rhumbs,  697,  964 

Right  ascension,  600 

Rime,  975 

Rings,  coloured,  666  ;  in  biaxial  crys- 
tals, 667;  Newton's,  650,  651;  No- 
bili's,  850 


968 


Index. 


KIT 

Ritchie's  experiment,  426 

Ritteric  rays,  433 

Robinson's  anemometer,  963 

Rock  salt,  heat  transmitted  through,  437 

Rods,  vibrations  of,  281 

Roget's  vibrating  spiral,  857 

Rose's  fusible  metal,  340 

Rotating  mirror,  795 

Rotation,  electrodynamic  and  electro- 
magnetic, of  liquids.  867 

Rotation  of  the  earth,  81 ;  of  magnets 
by  currents,  910  ;  of  currents  by  mag- 
nets, 866 ;  of  induced  currents  by 
magnets,  922 

Rotatory  power  of  liquids,  676  ;  polari- 
sation, 673,  674  ;  coloration  produced 
by,  675 

Rousseau's  densimeter,  131 

Roy  and  Ramsden's  measurement  of 
linear  expansion,  316 

Rubbers,  753 

Rubidium,  578 

Ruhlmann's  barometric  and  thermome- 
tric  observations,  173 

Ruhmkorff's  coil,  917  ;  effects  produced 
by,  919 

Rumford's  photometer,  509 

Rutherford's  thermometers,  310 


QACCHARIMETER,  677 

^^     Saccharometer,  127 

Safety-valve,     109,     371  ;     tube,     379  ; 

whistle,  466 
Sagitta  of  meniscus,  163 
Salimeters,  130 
Salts,  decomposition  of,  842 
Saturation,    degree   of,    392 ;   magnetic, 

716  ;  of  colours,  570 
Saussure's  hygrometer,  399 
Savart's  toothed  wheel,  241 
Scale  of  hardness,  94 
Scales  in  music,    248  ;  chromatic,   250  ; 

of  a  thermometer,  303  ;  conversion  of, 

into  one  another,  303 
Scattered  heat,  424;  light,  518 
Schehallien  experiment,  68 
Sclerotica,  612 
Scott's  phonautograph,  287 
Screw,  ii,  45 

Secchi's  meteorograph,  963 
Secondary    axis,    555 ;    batteries,     847  ; 

currents,  806  ;  coil,  890 
Second  of  time,  21,  25 
Seconds  pendulum,  80 
Secular  magnetic  variations,  692 
Segments,  ventral  and  nodal,  216 


SOU 

Segner's  water-wheel,  218 

Selenite,  664 

Semicircular  deviation,  715 

Semi-conductors,  725 

Semiprism,  526 

Semitones,  249 

Senarmont's  experiment,  406 

Sensitive  membrane,  229 

Serein,  973 

Series,  thermo-electric,  934 

Serum,  12 

Sextant,  521 

Shadow,  503 

Shaft,  467 

Shock,  electric,  770-780  ;  return,  988 

Shooting  stars,  480 

Short  sight,  629 

Siemens's    armature,    912 ;    unit,    946  ; 

electrical  thermometer,  953- 
Sight,  line  of,  595 
Silver,  voltameter,  845 
Simoom,  966 
Sine  compass,  824 
Singing  of  liquids,  363 
Sinuous  currents,  859 
Sirocco,  966 
Size,  estimation  of,  618 
Sleet,  976 
Slide  valve,  467 
Smee's  battery,  8il 
Snow,  976  ;  line,  979 
Soap-bubble,  colours  of,  650 
Solar   microscope,    605 ;    light,    thermal 

analysis     of,     430 ;     radiation,     480  ; 

spectrum,  564;  properties  of  the,  573; 

dark   lines   of,    574,    579;   time,    21  ; 

day,  21 

SoleiPs  saccharimeter,  677 
Solenoids,    872-876  ;  action  of  currents 

on,  873 ;  of  magnets  and  of  earth  on, 

874,  875  ;  on  solenoids,  876 
Solidification,    343  ;    change   of  volume 

on,  343,  346 ;  retardation  of,  345 
Solidity,  4,  7 
Solids,    conductivity   of,    404 ;  index  of 

refraction   in,    548  ;  diamagnetism  of, 

932  ;  linear  and  cubical  expansion  of, 

3H,  319 

Solids,  formulae  of  expansion,  318 

Solution,  342 

Sondhauss's  experiments,  238 

Sonometer,  266 

Sonorous  body,  222 

Sound,  221  ;  cause  of,  223  ;  not  propa- 
gated in  vacuo,  222  ;  propagated  in  all 
elastic  bodies,  224 ;  propagation  of,  in 
air,  225  ;  causes  which  influence  in- 


Index, 


969 


sou 

nsity  of,  226  ;  apparatus  to  streng 

en   227  ;  interference  of,  261  ;  velocity 

of,  in  gases,  230-232;  in  liqui  ds,2 

solids,  235  ;  reflection  of,  236  ;  refrac- 

tion of,   237  ;    transmission  of,    228  ; 

waves,  229 

Sound,  Helmholtz's  analysis  of,  255 
Sound,  Konig's  apparatus,  255;  Kundt's, 

277 

Sounder,  893 
Sounds,  intensity  of,  289  ;  limit  of,  per- 

ceptible, 244  ;  synthesis  of,  257  ;  per- 

ceptions of,  260  ;  produced  by  currents, 

863 

Space,  measure  of,  22 
Spar,  Iceland,  659 
Spark  and  brush  discharge,    787  ;  elec- 

trical, 762,  787  ;  duration  and  velocity 

of,  795 

Speaking  trumpet,  239  ;  tubes,  228 
Specific  .gravity,   24,    120,    125  ;   bottle, 

122;  of  solids,    121  ;   of  gases,   335  ; 

of  liquids,  124;  tables  of,  125,  126 
Specific  heat,   448-461  ;  compound  bo- 

dies, 564  ;  determination  of,  by  fusion 

of  ice,  450  ;  by  method  of  mixtures, 

452  ;  by  Regnault's   apparatus,    454  ; 

of  solids  and    liquids,    456,    457  ;    of 

gases,  460 

Specific  inductive  capacity,  748 
Spectacles,  630 
Spectra,  648 
Spectral  analysis,  575  ;  colours  and  pig- 

ment, 571 
Spectroscope,    576  ;  direct  vision,  577  ; 

experiments  with,  578  ;  uses  of  the,  580 
Spectrum,  calorific,  573  ;  chemical,  573 
Spectrum,  430;    colours  of,  566;    pure, 

565  ;  solar,  564,  577 
Spectrum,  dark  lines  of,  574 
Spectrum,  diffraction,  648 
Spectrum,  luminous  properties  of,  573    " 
Spectrum  of  aurora  borealis,  991  ;  pro- 

perties of,  573 
Specular  reflection,  518 
Spherical  aberration,  533,  558  ;    mirrors, 

524  ;  focus  of,  525  ;  formulae  for,  530 
Spheroidal  form  of  liquids,   85  ;    state, 


o 

Spherometer,  n 

Spiral,  879  ;  Roget's  vibrating,  857 

Spirit-level,  in 

Sprengel's  air-pump,  195 

Springs,  998 

Stable  equilibrium,  71 

Stars,  spectral  analysis  of,  582 

Staubbach,  77 


TEM 

Steam-engines,  465  ;  boiler,  468  ;  double 
action,  or  Watt's,  467;  pipe,  197; 
various  kinds  of,  472 ;  work  of,  473  ; 
heating  by,  490 

Steeling,  855 

Stereoscopes,  622-624 

Stethoscope,  240 

Stills,  376 

Stool,  insulating,  762 

Stopcock,  doubly  exhausting,  192  ;  Gay- 
Lussac's,  382 

Storms,  magnetic,  694 

Stoves,  489  ;  Norwegian,  410 

Stratification  of  electric  light,  920 

Stratus,  969 

Stringed  instruments,  279 

Strings,  265  ;  transverse  vibration  of,  265 

Subdominant  chords,  248 

Suction  pump,  206 ;  and  force  pump, 
207  ;  load  which  piston  supports,  208 

Sulphate  of  mercury  battery,  812 

Sun,  510;  analysis  of,  579;  constitution 
of,  579 

Sun-spots,  701 

Surface  level,  68  ;  tension,  138 

Suspension,  axis  of,  72  ;  Cardan's,  1 60 

Suspensory  ligament,  612 

Swimming,  1 1 9  ;  bladder  of  fishes,  118 

Symmer's  theory  of  electricity,  728 

Synthesis  of  sounds,  257 

Syphon,  203 ;  barometer,  161  ;  inter- 
mittent, 204 ;  recorder,  889 

Syren,  242 

Syringe,  pneumatic,  148,  479 


*~pAMTAM  metal,  95 
J_       Tangent  compass,    or  galvanome- 
ter, 823,  846 

Tasimeter,  927 

Telegraph,  cables,  Cowper's  writing, 
887  ;  induction  in,  888  ;  electric,  883  ; 
dial,  885  ;  Morse's,  886 

Telegraphy,  duplex,  890 

Telephone,  882,  924 

Telescopes,  595-601  ;  astronomical,  595  ; 
Galilean,  597  ;  Gregorian,  599  ;  Her- 
schelian,  60 1  ;  Newtonian,  600  ;  re- 
flecting, Rosse's,  601 

Telluric  lines,  573 

Temper,  95 

Temperature,  297,  448  ;  correction  for, 
in  barometer,  164  ;  critical,  370  ;  of  a 
body,  297  ;  determined  by  specific 
heat,  457 

Temperature,  absolute  zero  of,  496  ;  in- 
fluence of,  on  specific  gravity,  124  ; 


U  U 


9/0 


I  tide. v. 


TEM 

mean,  992  ;  how  modified,  993  ;  dis- 
tribution of,  997  ;  of  lakes,  seas,  and 
springs,  998 
Temperatures,  different  remarkable,  312  ; 

influence  on  expansion,  318 
Tempering,  91,  95 
Tenacity,  7,  92 

Tension,   118,   736,  918  ;    maximum  of, 
electrical  machine,  755  ;  maximum  of, 
vapours,    353  ;  of  aqueous  vapour  at 
various     temperatures,    357-361  ;     of 
vapours  of  different  liquids,    359  ;   of 
mixed  liquids  in   two  communicating 
vessels,  361  ;  free  surface,  138 
Terquem's  experiment,  735 
Terrestrial    currents,    898 ;    heat,    481  ; 

magnetic  couple,  690  ;  telescope,  596 
Terrestrial  gravitation,  68,  83 
Terrestrial  magnetic  couple,  690 
Tetanus,  827 
Thallium,  578 
Thaumatrope,  625 
Theodolite,  10 
Theory,  5  ;  of  induction,  747 
Thermal  analysis,  430 ;  unit,  447,  484  ; 

springs,  998 

Thermal  effects  of  the  current,  829,  830 
Thermal   rays,    transmutation    of,    434  ; 

unit,  447 

Thermo-barometer,  369 
Thermocrose,  436 

Thermo-electric     battery,      412,      938 ; 
couples,  936  ;  currents,  935,  937,  941 ; 
pile,  412,  431,  937  ;  series,  934 
Thermo-electricity,  933 
Thermo-element,  934 
Thermometer,  electric,  792 
Thermometers,    298 ;    Becquerel's   elec- 
trical, 942  ;  correction  of  readings,  328  ; 
division  of  tubes  in,  299  ;  filling,  300  ; 
graduation  of,   301  ;  determination  of 
fixed  points   of,   302  ;  scale  of,   303  ; 
displacement  of  zero,    304  ;  limits  to 
use  of,  305  ;  alcohol,  306  ;  conditions 
of  delicacy  of,  307  ;  Kinnersley's,  779  ; 
Leslie's,    308 ;     Matthiessen's,     308 ; 
Breguet's,    309  ;    maximum  and  mini- 
mum,  310;  Siemens'  electrical,    953  ; 
weight,  323  ;  air,  331,  332 
Thermometry,  297-300 
Thermo-multiplier,  Melloni's,  940 
Thermoinotive  wheel,  476 
Thermoscope,  308 

Thomson's  electrometers,  780,  781  ;  gal- 
vanometer, 822  ;  apparatus  for  atmo- 
spheric electricity,  981 
Thread  of  a  screw,  45 


VAC 

Thunder,  986 

Timbre,  246 

Time,  measure  of,  21  ;  mean  solar,  21 

Tint,  570  ;  transition,  677 

Tones,  combinational,   263  ;  differential, 

263 

Tonic,  248 
Torricelli's   experiment,    155;    theorem, 

210  ;  vacuum,  162 
Torsion,  angle  of,  90  ;  balance,  90,  704, 

734  ;  force  of,  90 
Total  reflection,  540 
Tourmaline,  658,  732  j  pincette,  666 
Tourniquet,  hydraulic,  217 
Traction,  elasticity  of,  89 
Trajectory,  25 

Transformation  of  energy,  65 
Transition  tint,  677 
Translucent  bodies,  500 
Transmission  of  heat,  403  ;  of  light,  499, 

542 ;  by  the  current,  843 
Transmission  of  sound,  228 
Transparency,  7,  500 
Transparent  media,  542-549 
Transpiration  of  gases,  143 
Triad,  harmonic,  247 
Triangle,  281 
Triangle  of  forces,  35 
Trumpet,  speaking,  ear,  239 
Tubes,   Geissler's,    195,  921  ;    luminous, 

789  ;  safety,  379  ;  speaking,  228 
Tuning-fork,  251,  281,  290 
Turbines,  218 
Twilight,  518 
Tympanum,  260 
Tyridall's  researches,  431,  974,  979 


UNANNEALED  glass,  colours  pro- 
duced by,  668 
Undershot  wheels,  218 
Undulation,  length  of,  225,  637 
Undulatory  theory,  499 
Uniaxial  crystals,  640  ;  double  refraction 

in,  642  ;  positive  and  negative,  643 
Unit  jar,  Harris's,  778  ;  Siemens's,  946  ; 

thermal,  447 
Unit  of  length,   area  and  volume,    22  ; 

heat,  447  ;  of  work,  62 
Unstable  equilibrium,  71 
Urinometer,  130 


VACUUM,    application   of,    to   con- 
struction of  air-pump,  190;  extent 
of,  produced  by  air-pump,  191  ;  fall  of 
bodies  in  a,   77  >  formation  of  vapour 


Index. 


971 


YAL 

in,   352;    heat  radiated  in,   413;  re- 
flection in  a,  421  ;  Torricellian,  162 
Valve,  safety,  109,  371  ;  chest,  466 
Vane,  electrical,  764 
Vaporisation,    350  ;  latent  heat  of,   372, 

462 

Vapour,  aqueous,  tension  of,  at  various 
temperatures,  357-361  ;  formation  of, 
in  closed  tube,  370  ;  latent  heat  of,  372 
Vapours,  349  ;  absorption  of  heat  by. 
435  ;  absorptive  powers  of,  440 ; 
density  of,  Gay-Lussac's  method,  380  ; 
Ilofmann's,  387;  determination  of 
latent  heat  of,  461  ;  Dumas 's  method, 
388;  elastic  force  of,  351;  formation 
of,  in  vacuo,  352 ;  saturated,  353  ; 
unsaturated,  354  ;  tension  of  different 
liquids,  359 ;  of  mixed  liquids,  360  ; 
in  communicating  vessels,  361 

Variations,  annual,  693 ;  accidental, 
694 ;  barometric,  165  ;  causes  of, 
1 66;  diurnal,  693;  relation  of,  to 
weather,  166  ;  in  magnetic  declination, 
691,  695 

Varley  unit,  946 

Velocity,  25  ;  direction  of,  56  ;  of  efflux, 
210 ;  of  electricity,  795  ;  of  light, 
505-507 ;  graphic  representation  of 
changes  of,  56 ;  molecular,  294 ;  of 
sound  in  gases,  230,  231  ;  formula  for 
calculating,  231;  of  winds,  964 

Velocities,  composition  of,  52  ;  examples 
of,  25 

Vena  contracta,  213 

Ventral  and  nodal  segment,  216,  269, 
274 

\  ernier,  10 

Vertical  line,  68 

Vestibule  of  the  ear,  260 

Vibrating  spiral,  Roget's,  857 

Vibration,  222  ;  arc  of,  55  ;  produced  by 
currents,  881 ;  of  tuning-forks,  290 

Vibrations,  262 ;  formulae,  275  ;  of 
membranes,  283  ;  laws  of,  267  ;  mea- 
surement of  number  of,  241 ;  number 
of,  producing  each  note,  251  ;  of  mu- 
sical pipe,  275  ;  of  rods,  281  ;  of 
plates,  282;  of  strings,  265,  267,  270 

Victoria  Regia,  485 

View,  field  of,  593 

Vinometers,  130 

Virtual  and  real  images,  514  ;  focus, 
525  ;  velocity,  46 

Viscosity,  97  ;  of  gases,  246 

Vision,  distance  of  distinct,  619  ;  bino- 
cular, 621 

Visual  angle,  617 


WHI 

Vis  viva,  60,  448,  477 

Vital  fluid,  797 

Vitreous  body,  612 ;  electricity,  727  ; 
fusion,  338  ;  humour,  612 

Vocal  chords,  259 

Volatile  liquids,  349 

Volta's  condensing  electroscope,  779 ; 
electrophorus,  752;  fundamental  ex- 
periment, 798 

Voltaic  arc,  833  ;  couple,  801  ;  currents, 
819  ;  induction,  897  ;  pile  and  battery, 
804,805,815,832 

Voltameter,  silver,  845  ;  Faraday's,  845 

Volume,  22 ;  unit  of,  22,  24  ;  determi- 
nation of,  115;  change  of,  on  solidi- 
fication, 346  ;  of  a  liquid  and  that  of 
its  vapour,  relation  between,  390 

Volumometer,  180 

Von  Ebner's  electrical  machine,  794 


WALKER'S  battery,  811,  883 
Water  bellows,  197  ;  decompo- 
sition of,  124  ;  hammer,  77  ;  hot,  heat- 
ing by,  492  ;  level,  no 

Water,  maximum  density  of,  330 ;  spouts, 
972  ;  wheels,  218 

Watt's  engine,  467 

Wave,  condensed,  225  ;  expanded,  225  ; 
lengths,  637,  649  ;  plane,  642 

Weather,  its  influence  on  barometric  va- 
riations, 165,  1 66;  glasses,  168;  charts, 
9670;  forecasts,  9670: 

Wedge,  44 

Wedgewood's  pyrometer,  311 

Weighing,  method  of  double,  76 

Weight,  23,  83  ;  relative,  43 ;  of  bodies 
weighed  in  air,  correction  for  loss  of, 
402;  of  gases,  150;  thermometer,  324 

Weights  and  measures,  126 

Wells,  artesian,  112 

Wells's  theory  of  dew,  975 

Wet  bulb  hygrometer,  398 

Wheatstone's  bridge,  948  ;  photometer, 
509 ;  rheostat,  945  ;  rotating  mirror, 
795  ;  and  Cooke's  telegraph,  884 

Wheel  and  axle,  42 

Wheel  barometer,  168;  thermomotive, 
476 

Wheels,  friction,  78;  escapement,  82  ; 
water,  218 

Whirl,  electrical,  764 

Whispering  galleries,  237 

Whistle,  safety,  466 

White  light,  decomposition  of,  564 ;  re- 
composition  of,  567 

White's  pulley,  41 


972 


Index, 


WIE 

Wiedemann  and  Franz's  tables  of  con- 
ductivity, 404 

Wiedemann's  determination  of  electro- 
motive force,  952 

Wild's  magneto-electrical  machine,  913 

Winckler's  cushions,  753 

Wind  chest,  272 ;  instruments,  270,  280 

Winds,  causes  of,  965  ;  direction  and 
velocity  of,  963,  964,  993  ;  law  of  ro- 
tation of,  967  ;  periodical,  regular,  and 
variable,  966 

Wines,  alcoholic  value  of,  378 

Wollaston's  battery,  805 ;  cryophorus, 
373  ;  doublet,  585 

WTood,  conductivity  of,  404 

Wood's  fusible  metal,  340 

Work,  34,  60 ;  measure  of,  61  ;  of  an 
engine,  472 ;  rate  of,  473  ;  unit  of,  62 ; 


ZON 


internal  and  external,  of  bodies,  295  ; 
of  a  voltaic  battery,  832  ;  required  for 
the  production  of  electricity,  761 
Writing  telegraphs,  886,  887 


YARD,  British,  22,  126 
Young  and  Fresnel's  experiment, 
645 


yAMBONFS  pile,  817 

/^  Zero,  absolute,  496  ;  aqueous  va- 
pours below,  355  ;  displacement  of, 
304 

Zinc,  amalgamated,  816  ;  carbon  battery, 
810 

Zone,  isothermal,  995 


LONDON  :     PRINTED     BY 

SPOTTISWOODE     AND     CO.,      NEW-STREET     SQUARE 
AND     PARLIAMENT     STREET 


>3> 


OF 


LT.BRAF 


>    *      * 
* 


>>  >: 


»    >      >    J2 
»     >        ^     > 


3>    ^ 


YC  83227 


>  ,  >    .    . 

>  >  >       <  •         ) 


II 


& 


' 

• 


